Closed Conduit Flow Expt
Closed Conduit Flow Expt
Closed Conduit Flow Expt
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We would like to thank all who helped and encouraged us to complete this
laboratory manual; especially, our fluid mechanics professor, Prof. Cornelio Dizon
for guiding us throughout our research work.
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Alvin Seria
Imee Bren Villalba
Jannebelle Dellosa
Jaime Angelo Victor
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Introduction ..
24
38
53
58
70
78
References .
86
Appendix A: .
87
92
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There are two main classes of flow in fluid mechanics. The flow of fluids around bodies such as airfoils,
rockets, and marine vessels is called external flow. This becomes the case when the other boundaries
of the flow are comparatively distant from the body. One general type of this flow is open channel
flow, also called free surface flow, wherein the fluid stream has a free surface exposed to atmospheric
pressure, and gravity is the only component acting along the channel slope. This type of flow is
encountered in natural bodies of water such as rivers, streams, and oceans, as well as in man-made
hydraulic structures such as floodways, dams, and canals. On the other hand, flows that are enclosed
by boundaries are termed internal flows. Examples of this type of flow include the flow through pipes,
ducts, and nozzles.
This research paper focuses primarily on the latter class of flow, that is, the flow of fluids in closed
conduits such as pipes. Different topics under this type of flow were discussed in detail. These topics
include laminar and turbulent flow, circular and non-circular conduits, smooth and rough pipes, major
and minor losses in pipes, single-pipe flow problems, series and parallel pipes, and branching pipes.
Moreover, much attention is given to the detailed discussion of the different experimental apparatuses
used in the study of flow in pressure conduits. Such apparatuses include the oil pipe ass embly, air pipe
assembly, water pipe assembly, water tunnel, and hydraulic bench. Finally, different experiments that
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Pipes are the most common tools used in the analysis of closed conduit flow. Usually, pipes used in
engineering practice are long hollow cylinders; however, cross sections of a different geometry are
used occasionally. Pipes can be smooth or rough, depending on the type of material from which they
were constructed. There are commercially available pipes made of cast iron, galvanized iron,
commercial steel, brass, lead, copper, glass, smooth plastic, and concrete, to name a few.
Moreover, the pipe system will not be complete without pipe fittings. Pipe fittings or connections are
used to join different pipes, such as, bends, junctions, tees, etc. They are also used to control or alter
the flow of the fluid through the pipe, this includes valves, gradual contraction and expansion, sudden
contraction and expansion, bell-mouthed entrance and more others.
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Figure 2.
Reynolds Experiment
With the outlet valve only slightly opened, that is, when the velocity of the liquid in the tube is small,
he observed that the colored liquid moved in a straight line as illustrated in Figure 2a. As the valve was
progressively opened, the velocity of the liquid in the tube gradually increased, and a fluctuating
motion of the colored fluid was observed as it moved through the length of the tube (Figure 2b).
Finally, when the valve was further opened, it was observed that the colored liquid is already
completely dispersed at a short distance from the entrance of the tube such that no streamlines could
be distinguished (Figure 2c).
The type of flow illustrated in Figure 2a is known as laminar flow, also called streamline flow.
Reynolds described it as a well-ordered pattern whereby fluid layers are assumed to slide over one
another.. Figure 2b shows a transition flow from the previous laminar flow to an unstable type of flow.
Finally, Figure 2c demonstrates a completely irregular flow called turbulent flow.
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Energy Losses
Fluid in motion offers frictional resistance to flow; wherein some part of the energy of the system is
converted into thermal energy (heat). In fluid mechanics this converted energy is referred as energy
loss or head loss. This energy loss is due to fluid friction as well as to valves and fittings. The former
is more known as major losses; while, the latter as minor losses. The energy loss in long pipelines, with
length to diameter ratio exceeding 2000, is mainly due to major losses, while minor losses are
negligible. Otherwise, minor losses are dominant over minor losses in short pipelines.
Major Losses
These are the energy dissipated through the walls of the pipe in which the fluid is flowing. Moreover,
the magnitude of the energy loss is dependent on the properties of the fluid, the flow velocity, the pipe
size, and smoothness of the pipe wall, and the length of the pipe.
Minor Losses
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Elements that control the direction or flow rate of a fluid in a system typically set up local turbulence in
the fluid, causing energy to be dissipated as heat. Whenever, there is a restriction, a change in flow
velocity, or a change in the direction of flow, these energy losses occur. Moreover, in large systems the
magnitude of losses due to valves and fittings is usually small compared to frictional losses; hence, they
are referred as minor losses.
Objective:
1.)
2.)
3.)
4.)
To determine the range of Reynolds number for laminar, transition and turbulent flow.
To verify that the friction loss in laminar flow is equivalent to 64/Re.
To verify the Hagen-Poiseuille equation.
To determine the measurement uncertainties, and compare the results with benchmark data.
Introduction:
Energy losses in closed conduits are classified into major and minor losses. Major losses result from the
resistance of the conduit walls to the flow and minor losses are due to pipe appurtenances that cause a
change in the magnitude and/or direction of the flow velocity. The determination of these losses is
important for the specification of a pipeline design.
Head losses mainly results from internal pipe friction when the ratio of the length of a pipeline to its
diameter exceeds 2000 and minor pipe appurtenances are not present in a pipe. In this experiment,
major losses are calculated and minor losses are assumed negligible.
Theoretical background:
The head loss for a pipe system is determined by the energy equation between two sections of the
pipe given by
P1/ + Z1 + V12/2g = P2/ + Z2 + V22/2g + HL
(1)
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Where P is the pressure at the centreline of the pipe, is the specific weight of the fluid, Z is the
elevation of the centreline of the pipe relative to an arbitrary datum, V is the average flow velocity, g is
the gravitational constant and H L is the total energy loss between section 1 and 2. When minor losses
are negligible, HL is mainly due to frictional losses only.
The velocity is determined when the discharge is known, using the equation
Q = AV
(2)
Where Q is the discharge, A is the area of the pipe, and V is the velocity in the pipe.
If the pressures at section 1 and 2 are known, the energy equation can be used to determine the head
loss along the pipe.
The pipe head loss due to friction is obtained using the Darcy-Weisbach equation:
f = HL LV2 / 2Dg
(3)
Where f is the friction factor, L is the length of the pipe section, and D is the pipe diameter.
The Moody diagram shows the relationship between the friction factor, relative roughness of the pipe
and Reynolds Number. There are three zones of flow in the diagram, namely, laminar, transition and
turbulent.
