CH6304 Fluid mechanics Department of Chemical Engineering 2015-2016

B.Tech Chemical Engineering - II Year –III Semester

UNIT I
PART A
1. Distinguish between Rotational and Irrotational flow. (Nov/Dec 2014)(May/June 2007)
 Irrotational flow: The flow of ideal fluid, having zero viscosity, is called Irrotational flow or
Potential flow. For such flow, neither circulations nor eddies can form within the fluid stream
and friction cannot develop (so that there is no dissipation of mechanical energy into heat).
 Rotational flow: The flow of fluid, having definite viscosity, with circulations or eddies
within the stream of fluid is called Rotational flow. This type of flow develops friction and
dissipates mechanical energy into heat.

2. Differentiate Newtonian and Non-Newtonian fluids.

(Nov/Dec 2012) (Nov/Dec 2010) (May/June 2013)( Nov/Dec 2013)
 Newtonian fluids: The fluids which obeys the Newton’s linear law of viscosity
[ =  (du/dy)] is said to be Newtonian fluids. Gases and most liquids are Newtonian.
 Non-Newtonian fluids: For this fluids    (du/dy). Such fluids are classified as
 Bingham plastics: This fluid does not flow at all until threshold shear stresses, denoted
by‘o’, is attained and then flow linearly at shear stresses greater than ‘o’. Sewage sludge is
the better example for such fluids.
 Pseudo plastic fluid: For this fluid the ‘’ vs. ‘du/dy’ behaviour is concave upward at low
shear and becomes nearly linear at high shear. These fluids are said to be ‘Shear rate
thinning’.Rubber later is an example of such fluids.
 Dilatant fluid: For this fluid the ‘’ vs. ‘du/dy’ behaviour is concave downward at low shear
and almost linear at high shear. These fluids are said to be ‘Shear rate thickening’. Quicksand
and sand-filled emulsions are example of such fluids.

3. Define the Continuum concept of a fluid. (April/May 2010)

In dealing with fluid-flow relations on a mathematical or analytical basis, it is necessary to
consider that the actual molecular structure is replaced by a hypothetical continuous medium,
called the Continuum.

4. Differentiate Compressible and Incompressible fluid. (April/May 2011)(Nov/Dec 2013)

 Incompressible fluid: If the density changes, only slightly, with moderate changes in
temperature and pressure, then the fluid is said to be Incompressible. Liquids are generally
considered to be incompressible.
 Compressible fluid: If the changes in density are significant with moderate changes in
temperature and pressure, then the fluid is said to be Compressible. Gases and vapors are
generally considered to be compressible.

5. Define Viscosity and give its units. (Nov/Dec 2011)

 Viscosity may be defined as the property of a fluid which determines its resistance to shearing
stresses. (or) It is a measure of the internal fluid friction which causes resistance to fluid flow.
 The origin of viscosity is due to cohesion and molecular momentum transfer. These two
factors add up to provide the resistance to shearing reckoned by the property of viscosity.
 It is denoted by ‘’ and has the units of ‘kg/m-s’, ‘N-s/m2’ in SI and ‘cP’ in CGS. (1cP = 10-2
P, Poise = 10-2 g/cm-s).

6. Define Kinematic viscosity and give its unit. (April/may2012)

 The ratio of the absolute viscosity to the density of a fluid (/) is called the Kinematic
viscosity, which is often a useful property of a fluid.
 It is denoted by ‘’ and has the units of ‘m2/s’ in SI and ‘stoke (cm2/s)’ in CGS.

7. State Newton’s law of viscosity. (April/may2007)

According to Newton’s law of viscosity, the shear stress on a fluid element layer () is directly
proportional to the rate of shear strain (du/dy) and the proportionality constant being called the
coefficient of viscosity (). Mathematically, it is given by  =  (du/dy).

8. Explain Capillarity. (April/may2008)

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 Capillarity implies the rise or depression of the level of a liquid in a capillary tube when it is
held vertically or inclined in the liquid.
 Capillarity phenomena are based on the angle of contact between the liquid and the capillary
material and the balance of force on the column of the liquid in them; it is due to combined
effect of adhesion and cohesion of liquid particles in the capillary.

9. Define Fluid mechanics.

Fluid mechanics may be defined as the branch of engineering science which deals with the
behavior of fluids (liquids, gases, and vapors) under the conditions of rest and motion.

10. Define the terms fluid and flow.

 A fluid is a substance that does not permanently resist distortion.
 A fluid is a substance which is capable of flowing.
 A fluid is a substance, which deforms continuously when subjected to external shearing force.
 Flow is the movement of the fluid along some distance.

11. Differentiate ideal and real fluids.

The behavior of a flowing fluid depends strongly on whether the fluid is under the influence of
solid boundaries.
 In the region where the influence of the wall is small, the shear stress may be negligible
(viscosity is zero) and the fluid behavior may approach that of an ideal fluid. That is, Ideal
fluid is one that is incompressible and has zero viscosity.
 In the region where the influence of the wall is significant, the shear stress cannot be neglected
(non-zero viscosity) and the fluid behavior may approach that of an real fluid. That is, Real
fluid is one that is incompressible and has non-zero viscosity.

12. Explain Power law for fluids.

 Over some range of shear stress, Dilatant and Pseudo plastic fluids often follow a Power law,
also called as Ostwald-de Waele equation, is given by  = K (du/dy)n Where ‘K’ and ‘n’ are
constants called the ‘Flow consistency index’ and the ‘Flow behavior index’. Such fluids are
known as ‘Power law fluids’.
 For Pseudo plastic fluids, n < 1; for Dilatant fluids, n > l; Clearly, n = 1 for Newtonian fluids.

13. Define fluid dynamics and fluid kinematics.

 Fluid dynamics deals with fluids when portions of the fluid are in motion relative to other
parts. It is the study of the state of motion under the influence of external forces and moments.
 It deals with the relations between velocities, acceleration and the force exerted by or upon
fluids in motion.
 Fluid kinematics
 Fluid kinematics deals with fluids when the motion of the fluid relative to velocity field.
 It deals with the velocities, streamlines and the patterns of flow without considering forces or
energy.

14. Define Shear stress of fluid.

 Shear stress is defined as the shear force exerted by the flowing fluid, which acts parallel to the
plane of shear, per unit area of the shearing plane.
 It is denoted by ‘’ and has the units of ‘N/m2’.

15. Define Bulk modulus.

 The Bulk modulus ‘Ev’ or volume modulus of elasticity is defined as the compressive stress
per unit volumetric strain.
 It is inversely proportional to the compressibility (change in volume due to change in pressure)
of a liquid and it measures the same.
 It is given by Ev = - v dp/dv = - (v/dv) dp; where ‘v’ = specific volume and ‘p’ = pressure.
 As (v/dv) is a dimensionless; the units of ‘Ev’ and ‘p’ are identical.

16. Define Surface tension and give its unit.

 Surface tension is the property of the apparent tension effect which occurs at the interface of a
liquid and a gas or at the interface of two immiscible liquids.
 The origin of surface tension is explained by the mechanism of cohesive forces within a liquid.

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 It is denoted by ‘’ and has the units of ‘N/m’ in SI.

17. State the Pascal’s law for pressure at a point.

 The pressure at a point in a fluid is defined as the intensity of compressive force, that is, the
normal compressive force per unit area on that point.
 According to Pascal’s law, the pressure at a point in a static fluid is equal in all directions in
space.

