NR-220301 - Mechanics of Fluids
NR-220301 - Mechanics of Fluids
NR-220301 - Mechanics of Fluids
2.a) Define and distinguish between steady flow and uniform flow. Give two
examples of each flow.
b) Define stream line and derive the equation of a stream line.
3.a) Derive Euler’s equation of motion along a stream line. State assumptions made in
the derivation.
In an inclined pipe of uniform diameter 25 cm, a pressure of 50 kPa was observed
at section – 1 which was at elevation 10.0 m. At another section – 2 at elevation
12.0 m, the pressure was 20 kPa and the velocity was 1.25 m/s. Determine the
direction of flow and the head loss between these two sections. The fluid in the
pipe is water.
4.a) Sketch the growth of boundary layer on a flat plate and explain the different
regions of it.
b) Find the displacement thickness and wall shear stress for the velocity distribution
in a boundary layer (u / U) = (y / δ) where U is the Velocity and δ is the boundary
layer thickness.
Contd..2
Code No: 220301 -2- Set No.1
6.a) Prove that in a steady uniform laminar flow, the pressure gradient in the direction
of flow is equal to the shear stress gradient in the normal direction.
b) In an experiment, the details of laminar flow of fluid are as follows. Determine
the discharge in the pipe.
Specific gravity = 1.67
Viscosity = 1.56 poise
Diameter of pipe = 15 cm
Length of the pipe = 2000 m
Loss of head = 0.45 m
7.a) Define and explain the terms hydraulic gradient line and total energy line.
b) A pipe 20cm diameter and 1800 m long connects two reservoirs one being 30m
below the other. The pipe line crosses a ridge whose summit is 7.5m above the
upper reservoir. What will be the minimum depth of the pipe below the summit of
the ridge in order that the pressure at the apex doesn’t fall below 7.5m vacuum?
The length of the pipe from the upper reservoir to the apex is 300m. Taking f=
0.032 determine the rate of flow to the lower reservoir in lit/min.
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Code No: 220301 Set No.
2.a) Define and derive the equation of rotation for a fluid particle in a flow field about
any axis.
b) A fluid flow field is given by V = xy i+ 2yz j – (yz +z2) k
Determine whether this is a possible steady incompressible fluid flow. If so,
determine the value of rotation at the point P (1,2,3).
6.a) Enumerate distinguish characteristics of laminar flow? Give examples where such
a flow is encountered.
b) Oil of absolute viscosity 1.5 poise and relative density 0.85 flows through a 30 cm
diameter pipe. If the headloss in 3000m length of pipe is 20m, estimate the
friction factor by assuming the flow to be laminar.
Contd..2
Code No:220301 -2- Set No.2
7.a) Obtain an expression for head loss due to sudden expansion in the pipe. List all
the assumptions made in the derivation.
b) If two pipes of diameters D and d and equal length L are arranged in parallel, the
loss of head for a flow of Q is h. If the same pipes are arranged in series, the loss
of head for the same flow Q is H. If d = 0.5D, find the percentage of total flow
through each pipe when placed in parallel and the ratio (H/h). Neglect minor
losses and assume f to be constant.
8. Explain orifice meter in detail with diagram. Also derive an expression for
finding out the actual discharge from a given orifice meter.
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Code No: 220301 Set No.
3.a) What are the body forces considered in fluid flow problems?
b) A 15-cm diameter pipe is reduced to 7.5 cm diameter through a gradual
contraction. The difference between the piezometric heads at the main and
contracted section is 4 cm of mercury. By neglecting losses calculate the
discharge of water.
4.a) Define coefficients of drag and lift and state factors affecting on which those
coefficients depend.
b) A kite has an effective area of 0.4 m 2 and weighs 2.0 N in a wind of 40 km/hr., the
drag on the kite is 12 N. Determine the tension in chord if the chord make an
angle of 45o with the horizontal. Also determine lift coefficient
Contd..2
Code No:220301 -2- Set No.3
6.a) Derive Hazen-Poiseuille equation for laminar flow in the circular pipes.
b) Glycerin of viscosity 1.5 pascal-sec and mass density 1200 kg/m3 flows at a
velocity of 5 m/sec in a 10 cm diameter pipe. Check whether the flow is laminar
in pipe line. Find the boundary shear stress in the pipe.
7.a) Obtain an expression for the optimum exit diameter of a nozzle to be fitted at the
service end of a pipe for maximum power transmission.
b) Find the loss of head when a pipe of diameter 20cm is suddenly enlarged to a
diameter of 40cm. The rate of flow of water through the pipe is 250lit/sec.
8.a) The rate of flow of water in a 150mm diameter pipe is measured with a
venturimeter with a 50mm dia. throat. When a mercury manometer is connected
across the converging section reads 8mm, the flow rate is 2.7 kg/s. What is the
coefficient of discharge at that flow rate and what is permanent loss of head?
Specific gravity of mercury = 13.6
b) What is the device used for measuring fluid pressure? Explain briefly the principle of an
inclined Manometer.
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Code No: 220301 Set No.
3.a) Define the terms (i) Vortex flow (ii) Forced vertex flow (iii) Free vortex flow.
Give suitable examples.
b) A rectangular duct of width 25 cm has a two dimensional irrotational flow. It has
an elbow made up of circular arcs of radius 40 cm and 65 cm for the inner and
outer walls respectively. Calculate the discharge per unit width of the duct when
the difference in pressure between outer and inner walls in the elbow is 30 kPa
4.a) State stokes law. Prove that the drag coefficient for sphere for Reynolds number
up to 0.2 is given by CD = 24/R
b) A spherical sand particle of 0.1-mm diameter falls under the action of gravity in
water. Determine its terminal fall velocity.
c) Determine the bending moment at the base of a 40 m high chimney of cylindrical
shape of diameter 2.5 m in a wind of uniform velocity 25 m / s. Take CD = 0.35
and pair = 1.25 kg / m3.
Contd..2
Code No:220301 -2- Set No.4
6.a) Sketch the velocity distribution of laminar flow in ideal and real fluid flow and
explain it in detail.
b) A fluid of viscosity 0.883 pascal-sec and specific gravity 1.26 is pumped along a
horizontal pipe 65 m long and 10 cm diameter at a flow rate of 0.18 m 3/sec.
Determine the Reynolds Number and calculate the pressure loss in the pipe of the
flow is laminar.
7.a) What is siphon? On what principle it works? Under what conditions would it stop
functioning?
b) A horizontal pipe of diameter 50cm is suddenly contracted to a diameter of 25cm.
The pressure intensities in the large and smaller pipe are given as 13.734N/cm 2
and 11.772 N/cm2 respectively. If the rate of flow of water is 300lit/sec, find the
value of coefficient of contraction.
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