Type of flow
Laminar
Transition
Turbulent
Reynolds Number
Re<2000
2000<Re<10^5
Re>10^5
Friction Factor
f=64/Re
f=0.316/Re^0.25
1/ =2.0log(Re ) 0.8
The Reynolds Number is a dimensionless quantity used in the determination of the type flow. It is given
as,
Re=VD/
(4)
Where is the kinematic viscosity of the fluid.
The Hagen-Poiseuille equation is used to describe slow viscous incompressible flow through a constant
circular section. This equation can be derived from the Navier-Stokes equation given as,
(5)
Where P is the pressure drop and is the dynamic viscosity of the fluid.
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P = 128LQ/D4
The energy grade line is a plot of the total head versus the length of the pipe. The total head is the sum
of the pressure head, velocity head and elevation head at a particular point. The plot of piezometric
head versus the length of the pipe is called the hydraulic grade line. The piezometric head is the sum of
the elevation head and pressure head at a particular point.
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The experiment is conducted in an oil pipe assembly. The oil is pumped from the reservoir by the
centrifugal pump. The gate valve controls the discharge from the upstream end of the section.
Pressure taps are provided throughout the length of the pipe and connected to a manometer bank for
head loss measurement. The pipe characteristics are provided below. The jet trajectory of the oil is
observed at the transparent housing at the end of the pipe. At the downstream end of the system, the
oil is collected in the weighing tank and the discharge is measured. The oil is then returned back into
the reservoir.
PARTS OF THE OIL PIPE ASSEMBLY
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head loss.
characteristics
of
the
jet
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13
pipe.
reservoir,
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The weighing tank (Figure 9) is used to measure the discharge by noting the
time it takes to collect a certain amount of oil as it leaves the test section into
the weighing tank at the downstream end. Oil which has accumulated in the
weighing tank may be returned to the reservoir by means of the overflow
conduit or by a quick-acting gate valve (Figure 10). This valve is linked to
another quick acting valve in the supply line that would interrupt the flow into
the test section while the weighing tank is being emptied.
Figure 10. Quick Acting gate valve
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Piezometer taps are provided for measuring the head loss either by an oil manometer or a mercury
manometer depending on the magnitude of the pressures. The location of these taps is provided in
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Figure 12.
Procedure:
1. Determine the pipe diameter, dimensions of the pipe assembly, distance between taps and the
type of fluid to be used.
2. Determine the density of the fluid by using a beam balance and graduated cylinder. The density is
calculated using the following equation.
(6)
3. Turn on the pump and check that the flow is following the correct path.
4. For each trial, set the flow rate to the desired flow of either laminar, transition, and
type of flow is determined by observations of the jet trajectory.
(a)Laminar
(b)Transition
turbulent. The
(c)Turbulent
Figure 13. Jet trajectory for a) laminar, b) transition, and c) turbulent flow
5. Once the flow has stabilized, determine the discharge by getting the change in weight in the
weighing scale over the time interval. Record the head loss across pipe length using the
piezometer readings and the corresponding discharge. Record two readings of the piezometer for
every discharge and get the average.
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5. The discharge, velocity and Reynolds Number are calculated using the following equations.
Q=
(7)
Velocity =
(8)
(9)
EXPERIMENTS
Laminar and Turbulent Flow
Results:
1. Calculate the Reynolds number and then the friction factor. What type of flow is occurring within the
pipe?
2. Using the results from (1) and the Darcy-Weisbach equation, compute the theoretical head loss for
each flow rate. Quantitatively compare the theoretical values to your measured head loss data
obtained using the differential manometer. Discuss your results.
3. Draw the energy and hydraulic grade lines for the different discharges. Qualitatively indicate
elevation and pressure heads, but numerically identify the velocity head component of total energy
and the head loss over the length of pipe.
4. Compute the discharge using the Hagen-Poiseuille equation and compare with the actual discharge.
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5. Verify that for a laminar flow, the friction loss is equivalent to 64/Re.
LAMINAR
10
reading 1
reading 2
Average
reading 1
reading 2
Average
TRANSITION
reading 1
reading 2
Average
reading 1
reading 2
Average
TURBULENT
reading 1
reading 2
Average
reading 1
Average
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reading 2
Weight
(lbs)
Reading 1
1
Reading 2
Average
Reading 1
Reading 2
Average
Reading 1
Reading 2
Average
Reading 1
Reading 2
Average
Reading 1
Reading 2
Average
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Reading 1
Reading 2
Average
26.8
0.001524
e/d
(mm2/s)
(kg/mm-s)
5.69E-05
16.5
1.42E-05
564.1
Trial 2
Average
115
179.5
170.9
75
64.5
0.00086
860
8.6E-07
65
55.9
0.00086
860
8.6E-07
0.00086
860
8.6E-07
Reading 1
Reading 2
Average
2
580
600
590
3
555
555
555
4
430
420
425
5
340
340
340
6
225
225
225
7
-
8
90
80
85
9
-
10
-
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LAMINAR
1
680
670
675
Weight
(lbs)
reading 1
reading 2
average
Weight Volume
(kg)
(mm3)
220
224
4
1.814
2109302
Time
(s)
Discharge Velocity
Re
3
(mm /s) (mm/s) DV/
8
7.5
7.75
272168
482
784
D4 /128 =
879027684.3 kg5 /mms
p/L
p/L
0.1405
0.001184
Q from
HP
equation
(mm3/s)
572488
Qexpt
(mm3/s)
Deviation
(%)
272168
52%
Extension Experiment
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Experiments on velocity distribution for laminar flow maybe conducted on the oil pipe assembly where
a stagnation tube is provided in the transparent test section. The experimental programs should
consider of such parameters as the location where the velocity is measured and the Reynolds number.
The position of the stagnation tube may be may moved vertically along the diameter of the pipe and its
location is measured by the vernier attached. Stagnation pressure may be measured by an oil
manometer or by a mercury manometer depending on the magnitude of the pressure. The static
pressure may be determined from the values of the pressures upstream of the stagnation tube. The
velocity and Reynolds number may be varied by changing the discharge.
For laminar flow, the velocity distribution may be determined using the equations of motions on a
free-body diagram of a fluid element where the shearing stresses are formulated in accordance with
Newtons Law of Viscosity. The result is a parabolic distribution, which for a horizontal pipe is as
follows,
u= (ro2-r2/4)(dp/dx)
(10)
Where u is the velocity at a distance r from the centerline, ro is the radius of the pipe, is
the dynamic viscosity, and dp/dx is the rate of pressure drop.
In terms of maximum velocity (umax) at which r=ro, the velocity distribution may be written as follows:
u = umax (r2/4)(dp/dx)
(11)
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Analysis of the experimental values may be correlated with the analytical values. One way of plotting
the experimental results is shown below.