18. State the law of Buoyancy. (April/ May 2011)

 If a body is submerged in a fluid, wholly or partially, the body experiences an upward force
due to the fluid surrounding it. The phenomenon of upward force exerted by a fluid on the
body is called ‘Buoyancy’ and the force is called ‘Buoyant force’.
 The body experiences buoyancy whether it floats or sinks under its own weight or due to other
forces applied on it.
 The Archimedes principle of buoyancy states that a body immersed in a fluid experiences an
upward buoyancy force equivalent to the weight of the fluid displaced by the body. It follows
that a body floats partially immersed in a fluid to the extent that the weight of the fluid
displaced equals the weight of the body.

19. Distinguish between Laminar and Turbulent flow. (Nov/Dec 2011)

 Laminar flow: At low velocities, fluid tends to flow without lateral mixing, and adjacent layers
slide past one another as playing cards do. There are neither cross-currents nor eddies. This
regime is called Laminar flow. The velocity profile is parabolic, when the fluid flows through
a smooth circular conduit.
 Turbulent flow: At higher velocities, turbulence (cross-current) appears and eddies form,
which leads to lateral mixing. Such regime is called Turbulent flow. The velocity profile if
nearly flat, when the fluid flows through a smooth circular conduit.

20. Define Reynolds number. Explain its physical significance.

 It is defined as the ratio of the Inertial force (mass x acceleration) to the Viscous force (area x
shear stress). It is denoted by ‘NRe’ and dimensionless.
 Significance: For flow in a pipe, NRe< 2100 represents the flow as Laminar; NRe > 4000
represents the flow as Turbulent; for 2100 < NRe < 4000, a Transition region is found where
the flow may be either laminar or turbulent.
 Osborne Reynold’s in 1883 demonstrated the types of fluid flow and explained the above
significances with respect a dimensionless number, NRe.

21. Define Meta centre. (Nov/Dec 2011)

It is defined as the point which a body starts oscillating when the body is tilted by a small
angle. The Meta centre may also be defined as the point at which the line of action of the force
of buoyancy will meet the normal axis of the body when the body is given a small angular
displacement.
PART-B

1. A cylinder of 15cm radius rotates concentrically inside a fixed hollow cylinder of radius 15.5
cm. both cylinders are 30 cm long. A liquid whose viscosity is to be determined fills the space
between the cylinders. A torque of 0.98 Nm is required to rotate the inner cylinder at 60 rpm.
The outer cylinder is stationary. Determine the viscosity of the liquid. This is a rotating cup
viscometer experiment, where
Torque=(shear stress)(area) (arm length) ( Nov/Dec 2014)
2. With a neat sketch rheological diagram and explain the behavior of Newtonian fluid and non
Newtonian fluids. (Nov/ Dec 2013)
3. Define the following terms with its SI units: (April/May 2011)
i) specific gravity ii) specific volume iii) kinematic viscosity iv) shear stress v) dynamic
viscosity vi) weight density
4. i) Find the specific gravity, dynamic viscosity and kinematic viscosity of oil having density
981 kg /m3.
ii) The shear stress at a point in oil is 0.25 N/m2 and velocity gradient at the point is 0.2 per
second. Also determine the compressibility of the liquid, if the pressure is increased from 0.7
Mpa to 1.3 Mpa while the volume decreases by 0.15 percent. (Nov/Dec 2010)

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5. A helium balloon is at the same pressure and temperature as the surrounding air of 1
atmosphere and 20 º C. The diameter of the balloon is 3m. How much payload can the balloon
lift, if the weight of the plastic skin of the balloon is negligible? (Nov/Dec 2010)
6. Represent five types on the shear stress velocity gradient graphical form.
7. Explain the terms buoyancy, centre of buoyancy, Meta centre and Meta centric height.
(Nov/Dec 2010)
-3
8. A plate, 0.025 X10 m distant from a fixed plate, moves at 0.6 m/s and requires a force of 2
N/m2 to maintain this speed. Determine the viscosity in poise between the plates.
(Nov/Dec 2012)
9. Find the volume of the water displaced and position of centre of buoyancy for a wooden block
of width 2.5 m and depth of 1.5 m when it floats horizontally in water. The density of wooden
block is 650 kg/m3 and its length 6.0 m (Nov/Dec 2012)
10. Explain the following terms in detail i) steady and unsteady flows ii) uniform and non uniform
flows iii) laminar and turbulent flows iv) compressible and incompressible flows v) rotational
and irrotational flows vi) one, two and three dimensional flows.
11. i) What is meant by physical properties of fluid? (Nov/Dec 2011)
ii) Explain the phenomenon of capillarity rise and capillarity fall and obtain its expression.

UNIT II
PART A

1. If Bernoulli’s equation is applicable for a fluid flow through a horizontal constant

diameter pipeline, will there be a pressure loss? Why? (Nov/Dec 2014)
Pressure loss doesn’t give much impact on the fluid flow because it is horizontal constant
diameter pipeline. If Bernoulli’s equation is applied for this system pressure head term will be
negligible.

2. What is the main use of manometer? (Nov/Dec 2011)

Manometers are device which is used for measuring the pressure at a point in a fluid by
balancing the column of fluid by the same or another column of the fluid.

3. Write general continuity equation (Nov/Dec 2012)

AV=CONSTANT

4. Define fluid statics.

 Fluid statics deals with fluids in the equilibrium state of no shear stress.
 The study of incompressible fluids under static conditions is called hydrostatics and that
dealing with the compressible fluids is termed as aerostatics.

5. What is meant by Hydrostatic equilibrium? (Nov/Dec 2012)

 In a stationary mass of a single static fluid, under gravitational field, hydrostatic equilibrium
says that the pressure is constant in any cross section parallel to the earth’s surface but varies
from height to height.
 Mathematically, the condition of hydrostatic equilibrium is (P/) + (g Z) = constant.
 This is applicable for incompressible or compressible fluids as long as the density ‘’ is taken
into account and valid for viscous fluids, since the fluid under consideration is rest and
shearing effect does not come into play.

6. Define manometric pressure.

Manometers measure a pressure difference by balancing the weight of a fluid column between
the two pressures of interest. Large pressure differences are measured with heavy fluids, such
as mercury (e.g. 760 mm Hg = 1 atmosphere). Small pressure differences, such as those
experienced in experimental wind tunnels or venturimeter are measured by lighter fluids such
as water (27.7 inch H2O = 1 psi; 1 cm H2O = 98.1 Pa).

7. Write the ‘Barometric equation’ of fluid static.

The Barometric equation, between levels ‘a’ and ‘b’ in a static fluid (ideal gas), is given by
Pb/Pb = exp {[- g M (Zb – Za)] / (R T)}
Where ‘M’ is the molecular weight of the fluid and ‘T’ is the absolute- temperature.

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8. State the steady flow energy equation. (April/May 2007)

The steady flow energy equation relates to open systems working under steady conditions i.e.
in which conditions do not change with time. The boundary encloses a system through which
fluid flows at a constant rate, whilst heat transfer occurs and external work is done all under
steady conditions, that is, the rates of mass flow and energy flow are constant with respect to
time.
The equation for steady flow (the steady flow energy equation) is generally written per unit
mass as
q = heat transfer across boundary per unit mass
w = external work done by system per unit mass
z = fluid height
v = fluid velocity
h = fluid enthalpy ( u (internal energy) + pv (pressure. specific volume) )
‘Shear rate thickening’. Bentonite clay suspensions and gypsum suspensions are example for
such fluids.

