INTRODUCTION
Bernoulli’s principle describes the relationship between the flow velocity of a fluid and its
pressure. An increase in velocity leads to a reduction in pressure in a flowing fluid, and
vice versa. The total pressure of the fluid remains constant. Bernoulli’s equation is also
known as the principle of conservation of energy of the flow.
The HM 150.07 experimental unit is used to demonstrate Bernoulli’s principle by
determining the pressures in a Venturi nozzle.
In addition, the total pressure can be measured at various points on the Venturi nozzle.
Measurements are carried out using a probe that can move in an axial direction to
theVenturi nozzle. The probe is sealed by a compression gland. The water supply is
drawn either from the HM 150 Base Module for Experiments in Fluid Mechanics or from
the laboratory network. The HM 150 can be used to set up a closed water circuit.
The Venturi nozzle is equipped with pressure measuring points to determine the static
pressures. The pressures are displayed on the six tube manometers. The total pressure
is measured by the Pitot tube and displayed on another single tube manometer.
The experimental unit is positioned easily and securely on the work surface of
the HM 150base module. The water is supplied and the flow rate measured by HM 150.
Alternatively, the experimental unit can be operated by the laboratory supply. [1]
The flow of a fluid has to conform with a number of scientific principles in particular the
conservation of mass and the conservation of energy. The first of these when applied to
a liquid
flowing through a ventuti tube requires that for steady flow the velocity will be inversely
proportional to the flow area. The second requires that if the velocity increases then the
pressure must decrease.
Bernoulli's apparatus demonstrates both of these principles and can also be used to
examine the
onset of turbulence in an accelerating fluid stream.[2]
OBJECTIVE (S)
1. To verify energy conservation or Bernoulli principle in pipe flow .
2. To measure the pressure curve or distribution in a Venturi nozzle.
3. To measure the velocity curve or distribution in a Venturi nozzle .
4. recognizing friction effects.
THEORY
Bernoulli's Theorem
Definition
According to Bernoulli’s theorem in physics, whenever there is an increase in the speed
of the liquid, there is a simultaneous decrease in the potential energy of the fluid or we
can say that there is a decrease in the pressure of the fluid. Basically, it is a principle of
conservation of energy in the case of ideal fluids. If the fluid flows horizontally such that
there is no change in the gravitational potential energy of the fluid then increase in
velocity of the fluid results in a decrease in pressure of the fluid and vice versa.
Venturi Meter
The venture meter is a tool used to measure the flow through a pipeline. This
apparatus consists of a venture tube and differential pressure gauge. The venturi tube
has a
converging portion, a throat and a diverging portion as shown in the figure below. The c
onverging
Portion’s function is to increase the velocity of the fluid and lower its static pressure. A
pressure difference between inlet and throat is thus developed, which pressure differenc
e is correlated with the rate of discharge. The diverging cone serves to change the area
of the stream back to the entrance area and convert velocity head into pressure head.
Derivation (Proof)
We will prove the Bernoulli’s theorem here.
Let the velocity, pressure and area of a fluid column at a point X
be v1, p1 and A1 and at another point Y be v2, p2 and A2. Let the volume that is bounded by X
and Y be moved to M and N. let XM = L1 and YN = L2
Now if we can compress the fluid then we have,
A1 × L1= A2 × L2
We know that that the work done by the pressure difference per volume of the unit is equal to
the sum of the gain in kinetic energy and gain in potential energy per volume of the unit.
This implies
Work done= force × distance
⇒ Work done= p × volume
Therefore, net work done per volume = p1 – p2
1 1
Also, kinetic energy per unit volume = m v2 = ρ v2
2 2
Therefore, we have,
1
Kinetic energy gained per volume of unit ρ ((v2)2 – (v1)2)
2
And potential energy gained per volume of unit = p g (h2 – h1)
Here, h1and h2 are heights of X and Y
above the reference level taken in common.
Finally we have
1
p1 – p2= ρ ((v2)2 – (v1)2) + ρ g (h2 – h2)
2
1 1
⇒ p1+ ρ (v1)2 + ρ g h1 = p2 + ρ (v2)2 + ρ g h2
2 2
1
⇒ p+ ρ v2 + ρ g h is a constant
2
When we have h1= h2
1
Then we have, p+ ρ v2 is a constant.
2
This proves the Bernoulli’s Theorem
then
ρv 2 ρv 2
P2+ + ρgh1=p2+ + ρgh2=constant
2 2
ρv 2 ρv 2
P2+ = p2+ =constant
2 2
ρv 2
ρgh1+ ρv12/2= + ρgh2=constant
2
ρg(h1+v12 /2g)=g(h2+v22/2g)=constant
v2 v2
h1+ =h2+
2g 2g
The table below shows the standardised reference velocity w
This parameter is derived from the geometry of the venturi tube.
