University of Mauritius
FACULTY OF ENGINEERING
CIVIL ENGINEERING DEPARTMENT
B Eng (Hons) Civil Engineering-2008/2012
Year 2- Semester 1
CIVE 2003Y Fluid Mechanics
Assignment: Laboratory Report
Lecturer: Ms. Manta Nowbuth
Submitted by: JUTTUN Ghanisha Devi (ID: 0812567)
Date of submission: 29.12.09
Experiment to study flow a Venturi Meter
Introduction
The Bernoulli’s principle states that as the velocity of a fluid increases, its pressure
decreases. Bernoulli’s principle can be demonstrated by the Bernoulli equation. However,
Bernoulli’s principle can only be applied under certain conditions. Massey (2006 p.94)
states that:
“...the conditions to which Bernoulli’s equation applies are: the fluid must be frictionless
(inviscid) and of constant density; the flow must be steady, and the relation holds in
general for single streamlines”
These are therefore assumptions that are made.
Objective
The objective of the experiment is to verify the Bernoulli’s equation which relates the
pressure energy, kinetic energy and potential energy per unit weight from point to point
in the fluid. The equation is based upon the law of conservation of energy below.
Douglas et al (2005 p.169)
Pressure energy + Kinetic energy + Potential energy = Total energy = a constant
per unit weight
per unit weight
per unit weight
per unit weight
In this experiment water is made to flow in a Perspex tank in which the centreline of the
cross sections lies all on the same horizontal plane. There is no change in the potential
energy per unit weight as the fluid does not lose elevation during flow. The horizontal
plane is taken as the datum which reduces the potential energy variable in the equation to
zero. Thus the equation to be verified is as follows:
Pressure energy + Kinetic energy = Total energy = A constant
per unit weight
per unit weight
per unit weight
P/w + V2/2g = A constant
Where
1. w: ρg
2. P/w is the pressure head (i.e. – the height of the water in the Piezometer tube)
3. V2/2g is the velocity head
The heads are expressed in mm of water since velocities of flow are small.
Methodology
To carry out the experiment, water was allowed to flow in the Perspex tank and
the outflow was adjusted so that the water levels in the piezometers are steady.
Piezometer readings for pressure head are taken
The water is allowed to flow into the collecting vessel for a given time period, t
seconds, and the height, h, of water collected in the measuring tank is recorded.
The area of the tank, A is calculated.
The velocity, V, of flow at any section is then obtained by dividing the following
equation (A * h/t), by the area of the converging tube at that section.
The experiment was repeated with a lower head h in the tank that is with a lower
flow rate of fluid.
Calculation and Results
The calculation for V2/2g is done as follows:
V=576.39mm
g= acceleration due to gravity = 9810 mm2/s
V2/2g= 576.392 / (2x9810) = 17mm
The same procedure is followed for all the other values of velocity for all the
piezometers.
The calculation for P/w + V2/2g is done as follows:
It is done by adding the piezometer reading to the corresponding velocity head in the
table.
The results are tabulated as follows:
Section No.
Area (mm2)
Peizometer Reading
(mm)
V (mm/s)
V2/2g (mm)
P/w + V2/2g (mm)
.
1
300
418
2
275
414
3
250
409
4
225
401
5
200
395
6
175
282
7
150
365
576.39 618.98 680.87 756.53 851.10 972.68 1134.79
17
20
24
29
37
48
66
435
434
433
430
432
330
431
REPEATED EXPERIMENT
The experiment is repeated for a lower head in the tank
Section No.
Area (mm2)
Peizometer Reading (mm)
V (mm/s)
V2/2g (mm)
P/w + V2/2g (mm)
1
300
268
494.16
12
280
2
275
265
539
15
280
3
4
5
6
7
250
225
200
175
150
261
256
249
240
226
592.98 658.87 741.23 847.13 988.31
18
22
28
37
50
279
278
277
277
276
Data Analysis
1. A graph of P/w is plotted against Section No.
From the plots it can be seen that there is an overall decrease in pressure head
with decrease in cross sectional area of the piezometers.
This is demonstrated clearly in the lower head h series. In the higher head series
however, there is a sudden decrease in the pressure head at piezometer section no.
6.
2. A graph of V2/2g is plotted against Section No.
It can be seen that the velocity head at each piezometer section is increasing with
decrease in the cross sectional area of the piezometers according to the equation
Q = AV while the flow velocity in the tank is being kept nearly constant.
Q= discharge
A= cross sectional area (of the piezometers)
V= velocity of fluid at the piezometer
Upon comparison of the two plots of velocity head and pressure head above, it
can be observed that when the velocity in a fluid increases the pressure decreases.
3. A graph of (P/w + V2/2g) is plotted against Section No.
From the graph plotted for the lower head series it can be seen that the total energy per
unit weight of the fluid remains more or less constant along the flow at the piezometer
sections.
However for the higher head series it can be seen that the total energy per unit head drops
suddenly at section no. 6.
Discussion
Upon comparison of the two plots of velocity head and pressure head above, it can be
observed that when the velocity in a fluid increases the pressure decreases. Therefore it
can be said that the Bernoulli’s equation and principle are both valid.
At the piezometer section no. 6 it can be observed that the pressure head has dropped
abnormally low. This may be attributed to an experimental error.
Under ideal conditions the total energy per unit weight of the fluid at each piezometer
section should have been constant. However in practice they are not as shown in the
experiment carried out.
This may be because the flow rate causes formation of “eddies” which are fluid currents
whose prevalence increase with increase in fluid flow velocity due to friction with the
boundary causing loss of energy.
Also there are assumptions that have been made to create idealistic conditions for
Bernoulli’s principle to apply which could not be fully reproduced in this experiment. For
example the formation of eddy currents indicate that the flow has not been completely
steady as the eddies’ velocity fluctuates with time. In fact a high prevalence of “eddies” is
associated with turbulent flow.
However modifications could have been made on the apparatus to ensure a steady flow of
fluid. The coefficient of friction at the boundary could have been reduced by coating with
a near-frictionless material for example carbon-coating. Also the diameter of the tube
carrying the liquid from the perspex tank to the venturimeter can be made smaller to have
a steady flow at higher velocities of fluid flow.
References
Massey, B. (2006) Mechanics of Fluid. 8th ed. Taylor and Francis Press. New York, USA.
Douglas, J. F., Gasiorek J.M, Swaffield J.A & Jack L.B. (2005) Fluid Mechanics. 5th ed.
Pearson Prentice Hall. Harlow, Essex, England.