9. Write the momentum balance equation for steady state flow of fluid.
 The basic equation of the momentum balance is as follows;
Rate of momentum accumulation = Rate of momentum entering – Rate of momentum
leaving + Sum of forces acting on the system.
 At steady state, the above equation becomes
Sum of forces acting on the system,
 F = Rate of momentum leaving – Rate of momentum entering.

10. State the assumptions made in the derivation of the Bernoulli’s equation. (April/May
2007)
The assumptions made in the derivation of the Bernoulli’s equation may be summarized as
follows;
 The flow is potential (inviscid flow,  = 0).
 The flow is steady ( / t = 0).
 The flow is irrotational (the flow is along a streamline).
 The flow is two dimensional, in the presence of gravitational forces.

11. Write the Bernoulli’s equation of fluid flow. (Nov/Dec 2010)

 “In an ideal, incompressible fluid when the flow is steady and continuous, the sum of pressure
energy, potential energy and kinetic energy is constant along a stream line. Mathematically,
p v2
  z  const.
g 2g
 Bernoulli’s equation between two stations ‘1’ and ‘2’ of fluid flow system is
2 2
p1 v p v
 1  z1  1  1  z1  hL
g 2 g g 2 g
Where ‘P/( g)’ is the pressure head, ‘V2/(2 g)’ is the velocity head or kinetic head, and ‘Z’ is the
potential head.

12. Write Euler’s equation of motion. (Nov/Dec 2012)

 For constant density and zero viscosity (ideal fluid, potential flow), the equation of motion
(known as Euler’s equation) is
 (D V/Dt) = -P +  g(Vector form)
It is a special case of the Navier–Stoke’s equation.
 Euler’s equation of motion along the streamwise ‘x’ direction is given by
(1/) (dP/dx) + V (dV/dx) + g (dZ/dx) = 0

13. Define Momentum correction factor and kinetic energy correction factor.
 Momentum correction factor ‘’ is defined as
Momentum per unit time based on actual velocity

Momentum per unit time based on average velocity
For flow of liquid in a circular pipe,  = 4/3 and for turbulent flow, nearly  = 1.

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 Kinetic energy correction factor ‘’ is defined as

Kinetic energy based on actual velocity

Kinetic energy based on average velocity
For laminar flow of liquid in a circular pipe,  = 2 and for turbulent flow,  = 1.05

14. Write the equation of continuity for compressible fluids.

 The equation of continuity for compressible fluids is given by
uS = constant or (d/) + (dS/S) + (du/u) = 0
Where ‘S’ is the area of cross section and ‘’ is the density of the fluid.

15. Give the relationship between the head loss and the velocity in laminar and turbulent
flow regions.
 In case of laminar flow, the loss of head is directly proportional to the velocity of flow;
that is, H  V.
 In case of turbulent flow, the loss of head is directly proportional to the square of the
velocity of flow; that is, H  V2 (approximately) and H  Vn (more exactly), where ‘n’
varies form 1.75 to 2.0

16. Explain intensity and scale of turbulence.

 Turbulent fields are characterized by two average parameters;
 The first measures the intensity of the field and refers to the speed of rotation of the eddies and
the energy contained in an eddy of a specific size. Intensity is measured by the root mean
square of a velocity component.
 The second measures the size or scale of the eddies. The scale of turbulence is based on
correlation coefficients as a function of the distance between stations or points.

17. What do you mean by Reynold’s stresses?

It has long been known that shear forces much larger than those occurring in laminar flow
exist in turbulent flow wherever there is a velocity gradient across a shear plane. The
mechanism of turbulent shear depends upon the deviating velocities in anisotropic turbulence
(correlation coefficients are not equal to the root-mean-square components, for all directions at
a given point). Such turbulent shear stresses are called Reynold’s stresses.

18. What is meant by fully developed flow?

 In the boundary layer, for a straight - thin walled tube with fluid entering it at uniform
velocity, the velocity increases from zero at the wall to the constant velocity existing in the
core.
 As the stream moves farther down the tube, the boundary layer occupies an increasing
portion of the cross section. Finally, at a point well downstream from the entrance, the
boundary layer reaches the centre of the tube and occupies the entire cross section of the
stream.
 At this point, the velocity distribution in the tube reaches its final form and remains unchanged
during the remaining length of the tube. Such flow with an unchanging velocity distribution is
called ‘Fully developed flow’.

19. Define the stream function.

The stream function is defined for two-dimensional flows of various kinds. The stream
function can be used to plot streamlines, which represent the trajectories of particles in a
steady flow. Streamlines are perpendicular to equipotential lines. In most cases, the stream
function is the imaginary part of the complex potential, while the potential function is the real
part.

20. Explain Velocity field.

 When a stream of fluid is flowing in bulk past a solid wall, the fluid adheres to the solid at the
actual interface between solid and fluid. The adhesion is a result of the force fields at the
boundary, which are also responsible for the interfacial tension between the solid and fluid.
 If, therefore, the wall is at rest in the reference frame chosen for the fluid-solid system, the
velocity of the fluid at the interface is zero.

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 Since at distances away from the solid the velocity is not zero, there must be variations in
velocity from point to point in the flowing stream. Therefore, the velocity at any point is a
function of the space coordinates of that point, and a velocity field exists in the space occupied
by the fluid.
 The velocity at a given location may also vary with time. When the velocity at each location is
constant, the field is invariant with time ad the flow is said to be Steady.

21. State Navier–Stoke’s equation.

For a fluid of constant density and viscosity, the equation of motion (known as Navier–Stoke’s
equation) is  (D V/Dt) = -P +  2V +  g (Vector form) Where (D V/Dt) is the
substantial derivative or the derivative following the motion; this is the rate of velocity
change that would be noted by an observer moving downstream at the pressure of the fluid.
‘P’ is the divergence of the pressure vector or partial differentiation of ‘P’ along the directions
x, y, and z; ‘2V’ is the second order divergence of the velocity vector.

PART-B
1. i) Starting with the barometric equation derive the pressure variation in atmosphere assuming
isothermal condition.
ii) using the derived equation calculate the pressure at a height 2500m above sea level if the
atmospheric pressure is 101.3kPa, given density of air is 1.208 kg/m3 (clue: Ideal Gas)
(Nov/Dec 2014)
2. Through a vertical pipe a liquid of specific gravity 0.8 is flowing up. The vertical pipe at
section A has a diameter 8 cm and at a section B 2 meters above has a diameter 10 cm. the
pressure difference between sections A & B is 9810 N/m2. Calculate the flow rate of the liquid
using mechanical energy balance and equation of continuity. (Nov/Dec 2014)
3. What is a manometer? How they are classified? Explain how manometers are used in
determining the pressure of fluids. (Nov/Dec 2010)
4. Determine the pressure difference over a simple U-tube manometer which is installed across
an orifice meter. The manometer is filled with mercury having specific gravity 13.6 and the
liquid above the mercury is carbon tetrachloride having specific gravity 1.6 The manometer
reads 200 mm. (May/ June 2012) (April/May 2011)
5. The right limb of a simple U-tube manometer containing mercury (density 13600 Kg/m3) is
open to the atmosphere while the left limb is connected to a pipe in which a fluid of density
900 kg/m3 is flowing. The centre of the pipe is 12 cm below the level of mercury in the right
limb. Find the pressure of fluid in N/m2 in the pipe if the difference of mercury in the two
limbs is 20 cm. (Nov/Dec 2012)
6. Discuss about hydrostatic pressure distribution or general equation for variation of pressure
due to gravity at various heights in a static fluid. (April/May 2011) (Nov/Dec 2013)
7. Give the derivation of one dimensional flow continuity equation and three dimension.
(Apr/May 2010)
8. Explain the concept of boundary layer and also brief about the significance of correction of
energy (Bernoulli’s) equation for fluid friction. (Apr/May 2011)
9. i) Write the point form of Bernoulli’s equation.
ii) Derive Bernoulli’s equation for real fluids between point 1 and 2. (Nov/Dec 2010)
10. Derive the full form of Bernoulli equation with fluid friction and pump work
for the flow of an incompressible fluid. (May/June 2012)
11. In detail explain the difference between momentum and mechanical energy equation.
(Nov/Dec 2011)
12. i) Explain in detail about inclined manometers used for measurement of pressure drop and give
its derivation, with a neat diagram
ii) Explain in detail about differential manometers used for measurement of pressure drop and
give its derivation, with a neat diagram