Objective
1. To develop velocity distribution, to calculate head losses (frictional losses), and to prove the validity
of Reynolds Number in smooth and rough pipes using the air pipe assembly.
2.To compute actual friction factors and to compare these values from the theoretical values found in
the moody diagram.
3. To verify the Nikuradse equation.
4. To aim to plot the energy and hydraulic grade lines along the length of the pipe.
Introduction
Pipes are closed conduits used to convey fluids. Usually, pipes used in engineering practice are long
hollow cylinders; however, cross sections of a different geometry are used occasionally. Pipes can be
smooth or rough, depending on the type of material from which they were constructed. Commercially
available pipes are made of cast iron, galvanized iron, commercial steel, brass, lead, copper, glass,
smooth plastic, and concrete, to name a few.
For a simple pipe without a pump or turbine, the increase in the total mechanical energy of the fluid,
between any two selected sections of the pipe, is equal to the energy dissipated in head loss. The head
loss, in this case, can be subdivided into two categories: major losses and minor losses. Major losses
are those caused by pipe or wall friction; while minor losses include those losses due to changes in pipe
cross section, and the presence of pipe fittings, bends and elbows along the pipe length.
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If the pipe is of constant cross section throughout its length, and if there are no pipe fittings, bends, or
elbows, then the friction losses become the total head loss in the pipe. From several experiments, it
was proven that the friction inside the pipe does not only depend on the shape and size of the
projections on the internal pipe wall, but also on their distribution. The friction loss can be determined
using the formula
Theoretical background
If the head loss in the pipe is mainly due to friction, another expression for the head loss will be
hL = f (L/D) (V2 / 2g)
Equation (1) is called the Darcy Weisbach Equation, and is derived using dimensional analysis.
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where, f
(1)
(2)
The head loss hL can be calculated using (P/); the fluid velocity V, using the continuity equation ; and
the pipe diameter D and the pipe length L are readily available.
To determine the theoretical value of the friction factor, the equation derived by Haaland can be used,
that is,
1/sqrt (f) = -1.8 log {[(/D) / 3.7]1.11 + 6.9 / Re}
(3)
Equation (4) is valid for turbulent flow in all pipes, and is applicable for fluids having a Reynolds
number greater than or equal to 4000 but less than or equal to 108.
Other equations that can be used to calculate the friction factor of pipes are as follows:
For smooth pipes
1/sqrt (f) = 0.869 ln [Re sqrt (f)] 0.80
(4)
(5)
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Equations 4 and 5 are Nikuradse equations for smooth and rough pipes, respectively.
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Absolute Roughness,
x 10-6 feet
micron
(unless noted)
drawn brass
5
1.5
drawn copper
5
1.5
commercial steel
150
45
wrought iron
150
45
asphalted cast iron
400
120
galvanized iron
500
150
cast iron
850
260
wood stave
600 to 3000
0.2 to 0.9 mm
concrete
1000 to 10,000 0.3 to 3 mm
riveted steel
3000 to 30,000 0.9 to 9 mm
*Page 476, Fundament als of Fluid Mechanics 4th Edition - Munson - John Wiley and Sons
Relative pipe roughness is computed by dividing the absolute roughness e by the pipe diameter D,
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It can be inferred from the Moody chart that for laminar flow, f=64/R e . For moderate values of
Reynolds number (2,100 < Re < 4000), the flow may be considered as laminar or turbulent, based on
the actual situations. The friction factor in this case is a function of the relative roughness and Reynolds
number, that is, f= (R e , /D). However, for large enough Re, the friction factor is solely dependent on
the relative roughness. Thus, f= (/D). Such flows are called completely turbulent or wholly turbulent
flow. For pipes which are very smooth (=0), due to microscopic surface roughness, there is still head
loss in the pipe. Hence, the friction factor in a very smooth pipe is not zero.
Apparatus
An Air Pipe assembly is an instructional apparatus with a system of smooth and rough pipes with
pressure taps along its length to facilitate pressure drop measurement.
Brass Pipe
Piezometer
Taps
Valves
Manometer
Bank
Venturi Meters
In an experiment that will use an Air Pipe facility, there will be three different test pipes that can be
investigated, where all pipes are approximately 8.94m in length. This portion of the equipment consists
of a 125mm and a 500mm diameter Galvanized Iron (GI) pipe, and a 500mm diameter brass pipe.
The relative roughness for the brass pipe and galvanized iron are 0.0015mm and 0.15mm, respectively.
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In this set-up, pressure built in a large reservoir forces air to flow through a chosen straight
experimental pipe. The blast gate set between the compressor and the tank regulates the discharge
through the system. Discharge through the experimental pipes is measured by the Venturi meters
installed between the fluid source and the pipes. There are six gate valves that may be used to direct
fluid flow. The three upper valves manage flow through the experimental pipes, the other three valves
on the lower portion of the apparatus is used to select which Venturi meter will be appropriate to use.
Figure 3. (a) the Control Valves for the system, (b) the Venturi Meter,
(c) the reservoir, control knob, and blower
A number of piezometer taps are installed in the pipes to allow head measurement, specifically,
pressure drops along the pipe length. These taps are connected to a manometer bank where readings
are obtained. The first 12 manometers (Numbered 1-12) are for readings for the brass pipe, the
following 12 (Numbered 13-24) are for the galvanized iron pipe. Venturi readings are taken from
manometers numbered as 26-31.
(a)
brass pipe
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(b)
GI pipe
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In a typical experiment, different discharges per trial will be considered. It must be assumed that
discharge is constant throughout the system.
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Theoretical Data:
1. Compute Reynolds Number for the pipe flow
2. Given the relative roughness of the brass and galvanized iron pipe, obtain the theoretical friction
factors of the pipes using the Moody diagram.
3. Compare these theoretical values with the actual friction factor values.
4. For flow with Reynolds number greater than or equal to 4000 but less than or equal to 10 8, check
whether or not the Haaland Equation is verified.
5. Alternatively, check whether or not the Nikuradse Equations for smooth and rough pipes are
verified.
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6. Plot the Energy and Hydraulic Grade lines for each pipe.
Venturi Readings
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Trial 1
Trial 2
Trial 3
Trial 4
Trial 5
Trial 6
Trial 7
Trial 8
Trial 10
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Trial 9
Trial
Valve
Opening
1/16
Pipe
Brass
GI
Brass
Pipe
GI
Pipe
1
19
358
378
391
407
423
438
352
372
386
389
405
427
7
25
Venturi Meter
Readings
Inlet Throat
198
362
Discharge (cms)
0.025622725
Taps
Length(m)
2-3
3-4
4-5
5-6
2-6
2.058
1.982
1.982
1.982
8.003
Headloss
(m)
10.759
13.241
13.241
12.414
49.655
Velocity
(m/s)
13.057
13.057
13.057
13.057
13.057
Frictio
n
0.030
0.038
0.038
0.036
0.036
Reynolds
number
43524.692
43524.692
43524.692
43524.692
43524.692
1/SQRT(F)
5.766
5.100
5.100
5.267
5.293
0.869ln(R*sqrt(f))
-0.80
6.959
7.066
7.066
7.038
7.034
%difference
17.15
27.82
27.82
25.16
24.76
Questions
1. Explain why the valve controlling the pipe where readings are obtained should be fully opened while
the valve of the other pipe should be fully closed.