2)
point A(mm reference velocity(w)
1 338.6 1
2 233.5 1.45
3 84.6 4
4 170.2 1.99
5 255.2 1.33
6 338.6 1
[3]
Multiplying the reference velocity values with a starting value, we can calculate the
theoretical velocity values wcalc or v calc at the 6 measuring points of the venturi tube
v V̇
W calc =At where v=volume,or W calculated = A
Wmeasured =√(2ghdyn)
APARATUS
1. 150.07 demonstrator
2. HM 111 base stand
3. Pitot tube
4. Venture tube
5. Stop watch
THE TOTAL HM 150.07 DEMOSTATOR DIAGRAM
PROCEDURE
1. The general Start-up Procedures is performed
2. All manometer tubes are checked properly connected to the corresponding
pressure taps are air-bubble free
3. The discharged valve is adjusted to a high measureable flow rate.
4. After the level is stabilized, the water flow rate is measured using volumetric
method
5. The hyperdomic tube connected to manometer is gently slide, so that the cross
section of venturi tube at the first section reached its end
6. Step 5 is repeated for other cross sections
7. Step 3 to 6 is repeated with three other decreasing flow rates by regulating the
venturi discharged.
8. The velocity W measured; is calculated using the Bernoulli’s equation where W
measured=√(2ghdyn)
9. W calculated is calculated using the continuity equation where;
v V̇
W calc= =
At A
10.The difference between two calculated velocities is determined
Result
h =htotal-hstatic
dayinamic
(h1)dynamic=350-340=10
(h2)dynamic=345-315=30
(h3)dynamic=340-75=265
(h4)dynamic=310-75=110
(h5)dynamic=270-225=45
(h6)dynamic=265-240=25
TRIAL 1
Pressure graph
Volume=1.1 L TIME=5 Sec V̇ =0.22 L/ S (volume flow rate)
h1 h2 h3 h4 h5 h6 Time( volume
s)
htotal 350 345 340 310 270 265
hstatic 340 315 75 200 225 240
hdayinamic 10 30 265 110 45 25 1100ml
W1 W2 W3 W4 W5 W6
wmeasured 14.007 24.26 72.106 46.456 29.7 22.147
wcalculated 0.06497 0.0942 0.26 0.129 0.0862 0.06497
h total
h static
h static h total
h dynamic
h dynamics
0 1 2 3 4 5 6 7
Velocity graph
w measured=√(2ghdyn)
(w1)measured=√(2*9.81*10)=14.007
(w2)measured=√(2*9.81*30)=24.26
(w3)measured=√(2*9.81*265)=72.106
(w4)measured=√(2*9.81*110)=46.456
(w5)measured=√(2*9.81*45)=29.7
(w6)measured=√(2*9.81*25)=22.147
v
=At
W calc
0.0011
(w 1)calc= 0.003386 ∗5 m3/sm2=0.06497 m/s
0.0011
(w 2)calc= 0.002335 ∗5 m3/sm2=0.0942 m/s
0.001 1
(w 3)calc= 0.000846 ∗5 m3/sm2=0.26 m/s
0.0011
(w 4)calc= 0.001702∗ 5 m3/sm2=0.129 m/s
0.0011
(w5)calc= 0.002552∗ 5 m3/sm2=0.0862 m/s
0.0011
(w 6)calc= 0.003386 ∗5 m3/sm2=0.06497 m/s
W meas W calc
h1 14.007 0.06497
h2 24.26 0.0942
h3 72.106 0.26
h4 46.456 0.129
h5 29.7 0.0862
h6 22.147 0.06497
Trial 2
Volume=0.94L TIME=7 Sec V̇ =0.134285 L/s (volume flow rate)
In the same manner we can calculate the hdaynamic, W measured and Wcalculated given data.
The measured values are tabulated as shown below:-
h1 h2 h3 h4 h5 h6 Time( volume
s)
htotal 230 225 220 195 185 180
hstatic 215 208 40 125 140 155
hdayinamic 15 17 180 70 45 25 940 ml
W1 W2 W3 W4 W5 W6
wmeasured 17.1552 18.263 54 33.675 27 20.125
wcalculated 0.03966 0.0575 0.5873 0.07889 0.05262 0.03966
Pressure graph
H total
h static h static
h total
h dynamic
h dynami
0 1 2 3 4 5 6 7
Velocity graph