UNIT III
PART A
1. In a dimensional analysis problem there are 6 variables and 4 dimensions identified. How
many dimensionless parameters can be developed? (Nov/Dec 2014)
6 variables
4 dimensions
Generally dimensionless parameters can be determined by (n-dimensions)

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Therefore, dimensionless parameters= 6 - 4 = 2

2. What is Dimensional analysis? List the methods also. (Nov/Dec 2011)

 Dimensional analysis is a mathematical technique which makes use of the study of the
dimensions for solving several engineering problems.
 Dimensional analysis is particularly helpful in experimental work because it provides a guide
to those things that significantly influence the phenomena; thus, it indicates the direction in
which experimental work should go.
 Dimensional analysis is generally performed by two methods namely Rayleigh’s method and
Buckingham’s method.

3. In making dimensional analysis what rules do you follow for choosing the scaling
variables?
This method derives from the principle that each term in an equation depicting a physical
relationship must have the same dimension. Non-dimensional quantities expressing the
relationship among the variables are constructed e.g. [Length / (Velocity.Time)], or [Force /
(Mass /Acceleration)]. These are equated and then experiments are complete to determine their
functional relationship. It is characteristic of physical equations that only like quantities that is
those systems having the same dimensions, are added or equated.

4. Define Dimensional homogeneity.

Dimensional homogeneity states that every term in an equation, when reduced to fundamental
dimensions, must contain identical powers of each dimension.

5. What do you mean by a Model and Prototype? (Nov/Dec 2010)

A ‘Model’ is a small scale replica of the actual machine or structure, nothing but ‘Prototype’.
For the model (to give useful information about the characteristics of the prototype) the model
must have geometric, Kinematic and dynamic similarities with the prototype.

6. Define Froude number. Give its application.

 A dimensional quantity related to the ratio of the inertia forces to the gravity forces is called as
the ‘Froude number’. It is expressed as NFr = Fi = V
Fg Lg
 Systems involving gravity and inertia forces include the wave action set-up by a ship, the flow
of water in open channels, the forces of a stream on a bridge pier, the flow over a spillway, the
flow of a jet from an orifice, and other cases where gravity is the dominant factor.

7. State the Buckingham’s  - theorem. (Apr/May 2011)

The Buckingham’s  - theorem states that – If there are ‘n’ variables (dependent and
independent variables) in a dimensionally homogenous equation and if these variables contain
‘m’ fundamental dimensions (such as M, L, T etc.,), then the variables are arranged in to (n -
m) dimensionless terms. These dimensionless terms are called ‘ -terms’ or ‘ -groups’.

8. Define Euler number. Give its physical significance.

 A dimensional quantity related to the ratio of the inertia forces to the pressure forces is known
as the ‘Euler number’. It is expressed in a variety of ways, one form being
Fi V
NEu = =
Fp P/ 
 If only pressure and inertia influence the flow, the Euler number for any boundary form will
remain constant. If the other parameters (viscosity, gravity, etc.) cause the flow pattern to
change, however, Euler number will also change.

9. Explain Rayleigh’s method of dimensional analysis. (Apr/May 2010)

 Rayleigh’s method of dimensional analysis is useful when the number of variables is less. In
this method, the equations are expressed in exponential forms.
 The dimensionless parameters are obtained by first evaluating the exponents so that equation is
dimensionally homogenous, and then by grouping together the variables with like powers to
form dimensional less parameter or term or group.

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10. Define Weber number. Give its application.

 A dimensional quantity related to the ratio of the inertia forces to the surface tension is called
as the ‘Froude number’. It is expressed as
Fi V
NWr = =
Fs  /( L)
 One of the applications is at the leading edge of a very thin sheet liquid flowing over a surface.

11. What are model or similarity laws? List them.

 The laws on which the models are designed for dynamic similarity are called model or
similarity laws
 The model laws are: Reynolds model law, Froude model law, Euler model law, Weber
model law, and Mach model law.

12. Define Geometric similarity.

 Geometric similarity means the ratio of all linear dimensions of the model and that of the
prototype should be equal. That is, the model and its prototype be identical in shape but differ
only in size.

13. Define Kinematic similarity. (April/May 2010)

 Kinematic similarity means the similarity of motion between model and prototype. That is, it
implies the geometric similarity and in addition it implies the ratio of the velocities at all
corresponding points in the flow is the same

14. Define Dynamic similarity. (April/May 2010)

 Dynamic similarity means the similarity of forces between the model and prototype. That is
the corresponding forces must be in the same ratio in both model and prototype.

15. What do you mean by ‘Scale-up’?

Experimental data are often available for a laboratory-size or pilot plant system, and it is
desired to scale-up the results to design a full-scale unit. This transformation of pilot plant data
to large scale industrial unit is called ‘Scale-up’.

16. Define Mach number. Give its physical significance.

 The Mach number ‘Ma’, for compressible fluids, is defined as the ratio of the speed of the fluid
‘u’ to the speed of sound ‘a’ in the fluid under conditions of flow. That is, Ma = u / a.
 Significance: Ma <1 represents the flow as Subsonic; Ma = 1 represents the flow as Sonic; Ma
> 1 represents the flow as Supersonic.

17. What is BWG? Give its range.

 Birmingham Wire Gauge (BWG) indicates the wall thickness of tube construction for the flow
of fluids.
 It ranges from no. 10 to 18; no. 10 will come for some larger diameter tubes.

18. Define ‘Equivalent pipe’.

 It is defined as the pipe of uniform diameter having loss of head and discharge of a compound
pipe consisting of several pipes of different lengths and diameters.
 To determine the size of the equivalent pipe, Dupit’s equation is used.
L L L L L
5
 15  25  35  45 ....
D D1 D2 D3 D4

19. Distinguish between Rotational and Irrotational flow. (May/June 2007 )

 Irrotational flow: The flow of ideal fluid, having zero viscosity, is called Irrotational flow or
Potential flow. For such flow, neither circulations nor eddies can form within the fluid stream
and friction cannot develop (so that there is no dissipation of mechanical energy into heat).
 Rotational flow: The flow of fluid, having definite viscosity, with circulations or eddies
within the stream of fluid is called Rotational flow. This type of flow develops friction and
dissipates mechanical energy into heat.

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20. What do you mean by Uniform and Non-uniform flow?

 When the size and shape of cross section are constant along the length of channel (for fluid
flow) under consideration, the flow is said to be Uniform. A truly Uniform flow is one in
which the velocity is the same in both magnitude and direction at a given instant at every point
in the fluid. Example: Flow of liquid at a constant rate in a long straight pipe of constant
diameter.
 When the size and shape of cross section are changes along the length of channel (for fluid
flow) under consideration, the flow is said to be Non-uniform. Example: Flow of a liquid at a
constant rate through a conical pipe.