2. Enumerate the possible sources of errors in the experiment
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Extension experiments
Using set-ups such as like the one described above tends to be error-prone at times. A common source
of error may be described as a situation wherein pipes increase their actual friction factors due to
imperfections inside the pipe such as dirt and other particulates. Aged pipes typically exhibit rise in
apparent roughness. Leakage in the manometer bank also greatly affects the readings.
Modern Air Pipe Facilities have now refrained from taking measurements manually. Instead, they use
the Automated Data Acquisition System (ADAS).
Source: http://www.engineering.uiowa.edu/~fluids/Lab-documents/EFD/EFD%20Lab2/lab2.pdf
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Low
Pressure
LabView
Program
Capacitanceto-Voltage
Conversion
Capacitor,
C
To Pressure
Transducer
Display
E
Data
Store
Analog to
Digital (A/D)
Board
Flexible Metal
Diaphragm
High
(Deflects Under
Pressure
Pressure
6
Difference)
7
8
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Objectives:
1. To comprehend the principle behind the energy equation
2. To recognize the sources of minor losses
3. To be able to determine head losses and also to establish the friction coefficients of the
corresponding and the pipe fittings
Introduction:
The first law of thermodynamics, the law of conservation of energy states that energy is neither
created nor destroyed, it can only transform from one guise to the other. Universal as it is, the
hydraulic system is of no exemption. Wherein given a hydraulic system, the total energy at one section
is equal to the total energy at some other section within the system. In other words, the sum of the
energies in the system is a constant. More often, it seems that energy is reduced or lost after
undergoing a process; on the other hand, the apparent lost energy is actually converted into heat and
released to the environment. This energy conversion is mainly caused by friction.
Application:
Understanding this principle is useful in constructing optimum water system designs. Some of which
are as follow,
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It enables accurate selection of appropriate size and required number of pumps to be used in a
municipal water distribution system.
It can serve as a guide in selecting conduit sizes for a gravity-flow urban drainage project.
It can help identify the optimum size of valves and the radius of curvature of elbows to fit the
specifications of a pipeline designs.
Theoretical Background:
In hydrodynamics, fluids are assumed to be subjected to certain laws of physics; wherein one of which
is the law of conservation of energy. This was first recognized by Daniel Bernoulli (Switzerland, 17001782), and formed the basis for the Bernoullis equation
.
Bernoullis equation:
p 2A2
p 1 v 12
p 2 v 22
z1
z2 H
2g
2g
1g
2g
( 1)
L
Where,
P Pressure
Fluid density
g Acceleration due to gravity
9.81 m/s 2 (S.I.)
32.2 ft/s2 (English system)
v Average velocity
H Total hydraulic energy
z2
p 1A1
z1
Da tum
Moreover, all the constituent parts of the equation have units of length; hence, each term may be
regarded as head. Specifically,
p
Pressure head
g
v2
Kinetic or velocity head
2g
Z
Potential or elevation head
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The Bernoullis equation assumes that the fluid flowing is incompressible and no energy is supplied nor
extracted during the passage from entry to exit. Hence,
energy entering = energy leaving
Moreover, it also implies that the fluid is frictionless. If this were not so, frictional forces would
transform some of the energy into heat. Thus, there would be loss between 1 and 2 (refer to
Illustration 1). To account for this energy loss, the Bernoulli equation is transformed into the energy
equation,
v 12
z1
2g
p1
1g
p2
2g
v 22
z 2 hL
2g
(2)
hl k L
v2
2g
(3)
Where, hl is the minor head loss and kL is the constant dimensionless head loss coefficient of pipe
fittings. The actual value of kL is strongly dependent on the geometry of the fixtures being considered.
As for cases of sudden enlargement or sudden contraction, kL may be derived from the expression of
the area of the pipe. While, for all other cases, such as bends, valves, and junctions, the values of kL are
derived experimentally.
hl
8k L
Q2
2 4
g D
(4)
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Another way to express the minor loss equation in terms of the discharge,
Where, Q is the discharge and D is the diameter of the pipe. Moreover, minor losses can also be
converted into equivalent lengths of pipe having the same effect.
k LD
L equivalent
f
(5)
Where, f is the friction factor determined for the pipe flow.
Apparatus:
Water Pipe Assembly
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42
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43
Pipe Line #1
B Gradual enlargement
C Gradual contraction
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D 5 x 4 Venturi meter
Pipe Line #2
L Standard 90 elbow
I Sudden enlargement
M Standard tee
J Sudden contraction
N 2 Globe valve
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Standard tee
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46
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47
pA
1 1
2 2
( h1 h2 )
pB
(6)
pA
pB
h2 (
(7)
Where, pA and pB are the pressures at point A and point B, respectively; while, 1 and 2 are the specific
weights of the flowing fluid and the gage fluid. In this experiment, the flowing fluid is water and its
specific weight is 9810 N/m3. Also, the gage fluid is carbon tetrachloride and its specific weight at room
temperature (25C) is 15542.87 N/m3. Moreover, h2 is the difference between the manometer reading
of point A and B and it is denoted by h. Hence,
pA
p
pB
h( 5732 .87 )
h( 5732.87 )
(8)
(9)
Moreover, when the pipe lies on the same elevation, z 1 = z2; hence, the elevation head of the
Bernoullis equation cancels out.
p1
g
v12
2g
v22
2g
p2
g
hL
(10)
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48
hL
p1
p2
v12
v12
v 22
2g
g
h
v 22
2g
(11)
Using the continuity equation, the mean velocity can be derived by using the equation, V=Q/A or
V=4Q/ D4, where D is the diameter of the pipe. Also, if the diameter of the pipe is constant, the
velocity head is equal to zero.
(12)
Furthermore, the water pipe assembly also has two identical 60 triangular weir to measure the
discharge. Also a calibrated point gauge (stilling well) is attached to each tank to measure water
elevations in the tank.