21. What are time-dependent and time-independent fluids?

 Time independent fluids: Newtonian and Non-Newtonian fluids are time independent fluids.
 Time dependent fluids: For some Non-Newtonian fluids, the curve of ‘’ vs. ‘du/dy’ depend
on how long the shear has been active. Such fluids then become time dependent and given as
1. Thixotropic Liquids – break down under continued shear and on mixing give lower
shear stress for a given shear rate; that is, their apparent viscosity decreases with time.
These fluids are said to be ‘Shear rate thinning’. Some paints and polymer solutions are
example for such fluids.
2. Rheopectic Liquids – substance that behave in the reverse manner of thixotropic liquids,
and the shear stress increases with time, as does the apparent viscosity. These fluids are
said to be shear rate thinning’.

PART-B

1. Drag force FD (N) has been found to be dependet on length – L (m), Velocity – v (m/s) density
of fluid ρ - kg/m3 , Viscosity of the fluid – μ (kg/m.s) and gravity – g (m/s2).use Buckingham
Pi theorem to show. FD/ ρ υ 2L = fn (L υ ρ/ μ),( υ/√L.g) (clue) Repeating variables (L, υ, ρ).
(Nov/Dec 2014)
2. An industrial agitator is to be designed and operated, based on experiment in a model agitator.
What should be the rpm of the industrial agitator, if both the system is dynamically similar
with respect to Reynolds No. Reynolds number is given ( n.Da2. ρ/ μ) (n- speed of rotation,
Da- diameter of impeller, ρ & μ density and viscosity of liquid). The liquid used in the model
has density 1.2 times that of proto type and viscosity 0.9 times that of prototype liquid. The
model is operated at 100 rpm. The industrial agitator has a diameter 10 times that of model.
(Nov/Dec 2014)
0.8 0.67 0.33 -0.2 -0.47
3. Check the dimensional consistency of hi = 0.023 G k Cp D  where G is the
mass velocity and all other properties are represented by symbols. (Nov/Dec 2013)
4. Explain the principle of dimensional homogeneity with an example and also list the steps
involved in the pi- theorem of dimensional analysis. (Apr/May 2010)
5. The pressure difference Δp in a pipe diameter D and length L due to viscous flow depend on
the velocity V, viscosity μ and density ρ using Buckingham’s П- theorem, obtain an expression
for Δp. (Nov/Dec 2012)
6. i) Give a detailed note on general procedure for solving problems by rayleigh’s method.
ii) Discuss about the principle of dimensional homogeneity. (May/June 2012)
7. Using dimensional analysis, derive an equation connecting power number and Reynolds
number for scale up design. (May/June 2012)
8. The efficiency η of a fan depends on the density ρ, the dynamic viscosity μ of the fluid, the
angular velocity ω, diameter D of the rotor and the discharge Q. Express η in terms of
dimensionless parameters.
9. Find an expression for the drag force on smooth sphere of diameter D, moving with a uniform
velocity V in a fluid of density ρ and dynamic viscosity μ.
10. What are the methods of selecting the repeating variables?
11. Write a brief note on the similitude and explain the types of similarity
12. What are the methods available to determine the relation among variables? Give a detailed
note on general procedure for solving problems by Buckingham pi theorem.

UNIT IV
PART A
1. What is Hagen-Poiseuille law? Give its importance. (Nov/Dec 2014)
 The Hagen-Poiseuille law, for laminar flow in tubes, is given by
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hfs = Ps / = (32 L V ) / D2

where ‘hfs’ is the energy loss due to skin friction.
 Hagen, a German engineer, experimented with water flowing through small brass tubes and
published his results in 1839. Poiseuille, a French scientist, experimented with water flowing
through capillary tubes in order to determine the laws of flow of blood through veins of the
body and published his studies in 1840.
 One of its important uses is in the experimental measurement of viscosity (), by measuring
the pressure drop (Ps) and volumetric flow rate (from which, we get ‘V’) through a tube of
known length (L) and diameter (D).

2. What does the equation kozeny carman equation represent? Explain the terms. (Nov/Dec
2014)

For the system flow is proportional to pressure drop and inversely proportional to the fluid
viscosity.

3. Define Boundary layer. (April/May 2010)

 A boundary layer is defined as that part of a moving fluid in which the fluid motion is
influenced by the presence of a solid boundary.
 It is a narrow region, near the solid surface, over which velocity gradients and shear stresses
are large.

4. Define Boundary layer thickness. (April/May 2012)

In boundary layer flow, a limit is placed at a distance where the velocity reaches 99% of the
main stream velocity and the distance where 99% velocity is reached is called Boundary-layer
thickness. It is denoted by ‘’ and has the units of ‘m’ in SI.
5. Define the term boundary layer separation. (April/May 2011)
Boundary layer separation is when the thin layer of viscous fluid leaves the surface of the body
that it is flowing over. The viscosity of the fluid causes the boundary layer separation. It is well
known that as the Reynolds number increases, the likelihood of the boundary separating
increases.

6. What is meant by rough pipe and smooth pipe? (Nov/Dec 2011)

The average height of the irregularities (K) projecting from the surface of a boundary. If the
value of K is large for a boundary is called rough pipe or rough boundary. If the value of K is
less then boundary is known as smooth pipe or smooth boundary.

7. Define Streamline and Stream tube. (Nov /Dec 2010)

 A streamline is an imaginary path in a mass of flowing fluid so drawn that at every point the
vector of the net velocity along the streamline ‘u’ is tangent to the streamline. There is no net
flow across such a line; In turbulent flow, eddies do cross and re cross the streamline, but the
net flow from such eddies in any direction other than that of the flow is zero. Flow along the
streamline is uni-directional or one-dimensional.
 A stream tube is a tube of large or small cross section and of any convenient cross-sectional
shape that is entirely bounded by streamlines. A stream tube can be visualized as an imaginary
pipe in the mass of flowing fluid through the walls of which there in no bet flow.

8. What are Wall drag and Form drag? (April/May 2009)(Nov /Dec 2013)
Wall Drag: When the wall of the body is parallel with the direction of flow, the only drag force
is the wall shear ‘w’. More generally, the wall of an immersed body makes an angle with the
direction of flow. Then the component of the wall shear in the direction of flow contributes to
drag. Thus, the total integrated drag from wall shear is called ‘Wall Drag’.
 Form Drag: If the fluid pressure acts in a direction normal to the wall, then the drag comes
from the pressure component in the direction of flow. Thus, the total integrated drag from
pressure is called ‘Form drag’.

9. Define Drag and Drag coefficient.

 Drag: The force in the direction of flow exerted by the fluid on the solid is called ‘Drag’.
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 Drag Coefficient: It is defined as the ratio of (FD/AP) to the product of the density of the fluid
and the velocity head. It is denoted by ‘CD’ and dimensionless. Thus, CD = (FD/AP)/[ (Uo2/2)]
Where ‘AP’ is the projected area of the solid body as the area obtained by projecting the body
on a plane perpendicular to the direction of flow; ‘FD’ is the total drag (Form drag + Wall
drag), and ‘Uo’ is the velocity of the approaching stream (by assumption Uo is constant is
constant over AP).

10. What are the forces acting on a body immersed in a fluid and on a particle moving
through a fluid?
A body which is wholly immersed in a homogeneous fluid may be subject to two kinds of
forces arising from relative motion between the body and fluid.
These forces are termed the ‘Drag’ and the ‘Lift’, depending on whether the force is parallel to
the motion or at right angles to it, respectively.
The forces acts on a particle moving through a fluid are
 The external force, gravitational or centrifugal
 The buoyant force, which acts parallel with the external force but in the opposite direction and
 The drag force, which appears whenever there is relative motion between the particle and the
fluid; acts to oppose the motion and acts parallel with the direction of movement but in the
opposite direction.

11. Define terminal velocity.

 In gravitational settling, ‘g’ is constant, the drag always increases with velocity; the
acceleration decreases with time and approaches zero.
 The particle (which is under motion through fluid) quickly reaches a constant velocity, which
is the maximum attainable under the circumstances and which is called the Terminal
velocity.
 The equation for the terminal velocity ‘Ut’, for gravitational settling, is given by
Ut = SQRT {[2 g (p -) m] / (AP p CD )} Where ‘’ is the density of fluid, ‘p’ is
the density of the particle, ‘m’ is the mass of the particle, ‘CD’ is the drag coefficient, and
‘AP’ is the projected area of particle measured in plane perpendicular to direction of motion of
particle.

12. Distinguish between Free settling and Hindered settling.

Consider a mass of particles settling in a container, which is having the fluid, under
gravitational field.
 When the particle is at sufficient distance from the boundaries of the container and from other
particles, so that its fall is not affected by them, the process is called ‘Free Settling’.
 If the motion of the particle is impeded by other particles, which will happen when the
particles are near one another even though they may not actually be colliding, the process is
called ‘Hindered Settling’.
Note: The drag coefficient in hindered settling is greater than that in free settling.

13. Explain the phenomena of Fluidization.

 When a liquid or a gas is passed at very low velocity through a bed of solid particles, the
particles do not move, and the pressure drop remains constant.
 If the fluid velocity is steadily increased, the pressure drop and the drag on individual particles
increase, and eventually the particles start to move and become suspended in the fluid; the
suspension behaves as a dense fluid. Such phenomenon is called ‘Fluidization’.
 If the bed is tilted, the top surface remains horizontal and large objects will either float or sink
in the bed depending on their density relative to the suspension.
 The fluidized solids can be drained from the bed through pipes and valves, just as a liquid can,
and this fluidity is one of the main advantages of the use of fluidization for handling solids.

14. What is minimum fluidization velocity?

 When a fluid flows upwards through a packed bed of particles of at low velocities, the particles
remain stationary. Upon further increases in velocity, conditions finally occur where the force
of the pressure drop times the cross-sectional area equals the gravitational force on the mass of
particles. Then the particles begin to move, and this is the onset of ‘Fluidization’ or ‘minimum
fluidization’.

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 The fluid velocity at which fluidization begins is the ‘minimum fluidization velocity’ based on
the empty cross-section of the tower.

15. Distinguish between Particulate and Aggregative fluidization.

 In Particulate fluidization, as the fluid velocity is increased the bed continues to expand and
remains homogeneous for a time. The particles move farther apart and their motion becomes
more rapid. The average bed density at a given velocity is the same in all regions of the bed.
An example is catalytic cracking catalysts fluidized by gases.
 In Aggregative or Bubbling fluidization, the gas passes through the bed as voids or bubbles
which contain few particles, and only a small percentage of the gas passes in the spaces
between individual particles. The expansion of the bed is small as gas velocity is increased.
Sand and Glass beads provide examples of this behavior.

16. Give the applications of fluidization.

 Extensive use of fluidization began in the petroleum industry with the development of fluid-
bed catalytic cracking. Although the industry now generally uses riser or transport-line reactors
fro catalytic cracking, rather than fluid beds, the catalyst regeneration is still carried out in
fluid-bed reactors, which are as large as 10m in diameter.
 Fluidization is used in other catalytic processes, such as the synthesis of acrylonitrile, and for
carrying out gas-solid reactions. There is much interest in the fluidized-bed combustion of coal
as means of reducing boiler cost and decreasing the emission of pollutants.
 Fluidized beds are also used for roasting ores, drying fine solids, and adsorption of gases.

17. What are the advantages and disadvantages of fluidization?

Advantages of fluidization
 The chief advantages of fluidization are that the solid is vigorously agitated by the fluid
passing through the bed, and the mixing of the solids ensures that there are practically no
temperature gradients in the bed even with quite exothermic or endothermic reactions.
 The violent motion of the solids also gives high heat transfer rates to the wall or to cooling
tubes immersed in the bed.
 Because of the fluidity of the solids, it is easy to pass from one vessel to another.
Disadvantages of fluidization
 The main disadvantage of gas-solid fluidization is the uneven contacting of gas and solid,
which will decrease the overall conversion of gaseous reactant.
 Other disadvantages of fluidized beds, more easily dealt withy by proper design, include
erosion of vessel internal parts and attrition of the solids, leading to loss of fines.
Note: Most fluid-bed reactors have internal or external cyclones to recover fines, but filters and
scrubbers are often needed also.

18. Define fanning friction factor. Give its equation for laminar and turbulent flow.
 Fanning friction factor ‘f’ is defined as the ratio of the wall shear stress ‘w’ to the product
of the density ‘’ and the velocity head ‘V2/2’. Mathematically, it is f = w / [ (V2/2)].
 The equation of friction factor for the flow of liquids is
f = 16/NRe, for laminar flow f = 0.0791 NRe-0.25, for turbulent flow in smooth pipe.

19. Write the Darcy-Weisbach and Chezy’s equation for energy losses due to friction.
 Darcy - Weisbach formula (for loss of head due to friction) hfs = 4 f (L/D) (V2/2)
Where ‘f’ is the friction factor and f =  (NRe).
 Chezy’s formula (for loss of head due to friction) V  C mi

20. Define Sphericity and Porosity. (May/June 2013)

It is defined as the surface-volume ratio for a sphere of diameter ‘DP’ divided by the surface-
volume ratio for the particle whose nominal size is ‘DP’. It is denoted by ‘S’ and given as
S = (6/DP)/(SP/VP).Where (6/DP) is the surface-volume ratio for a sphere.
The Porosity or void fraction ‘’ of particle in the bed, for flow through bed of solids, is
defined as  = [Volume of voids in bed] / [Total volume of bed (voids + solids)].

21. Define equivalent diameter for noncircular channels.

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Equivalent diameter ‘Deq’ is defined as 4 times the hydraulic radius ‘rH’. The ‘rH’ in turn
defined as the ratio of the cross sectional area of the channel ‘S’ to the wetted perimeter of the
channel ‘LP’. Such that,
Deq = 4 rH = 4 (S/ LP).
An important case is the annulus between two concentric pipes. Here, the hydraulic
radius
rH = [ (Do2/4) -  (Di2/4)] / [ Do +  Di] = (Do – Di)/4 &
Deq = Do – Di
where Di & Do are the inside and outside diameters of the annulus respectively.