The crest elevation is measured by allowing the tank to drain to the level of the crest (vertex). Also, by
subtracting the crest elevation from that of the water surface gives the depth of the flow H in feet. The
equation for the discharge is expressed as,
5
1.434 H 2 (cfs)
(13)
Page
49
Qout
Qleft
Hence,
Qright
(14)
Procedure:
1. Open the main valve and the head tank valve
2. Let the water flow until it overflows the tanks containing the weir
3. Close the main valve, and let the water drain from the weir
4. Using the calibrated point gauge, measure and record the bottom of the stilling well and also
the height of the water contained for each of the weirs
5. Open the main valve
6. Once the water is flowing, fully open the valves in pipeline #1
7. Wait for the flow to be stable, then measure and record the height of the water surface flowing
from each weir
8. Record the readings on the manometer board (47 even numbers).
9. Close all the valves of pipeline #1
10. Fully open all the valves in pipeline #2
11. Repeat step 7
12. Repeat step 8 (47 odd numbers)
13. Adjust the appropriate valves to select and change discharge
14. Repeat step 6 to 12
Page
50
Right Weir
Left weir
Right weir
Pipeline #1
Height of the water (ft)
H (ft)
Discharge (cfs)
Sum of the discharges (cfs)
Taps#
Manometer
Reading (in)
Head Drops
Pressure
Head (in)
Velocity
Head (in)
Elevation
Head (in)
Head
Loss
(in)
v2
2g
kL
47
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
Page
51
34
36
38
40
42
44
46
Right weir
Manometer
Reading (in)
Head Drops
Pressure
Head (in)
Velocity
Head (in)
Elevation
Head (in)
Head
Loss
(in)
v2
2g
kL
Page
52
47
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
Page
53
The hydraulic bench (see Figure 1) is a simple apparatus designed to provide a clear demonstration of
some of the more common fluid flow phenomena. With this device, a number of experiments on
closed conduit flow can be conducted. These include determining the head losses in pipe transitions,
establishing the pressure distribution along the pipe, calculating the changes in the fluid pressure due
to varying pipe cross section, calibrating flow meters, and a lot more.
Figure 1.
The Hydraulic Bench
Page
54
Page
55
Page
56
Figure 11.
Another unit is shown in Figure 12, consisting of a constant head tank and a circular opening on the
lateral area of the tank. This is used in the analysis of the behavior of free jets. Moreover, it can also be
used to calibrate orifices. With the Bernoulli equation, the theoretical velocity of a fluid particle can be
calculated. Applying the principles of projectile motion, the actual velocity of the liquid can be
obtained. With these two values, a coefficient of velocity for a certain orifice can be determined. The
theoretical discharge can also be calculated by multiplying the theoretical velocity with the area of the
orifice. With the actual
discharge
measured
using the volumetric
tank, the coefficient of
discharge can also be
calculated.
Page
57
Figure 12.
Figure 13.
Introduction:
Flow meters are devices used for measuring fluid flow rate, whether it is in closed conduits or in open
channels. There are two basic types of flow meters: those that measure quantity, and those that
measure rate. Measurements of quantity are obtained by counting successive isolated portions of flow.
On the other hand, measurements of rate are determined f rom the observed effects on a measured
physical property of the flow.
Rate meters are devices used to measure the fluid flow rate as either volume per unit time or as mass
per unit time. One type of rate meter, placed directly in the flow line of closed conduits, introduces a
flow constriction that causes a decrease in pressure that is dependent on the rate of flow on the
constriction. This device is first known as the venturi tube, named after Giovanni B. Venturi, an Italian
Physicist who investigated its principles during the early 18th century.
Page
58
The venturi tube consists of an upstream section attached to the pipeline, and a converging section
that leads to a restriction or a smaller diameter pipe. This convergent zone is efficient in converting
pressure head to velocity head. Then, a divergent section is connected downstream to the pipeline,
converting the velocity head back to pressure head with slight friction loss. Piezometer tubes or static
pressure taps are attached at the upstream section and at the throat of the venturi tube. These are
then attached to the two sides of a differential manometer to easily measure the pressure difference
between the two points. Since there is a definite relation between the pressure drop and the discharge
of the fluid, the tube may be made to serve as a metering device called the venturi meter.
Figure 14.
The venturi meter
Considering the fluid to be incompressible, the continuity equation applied to the control volume gives
(1)
From Figure 14, A1 is larger than A2; thus, equation (1) implies that V 1 should be less than V2.
Page
59
Q = A1V1 = A2V2
(2)
Theoretically, the pressure in a fluid decreases with increasing velocity. As a result, there must be a
pressure drop existing in the venturi meter from point 1 to point 2. Rearranging equation (2) in such a
way that velocities are separated from the other quantities, we get
(3a)
Using equation (1), equation (3a) can be modified to
3b)
A2 / A1 = D24 / D14
(4)
Page
60
Solving for the volumetric flow rate Q in terms of the other variables, and noting that
Equation (5) is the theoretical equation for the discharge through the venturi meter for frictionless
incompressible flow.
The manometer reading provides the pressure drop ( P 1 P2 )/ required in equation (5). From the
differential manometer in figure N, we see that the fluids at points 1 and 2 are the same; thus, they
have the same density. From hydrostatics, proceeding from point 1 through the manometer tubing to
point 2 gives
P1 1h1 2H + 1h2 = P2
(6)
Where
P1 and P2 =
pressures at points 1 and 2, respectively
1 =
unit weight of the fluid in the venturi meter
2 =
unit weight of the fluid in the differential manometer
(7)
Since points 1 and 2 are of the same elevation, z1 z2 = 0. Substituting equation (7) to equation (5), the
final expression for the theoretical discharge will be obtained as
Page
61
(8)
The curve of the theoretical discharge Q versus the pressure drop H can be plotted using equation (8).
Using an apparatus such as the hydraulic bench, the actual discharge can be determined, and the Qactual
versus H can be plotted on the same graph. For any pressure drop H, there correspond two values for
the flow rate. The ratio of these values is called the venturi coefficient of discharge C v.
(9)
The actual discharge is different from the theoretical discharge because the effects of friction are not
accounted for in the Bernoulli equation from which the entire derivation of Theoretical was based. For
every C v obtained, there corresponds an upstream Reynolds number which can be calculated using the
formula
Re = 4 Qactual / D
(10)
Where
Page
62
With the obtained values, a plot of the discharge coefficient C v versus Reynolds number Re can now be
constructed semi-logarithmic coordinate plane.
Figure 17.
The Experimental Set-up
(Front view)
Figure 18.
The Experimental Set-up
(Left side view)
Page
63
Water from the reservoir below enters the tank through a plastic tube inserted on its base section
(refer to Figure 18). Before the actual flow measurements were done, the water level in the tank was
first allowed to stabilize.
Figure 19.
Piezometer tube
Page
64
Figure 21.