PART- B
1. Derive the equation to determine minimum fluidization velocity. (Nov/Dec 2014)
2. Calculate the Reynolds no and drag force FD on a ball of diameter 8 cm in a stream of air
flowing at 7 m/s density and kinemeatic viscosity of air are 1.25 kg/m3, and 1.5X 10-4 m2/s.
Date: If Re<0.2 CD= 24/Re
5<Re<1000 CD =0.4
1000< Re<100000 CD =0.5 (Nov/Dec 2014)
3. Water is flowing over a plate along 1 m length. The velocity of water is 0.15m/s. the viscosity
and density of water may be taken as 0.01 poise and 1000 kg/m3. if the flow is laminar the
boundary larger thickness at the end of the plate can be estimated by δ=5.48 X/√Rex Calculate
boundary layer thickness at 0.5m, and in along the length of the plate. (Nov/Dec 2014)
4. Water flows through a pipe AB 1.2 m diameter at 3 m/s and then passes through a pipe BC
1.5 m diameter. At C, the pipe branches. Branch CD is 0.8 m in diameter and carries one-third
of flow in AB. The flow velocity in branch CE is 2.5 m/s. Find the volume rate of flow in AB,
the velocity in BC, the velocity in CD and the diameter of CE.
5. Specify the Reynold’s number regimes and derive the expression for head loss due to friction
in circular pipes. (Apr/May 2011)
6. Water flows through 200 mm diameter steel pipe at an average velocity of 1.8 m/s.
downstream the pipe divides into a 200 mm main and a 50 mm bypass. The equivalent length
of the bypass 6.6 m. then the length of the 200 mm pipe in the bypassed section is 5.8 m.
Neglecting the minor losses, find what fraction of the total water will flow through the bypass?
(Apr/May2010)
7. Explain the fluid flow (concepts) through packed beds and fluidized beds.
(Nov/Dec 2010)
8. Describe the various losses encountered in multiple piping systems. (May/Jun 2012)
9. Derive Kozeny – Carman equation and Burke –plummer equation for the friction in flow of
fluids through the beds of solids. (May/Jun 2012) (Nov /Dec 2013)
10. i) Derive the friction loss from sudden expansion and sudden contraction of pipe cross section.
(Nov /Dec 2013)
ii) Discuss the friction factor for packed bed. (Nov/Dec 2012)
11. i) Discuss the laws used for characterizing the movement of solid through a liquid.
ii) A pipe of diameter 20 cm and length 10000m is used for transporting oil with a specific
gravity 0.9 and viscosity 1.5 poise. The flow rate is 20 liter/s. Estimate the pressure loss and
the power required to pump the oil. (Nov/Dec 2012)
12. Show that in laminar flow of Newtonian fluids through circular pipes, the average velocity is
one half of maximum velocity and also derive the relationship between friction factor and
Reynolds’s number for the above flow. (Apr/May 2011)
13. Obtain an expression for velocity distribution in turbulent flow for i) Smooth pipes ii) Rough
pipes (Nov/Dec 2010)

UNIT-V
PART A
1. Why do you call an orifice meter as constant area variable head flow meter? (Nov/Dec
2014)
As flow rate increases, the orifice area that the flow moves through also increases so
orifice meter is called as variable head flow meter.

2. Distinguish between Fan, blower, and compressor. (Nov/Dec 2012)

Fan, Blower and compressor are devices which convert mechanical energy to energy
which are used to transport compressible fluids, especially gases (usually air).
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 Fans discharge large volume of gas (usually air), at low pressures on the order of 0.04 atm,
into open space or large ducts.
 Blowers are high speed rotary devices (using either positive displacement or centrifugal force)
that develop a maximum pressure of about 2 atm.
 Compressors, which are also positive displacement or centrifugal machines, discharge at
pressures from 2 atm to several thousand atmospheres.
 In fans the density of the fluid does not changes appreciably, and may be assumed constant. In
blowers and compressors, however, the density change is too great to justify this assumption,
and in discussing these devices compressible flow theory is required.

3. List the uses of steam jet ejectors. (May/June2012) (May/June2013)

 It is mostly used for drawing a fairly high vacuum
 They are rarely used to produce absolute pressure below 1mm Hg.

4. What is meant by positive displacement pump? (May/June2013)

Positive displacement units apply pressure directly to the liquid by a reciprocating piston, or by
rotating members which form chambers alternately filled by and emptied of the liquid.

5. List the types of Valves commonly used.

The types of Valves commonly used in industry are;
 Gate valves and Globe valves
 Plug cocks and Ball valves
 Check valves  Lift check, Ball check, and Swing check valves.
 All valves have a common primary purpose – to slow down or stop the flow of a fluid.
Some valves work best in on-or-off service, fully open or fully closed.
 Others are designed to throttle, to reduce the pressure and flow rate of a fluid. Still others
permit flow in one direction only or only under certain conditions of temperature and
pressure.
 A steam trap, which is a special form of valve, allows water and inert gas to pass through
while holding back the steam.

6. Define a Pump.
 Pump is a mechanical device which converts mechanical energy into hydraulic energy, used to
transport incompressible fluids. (or) A fluid machine which operates to convert shaft power
into fluid power is called a Pump.
 Pumps increase the mechanical energy of the liquid – by increasing its velocity, pressure, or
elevation - or all three.

7. List the criteria to be adapted while selecting a pump. (Nov/Dec 2011)

 Characters of liquid to be handled
 Total dynamic head
 Suction and discharge heads
 Temperature and viscosity of the liquid to be handled
 Presence of solids and corrosion characteristics
 Space available.

8. Define NPSH. (May/June2012)(Nov/Dec 2013)

To avoid Cavitation, the pressure at the pump inlet must exceed the vapor pressure by a certain
value, called the Net Positive Suction Head (NPSH). It is customarily calculated as
NPSH = (1/g) {[(Pa – Pv)/] – hfs} - Za
Where ‘Pa’ is the absolute pressure at the surface of reservoir; ‘Pv’ is the vapor pressure of the
liquid; ‘Za’ is the suction head; ‘hfs’ is the friction in the suction line.For small Centrifugal
pumps, NPSH is about 2 to 3m and for large pumps, it is up to 50m. This NPSH increases the
pump capacity, impeller speed, and discharge pressure.

9. What are the types of pumps used in chemical industry? (Nov/Dec 2011)
The types of pumps used in chemical industry are
 Reciprocating pumps  Piston pumps, Plunger pumps, and Diaphragm pumps.

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 Rotary pumps  Gear pumps (spur gear & internal gear pumps), Lobe pumps, Screw pumps,
Cam pumps, and Vane pumps.
 Centrifugal pumps.

10. Explain Head developed by a pump.

The head developed by a pump, with the application of Bernoulli’s equation on the
pump’s suction side and discharge side, is given by
[H/g] = [P/( g)] + Z + [( V2)/(2 g)] Where [H/g] is the Total head developed by a
pump; P/( g) is the pressure head; ‘Z’ is the potential head; ( V2)/(2 g) is the kinetic head.
Each term in the above equation has the dimension of length.

11. Explain Cavitation in a pump. (May/June 2012) (Nov/Dec 2013)

The power developed by a pump depends on the difference in pressure between discharge and
suction and is independent of the pressure level. From energy considerations, it is immaterial
whether the suction pressure is below atmospheric pressure or well above it, as long as the
fluid remains liquid.
However, if the suction pressure is only slightly greater the vapor pressure, some liquid may
flash to vapor inside the pump, which greatly reduces the pump capacity and cause severe
erosion. Such process is called ‘Cavitation’.
If the suction pressure is actually less than the vapor pressure, there will be vaporization in the
suction line, and no liquid can be drawn into the pump.

12. Draw the performance characteristic curves of centrifugal pump.

Characteristic curves of a centrifugal pump in dependence
of the flow Q the following curves are shown:

 Head H(Q)
 Power P(Q), Shaft power P2(Q), Power input P1(Q)
 Efficiency
 Hydraulic efficieny hhydr
 NPSHreq(Q)
 Speed n(Q)

13. What type of pump would you select for;

(Nov/Dec 2011)
(i) Transportation of slurries---------- Centrifugal pumps
(ii) Transportation of viscous liquids----------Rotary Pumps
(iii) Transportation of toxic/corrosive liquids -----Diaphragm /Centrifugal pumps

14. What are the various losses occurring in a centrifugal pump?

Internal losses:
 Hydraulic losses or blade losses by friction, due to variations of the effective area or changes
of direction.
 Losses of quantity at the sealing places between impeller and housing, at the rotary shaft seals,
and sometimes at the balance piston.
 Wheel friction losses by friction at the external walls of the wheel.
External or mechanical losses:
 Sliding surface losses by bearing friction or seal friction.
 Air friction at the clutches.
 Energy consumption of directly propelled auxiliary machines.

15. What are the types of reciprocating pump and rotary pumps
Reciprocating pumps  Piston pumps, Plunger pumps, and Diaphragm pumps.
Rotary pumps  Gear pumps (spur gear & internal gear pumps), Lobe pumps, Screw pumps,
Cam pumps, and Vane pumps.

16. What are Variable head and Variable area meters?

Variable Head Meters

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 Variable head meters are flow (volumetric) measuring meters in which the variation of flow
rate through a constant area generates a variable pressure drop (pressure head), which is related
to the flow rate.
 The most common types are Venturi and Orifice meters. Other full-bore measuring devices
include V-element, magnetic, vortex-shedding, turbine, and positive displacement meters;
ultrasonic meters; and mass flow devices such as Coriolis flow meters.
Variable Area Meters
 Area meters are another class of flow meters consists of devices in which the pressure drop is
constant, or nearly so, and the area through which the fluid flows varies with the flow rate.
 The area is related, through proper calibration, to the flow rate. The most important area meter
is the ‘Rotameter’.
Note: All the above meters are said to be Full-bore meters which can operates on all the fluid
in the pipe or channel.

17. Write short notes on ‘Insertion meters’. (Nov/Dec 2010)

 Insertion meters are flow meters which measures the flow rate, or more commonly the fluid
(local) velocity, at one point only (along the diameter of pipe or channel).The total flow rate,
however, can often be inferred with considerable accuracy from this single-point measurement.
 ‘Pitot tube’ is such a device or meter used to measure the local velocity along a streamline,
which are small when compared to the size of the flow channel. The measured local velocity
must bear a constant and known relationship to the average velocity.

18. Draw a schematic diagram illustrating the function of a steam jet ejector.(April/may
2010)

19. Explain ‘Vena contracta’.

 Because of the sharpness of the Orifice, the fluid stream separates from the downstream side of
the orifice plate and forms a free-flowing jet in the downstream fluid called as ‘Vena
contracta’.
 The jet is not under the control of solid walls and the area of the jet varies from that of the
opening in the Orifice to that of the Vena contracta.
 The area at any given point (at the downstream tap of the Orifice) is not easily determinable
and the velocity of the jet is not easily re3lated to the diameter of the Orifice.

20. Distinguish between Venturi and Orifice meters. (April/May 2007)

Venturi meter
 Head loss across it is low (or) Pressure recovery is good.
 Typically installed in a pipe of small diameter.
 Length of the meter is long (because of the longer conical downstream only the pressure
recovery is good).
 It is expensive and its ratio of throat diameter to pipe diameter cannot be changed.
 The value of CD is 0.95 to 0.99 (based on smaller to larger pipe diameters).
 Power consumption is less.
Orifice meter
 Head loss across it is more (or) Pressure recovery is poor.
 Typically and easily installed in a pipe of larger diameter.
 It occupies lesser space (because it is a plate type device).
 Its cost is less and its ratio of orifice diameter to pipe diameter can be changed (because of this
it is used to measure larger flow rate also).

St.Joseph’s College of Engineering 17 ISO 9001:2008

CH6304 Fluid mechanics Department of Chemical Engineering 2015-2016

 The value of CD is 0.60 to 0.65 (For Reo > 30000, the value of CD is almost constant and
CD = 0.61)
 Larger power consumption (because of large head or frictional loss).

21. What are Notch’s and Weir’s? (Nov/Dec 2010)

 A notch is a sharp-edged device which permits the liquid go through it, the liquid being
exposed to the atmospheric pressure. Notches may be rectangular, triangular (also called as V-
notch or triangular weir consists of a V-cut sharp edged passage through which the liquid
passes), circular or trapezoidal in shape.
 A weir is an obstruction placed in an open channel over which the flow occurs. The weir is
generally in the form of a vertical wall with a sharp edge on the top, running all the way across
the open channel. When the liquid flows over the weir, the height of the liquid above the tip of
the sharp edge bears a relationship with the discharge across it.
Note: The only difference between a weir and a rectangular notch is that a weir runs all the
way cross the channel whereas a rectangular notch may be as wide as the channel.

PART- B

1) Derive from the fundamentals to show that flow rate through an orifice meter is proportional to
√∆H of the differential manometer connected across the meter. ( Nov/Dec 2014)
2) i) Derive the energy balance equation for steady state compressor operation. ( Nov/Dec 2014)
ii) Explain with reference to a centrifugal pump.
a) NPSH b) developed Head c) priming
3) List various flow meters used in practice and explain anyone with a neat sketch. Also write the
expression used to measure the flow using the flow meter considered above. (Apr/May 2010)
4) i) Discuss the relative merits and demerits of venturimeter with respect to orifice meter.
ii) Explain the working principles of venturimeter with a neat diagram. Derive the volumetric flow
rate expression. (Nov/Dec 2010)
5) Discuss the application and functioning of the following measuring devices with diagram i) orifice
flow meter ii) weir and notches (Nov/Dec 2012)
6) i) Briefly explain the working mechanism of diaphragm pump with a neat sketch
ii) Draw the Rotary pump and explain the types of rotary pump. (May/June2013)
7) Explain the working principle and characteristics of a Centrifugal pumps in detail.
(Nov/Dec 2011) (Apr/May 2011) (May/June 2012)
8) i) Describe the Fans, Blowers and Compressor in detail.
ii) Describe the working mechanism of jet ejectors with a neat sketch.
(May/june2013)(May/June 2012)
9) i) Explain the characteristics curves of centrifugal pump. (Nov/Dec 2013)
ii) With a neat sketch explain the working of a reciprocating pump.
(May/june2013) (Nov/Dec 2013)
10) Briefly explain the principle, operation and working mechanism of Air lift pump. (May/June2013)
11) i) Explain the working of reciprocating compressor and mention its application.
ii) A single acting reciprocating pump, running at 50 rpm, delivers at 0.01m3/s of water. The
diameter of the piston is 200mm and stroke length 400mm. Determine the following i) the
theoretical discharge of the pump ii) co efficient of discharge iii) slip and the percentage slip of the
pump. (Nov/Dec 2012)
12) i) Define cavitation. What are the effects of cavitation? How will you prevent cavitation in pump?
ii) A centrifugal pump delivers water against a net head of 14.5m and design speed of 1000 rpm.
The vanes are curved back to an angle of 30° with the periphery. The impeller diameter is 300 mm
and outlet width 50 mm. Determine the discharge of pump if manometric efficiency is 95%
(April/May 2010)
(Nov/Dec 2012)

St.Joseph’s College of Engineering 18 ISO 9001:2008