Piezometer taps
Page
65
Figure 22.
Dimensions
Page
66
9. Plot the Q versus H curve for the venturi meter. Obtain two curves, one for the theoretical
discharge and another for the actual discharge, in just one graphing plane (see Figure 15).
10. Calculate the Reynolds number for every coefficient of discharge using equation (10). Plot the
coefficient of discharge versus Reynolds number curve.
Trial
Theoretical
Actual
h1
h2
hinitial
hfinal
[cm]
[cm]
[cm]
[cm]
[s]
1
2
3
4
5
6
7
8
9
10
Trial
Theoretical
H
[m]
D2 / D1
Actual
Cv
A2
[m2 ]
[m3 /s]
[m]
[m3 /s]
Re
1
2
3
4
5
6
Page
67
7
8
9
10
2. What would happen to the coefficient of discharge if the venturi meter is positively inclined?
negatively inclined? vertical?
3. What are the factors that may reduce the coefficient of discharge of a venturi meter? Is the
coefficient of discharge dependent on the geometry of the venturi tube?
6. What can you conclude from the coefficient of discharge versus Reynolds number curve?
Page
68
5. In some cases, precise calibration of the venturi tube gives a value for the coefficient of
discharge greater than 1. What could be the reason for such abnormal result?
Page
69
4. The venturi tube gives a relationship between the pressure drop and the flow rate of the fluid
using a convergent and a divergent tube. If a new flow meter is constructed such that the
diverging tube comes first before the converging tube, would this be an acceptable flow meter?
Repeat the experiment using this new apparatus.
Use different fluids.
Page
70
The Bernoulli equation can be applied to the flow nozzle as was done for the venturi meter in the
previous experiment.. The results are identical for the theoretical flow rate.
(1)
A2
D1
D2
H
1
2
=
=
=
=
=
=
Equation (1) gives the theoretical flow rate through the flow nozzle.
In this case, the elevation differences are considered negligible because the flow nozzle is relatively
short. Moreover, the distance between the two static pressure taps (see Figure 1) is also small. In
practice, it is desirable an upstream approach length equivalent to about ten pipe diameters to ensure
uniform flow at the meter.
Page
71
Figure 1.
The Flow Nozzle
Again, the actual flow rate through the meter is less compared to the theoretical flow rate. This is due
to the friction losses that were not accounted for in the Berrnoulli equation, where the derivation of
equation 1 was based. Thus, we introduce a discharge coefficient for the nozzle defined as
C n = Q actual / Q theoretical
(2)
For every value of the coefficient of discharge, there correponds one pressure drop and an upstream
Reynolds number.
Re = 4 Qactual / D
(3)
Where,
= kinematic viscosity of the fluid in the flow nozzle
D = diameter of the pipe
Page
72
Using equation (3), the plot of the discharge coefficient versus Reynolds number can now be obtained.
At a high Reynolds number, the discharge coefficient is above 0.99. On the other hand, lower Reynolds
number gives a lower value for the coefficient of discharge. This is thecase because at relati vely low
Reynolds number, the sudden expansion outside the nozzle throat causes greater energy loss; thus, a
lower value for C n.
Figure 2.
The Experimental Set-up
Page
73
Figure 2.
The Experimental Set-up
Page
74
9. Plot the Q versus H curve for the venturi meter. Obtain two curves, one fo r the theoretical
discharge and another for the actual discharge, in just one graphing plane.
10. Calculate the Reynolds number for every coefficient of discharge using equation (3). Plot the
coefficient of discharge versus Reynolds number curve.
Trial
Theoretical
Actual
h1
h2
hinitial
hfinal
[cm]
[cm]
[cm]
[cm]
[s]
1
2
3
4
5
6
7
8
9
10
Trial
Theoretical
H
[m]
D2 / D1
Actual
Cv
A2
[m2 ]
[m3 /s]
[m]
[m3 /s]
Re
1
2
3
4
5
6
Page
75
7
8
9
10
2. What would happen to the coefficient of discharge if the venturi meter is positively inclined?
negatively inclined? vertical?
3. What are the factors that may reduce the coefficient of discharge of a flow nozzle? Is the
coefficient of discharge dependent on the geometry of the device?
Page
76
5. What are the advantages and disadvantages of using flow nozzles over any other dischargemeasuring device?
6. What can you conclude from the coefficient of discharge versus Reynolds number curve?
Page
77
3. Repeat the experiment using a flow nozzle having a different i nlet and nozzle diameters. Use
water as the confined fluid.
What is the effect of varying inlet and nozzle dimensions on the coefficient of discharge?
Page
78
The Bernoulli equation can be applied to the orifice meter (Figure 1) as was done for the venturi meter
in the previous experiment.. From point 1 to point 2, the theoretical flow rate is found to be
(1)
A2
D1
D2
H
1
2
=
=
=
=
=
=
Equation (1) gives the theoretical flow rate through the orifice meter. The area of the vena contracta is
very difficult to measure in the laboratory. However, it can be expressed in terms of the orifice area.
The resulting area is given by
A2 = C cA1
Where
A1
Cc
=
=
(2)
Page
79
Figure 1.
The Orifice Meter
(3)
Tests on a series of orifice meters yield data that can be presented in the form of C 0 versus Re plot,
where Re is the Reynolds number given by
Re = 4 Qactual / D
Where
(4)
Apparatus:
Page
80
The hydraulic bench and the experimental unit 1 are the main apparatuses to be used in this
experiment. The venturi meter attached to the unit must be replaced with an orifice meter. Figure 2
shows the complete experimental set-up. Figure 3 shows the orifice meter to be used in this
experiment.
Figure 2.
The Experimental Set-up
Figure 3.
The Orifice Meter
The hole in the orifice meter can either be sharp-edged or square-edged, as shown in Figure 4.
Figure 4.
Orifice meters:
Square-edged
Sharp-edged
Orifice Coefficient ( C0 )
0.65
0.64
0.63
0.62
0.61
0.6
0.59
0.58
1
100
10000
1000000 10000000
0
Page
81
Reynolds Number ( Re )
Procedure:
1. Check all the apparatus and materials to be used in the experiment. Establish the arrangement
shown in Figure 2, with the orifice meter (see Figure 3) attached to the test section.
2. Only the pressure drop between the orifice and the vena contracta needs to be calculated.
Using a rubber tubing (or any possible type of closed conduit boundary), connect the
piezometer tubes for the orifice and the vena contracta in such a way to form a differential
manometer. Make sure that the piezometer tubes are properly connected.
3. Switch the hydraulic bench on, and then open the butterfly valve to allow the water to pass
through the entire experimental unit. Choose a small discharge first.
4. Wait for the flow to become steady. A steady flow is one in which all conditions at any point in
a stream remain constant with respect to time.
5. After the establishment of a steady flow, measure the difference in the piezometric heads, H, in
the differential manometer. Calculate the theoretical discharge through the orifice meter using
equation (1).
6. Measure the actual discharge using the volumetric tank. This can be done by measuring the
change in the volume of the water in side the tank per unit time
7. Calculate the coefficient of discharge using equation (3). Then, adjust the butterfly valve to
slightly increase the discharge.
Page
82
9. Plot the Q versus H curve for the orifice meter. Obtain two curves, one for the theoretical
discharge and another for the actual discharge, in just one graphing plane.
10. Calculate the Reynolds number for every coefficient of discharge using equation (3). Plot the
coefficient of discharge versus Reynolds number curve.
Worksheet:
Diameter of Hole, D1:
Trial
Theoretical
Actual
h1
h2
hinitial
hfinal
[cm]
[cm]
[cm]
[cm]
[s]
1
2
3
4
5
6
7
8
9
Page
83
10
Trial
Theoretical
H
[m]
D2 / D1
Actual
A2
2
[m ]
Cv
[m]
[m3 /s]
[m /s]
Re
1
2
3
4
5
6
7
8
9
10
Questions:
1. What would happen if piezometers were used (instead of the differential manometer) in
measuring the pressure drop between the orifice and the vena contracta?
3. What are the factors that may reduce the coefficient of discharge of an orifice meter? Is the
coefficient of discharge dependent on the geometry of the device?
Page
84
2. What would happen to the coefficient of discharge if the pipe with the orifice meter is
positively inclined? negatively inclined? vertical?
5. What are the advantages and disadvantages of using orifice meters over any other dischargemeasuring device?
6. What can you conclude from the coefficient of discharge versus Reynolds number curve?
Extension Experiment:
1. Repeat the experiment using a fluid of a different viscosity.
Is the coefficient of discharge dependent on the type of fluid used?
What can you conclude from the coefficient of discharge versus Reynolds number
curve?
2. Repeat the experiment using a fluid with suspended particles.
Is there a change in the coefficient of discharge?
Is the flow nozzle efficient for all types of fluids?
Page
85
3. Repeat the experiment using a flow nozzle having a different inlet and nozzle diameters.
Use water as the confined fluid.
What is the effect of varying inlet and nozzle dimensions on the coefficient of discharge?
Chadwick, Andrew. Hydraulics in Civil and Environmental Engineering. 3rd edition. London and New
York: E & FNSPON, an imprint of Routledge, 1998.
Daniel Bernoulli.Online. Available URL: http://en.wikipedia.org/wiki/Daniel_Bernoulli,
Daniel Bernoulli.Online. Available URL: http://www.rinnovamento.it/d/da/daniel_bernoulli.html
Finnemore, E.J., and J.B. Franzini. Fluid Mechanics with Engineering Applications. 10th edition. New
York: McGraw-Hill Companies, Inc., 2002.
Froude. Online. Available URL: http://etc.usf.edu/clipart/500/582/Froude_1.htm
James Anthony Froude. Online. Available URL: http://en.wikipedia.org/wiki/James_Anthony_Froude/
Janna, W.S.. Introduction to Fluid Mechanics. 2nd edition. Boston, Massachusetts: PWS Publishers,
Boston, Massac, 1987.
Mott, R.L.. Applied fluid Mechanics. 5th edition. New Jersey: Prentice-Hall, Inc., 2000.
Munson, Bruce Roy, Donald F. Young, and Theodore H. Okiishi. Fundamentals of Fluid Mechanics. 3rd
edition. Philippines: Jemma, Inc, 1940.
Osborne Reynolds.Online. Available URL: http://en.wikipedia.org/wiki/Osborne_Reynolds/
Shames, I.H.. Mechanics of Fluids. 4th edition. New York: McGraw-Hill Companies, Inc., 2003.
Page
86
Simon, Andrew L., and Scott F. Korom. Hydraulics. 4th edition. Upper Saddle River, New Jersey: Prentice
Hall, Inc., Simon & Schuster/A Viacom Company, 1997.
KE
1 2
mv
2
1
2
A 1Lv 12
Datum
Illustration 1. Control Volume
(2)
On the other hand, potential energy is the stored energy in the body. It is equal to mgz, where, m is the mass of
the object, g is the acceleration due to gravity, and z is the height of the object from some arbitrary datum. The
equation for the potential energy of the fluid entering the system is
1
A 1Lgz1
(3)
Page
87
PE mgz
p1 A 1L
1
2
A 1Lv 12
A 1Lgz1
(4)
For convenience, Equation 4 is expressed in energy per unit weight of the fluid; where, the weight of the fluid
entering the system is 1gA1L.
p 1 A 1L
1
2
A 1Lv 12
1
A 1Lgz1
gA1L
p1
1g
v 12
2g
z1
(5)
Similarly, the total energy at the exit per unit weight of fluid leaving the system is
p2
2g
v 22
2g
z2
(6)
If the fluid flowing is incompressible, 1 must be equal to 2 , or (1 = 2 = ). Moreover, if during the passage
from the entry to the exit, no energy is supplied nor extracted, the sum of the energies is constant.
Bernoullis equation:
v 12
z1
2g
p2
2g
v 22
z2
2g
H
(7)
Page
88
p1
1g
p
g
N m3 s2
m 2 kg m
ML L3 T 2
L2T 2 M L
v2
2g
L2 T 2
T2 L
m2 s 2
s2 m
z L
All the constituent parts of the equation have units of length; hence, each term may be regarded as head.
Specifically,
p
g
Pressure head
Page
89
v2
2g
60
Page
90
h H
dQ
VdA
h o
h o
h H
h H
dQ
h o
VA
2gh 2 tan
h o
(H h)dh
8
tan
2gH2
15
2
This equation computes for theoretical flowrate or discharge when using a triangular weir.
However, a weir coefficient is added to the equation above to account for the real world effects neglected in the
analysis. Hence, forming the equation,
Page
91
Q 1.434H
5
2
Daniel Bernoulli (1700-1782) was born on January 29th 1700. He came from
a long line of mathematicians. His father Johann was head of mathematics at
Groningen University in the Netherlands.
Page
92
Johann tried to map out Daniel's life, selected a wife for him and decided he should be a merchant. Strangely
enough, his own father had tried a similar strategy but Johann had resisted - so did Daniel. However, Daniel
spent considerable time with his father and learned much about the secrets of the Calculus which Johann had
exploited to gain his fame. By the time Daniel was 13, Johann was reconciled to the fact that his son would never
be a merchant but absolutely refused to allow him to take up mathematics as a profession as there was little or
no money in it. He decreed that Daniel would become a doctor. For the next few years Daniel studied medicine
but never gave up his mathematics.
In time it became apparent that Daniel's interest in Mathematics was no passing fancy, so his father relented
and tutored him. Among the many topics they talked about, one was to have a substantial influence on Daniel's
future discoveries. It was called the "Law of Vis Viva Conservation" which today we know as the "Law of
Conservation of Energy". The young Bernoulli found a kindred spirit in the English physician William Harvey who
wrote in his book On the Movement of Heat and Blood in Animals that the heart was like a pump which forced
blood to flow like a fluid through our arteries. Daniel was attracted to Harvey's work because it combined his
two loves of mathematics and fluids whilst earning the medical degree his father expected of him.
After completing his medical studies at the age of 21, he sought an academic position so that he could further
investigate the basic rules by which fluids move; something which had eluded his father and even the great Isaac
Newton. Daniel applied for two chairs at Basel in anatomy and botany. These posts were awarded by lot, and
unfortunately for Daniel, he lost out both times.
1 2
u
2
p constant
Where p is pressure, rho is the density of the fluid and u is its velocity. A consequence of this law is that if the
velocity increases then the pressure falls. This is exploited by the wing of an aeroplane which is designed to
create an area of fast flowing air above its surface. The pressure of this area is lower and so the wing is sucked
upwards.
Page
93
Hydrodynamica
It took Daniel a further 3 years to complete his work on fluids. Daniel put in the
frontispiece "Hydrodynamica, by Daniel Bernoulli, Son of Johann". It is thought that he
identified himself in this humble fashion as an attempt to mend the feud between
himself and his father. But a year later his father published his own work called
Hydraulics which appeared to have a lot in common with that of his son and the talk was
of blatant plagiarism.
To some extent Daniel Bernoulli lost much of his drive in mathematics after these e vents
and turned more to medicine and physiology. He remained in Basel and died there on
March 17th, 1782 at the age of 82.
The son of R. H. Froude, archdeacon of Totnes, James Anthony was born at Dartington, Devon on April
23, 1818. He was the youngest of eight children, including engineer and naval architect William Froude
and Anglo-Catholic polemicist Richard Hurrell Froude, who was fifteen years his elder. By James' third
year his mother and five of his siblings had died of consumption, leaving James to what biographer
Herbert Paul describes as a "loveless, cheerless boyhood" with his cold, disciplinarian father and
brother Richard. He studied at Westminster School from age 11 until 15, where he was "persistently
bullied and tormented". Despite his unhappiness and his failure in formal education, Froude cherished
the classics and read widely in history and theology.
Early life and education (18181842)
Page
94
Beginning in 1836, he was educated at Oriel College, Oxford, then the centre of the ecclesiastical
revival now called the Oxford Movement. Here Froude began to thrive personally and intellectually,
motivated to succeed by a brief engagement in 1839 (although this was broken off by the lady's
father). He obtained a second class degree in 1840 and travelled to Delgany, Ireland as a private tutor.
He returned to Oxford in 1842, won the Chancellor's English essay prize for an essay on political
economy, and was elected a fellow of Exeter College.
Page
95
His plight won him the sympathy of kindred spirits, such as George Eliot, Elizabeth Gaskell, and later
Mrs. Humphrey Ward. Mrs. Ward's popular 1888 novel Robert Elsmere was largely inspired by this era
of Froude's life.
Page
96
On the death of his adversary Freeman in 1892, Froude was appointed, on the recommendation of
Lord Salisbury, to succeed him as Regius Professor of Modern History at Oxford. The choice was
controversial, as Froude's predecessors had been amongst his harshest critics, and his works were
generally considered literary works rather than books suited for academia. Nevertheless, his lectures
were very popular, largely because of the depth and variety of Froude's experience and he soon
became a Fellow of Oriel. Froude lectured mainly on the English Reformation, "English Sea-Men in the
Sixteenth Century," and Erasmus. The demanding lecture schedule was too much for the aging Froude,
however, and in 1894 he retired to Devonshire. He died on October 20, 1894.
Osborne Reynolds was born in Belfast and moved with his parents soon
afterward to Dedham, Essex. His father worked as a school headmaster
and clergyman, but was also a very able mathematician with a keen
interest in mechanics. The father took out a number of patents for
improvements to agricultural equipment, and the son credits him with
being his chief teacher as a boy. Osborne Reynolds attended Cambridge
University and graduated in 1867 with high honours in mathematics. In
1868 he was appointed a professor of engineering at Owens College in Manchester, becoming in that
year one of the first professors in UK university history to hold the title of "Professor of Engineering".
This professorship had been newly created and financed by a group of manufacturing industrialists in
the Manchester area, and they also had a leading role in selecting the 25 year old Reynolds to fill the
position.
Reynolds showed an early aptitude and liking for the study of mechanics. In his late teens, for the year
before entering university, he went to work as an apprentice at the workshop of a well known inventor
and mechanical engineer near Essex, where he obtained practical experience in the manufac ture and
fitting out of coastal steamers (and thus gained an early appreciation of the practical value of
understanding fluid dynamics). For the year immediately following his graduation from Cambridge he
again took up a post with an engineering firm, this time as a practicing civil engineer in the London
(Croydon) sewage transport system. He had chosen to study mathematics at Cambridge because, in his
own words in his 1868 application for the professorship, "From my earliest recollection I have had an
irresistible liking for mechanics and the physical laws on which mechanics as a science is based.... my
attention drawn to various mechanical phenomena, for the explanation of which I discovered that a
knowledge of mathematics was essential."
Page
97
Reynolds remained at Owens College for the rest of his career in 1880 the college was renamed
University of Manchester. He was elected a Fellow of the Royal Society in 1877 and awarded the Royal
Medal in 1888. He retired in 1905.
Reynolds' contributions to fluid mechanics were not lost on ship designers ("naval architects"). The
ability to make a small scale model of a ship, and extract useful predictive data with respect to a full
size ship, depends directly on the experimentalist applying Reynolds' turbulence principles to friction
drag computations, along with a proper application of William Froude's theories of gravity wave energy
and propagation. Reynolds himself had a number of papers concerning ship design published in
Transactions of the Institution of Naval Architects.
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Reynolds published about seventy science and engineering research reports. When towards the end of his
career these were republished as a collection they filled three volumes. For a catalogue and short summaries of
them see and. Areas covered besides fluid dynamics included thermodynamics, kinetic theory of gases,
condensation of steam, screw-propeller-type ship propulsion, turbine-type ship propulsion, hydraulic brakes,
hydrodynamic lubrication, and laboratory apparatus for better measurement of Joule's mechanical equivalent of
heat.