Experiment 8
VERIFICATION OF BERNOULLIS THEOREM
Aim
To Verify Bernoulli’s Equation
Apparatus
Bernoulli’s Theorem Apparatus and Hydraulic Bench
Theory: Bernoulli's law indicates that, if an inviscid fluid is flowing along a pipe of varying
cross section, then the pressure is lower at constrictions where the velocity is higher, and higher
where the pipe opens out and the fluid stagnates. The well-known Bernoulli equation is derived
under the following assumptions:
1. fluid is incompressible ( density  is constant );
2. flow is steady:
3. flow is frictionless ( = 0);
4. along a streamline;
Then, it is expressed with the following equation:
.
+
.
+
=
=const.
Where (in SI units):
p = fluid static pressure at the cross section in N/m2.
 = density of the flowing fluid in kg/m3
g = acceleration due to gravity in m/s2 (its value is 9.81 m/s2 = 9810 mm/s2)
v = mean velocity of fluid flow at the cross section in m/s
1
z = elevation head of the center of the cross section with respect to a datum z=0
H = total (stagnation) head in m
The terms on the left-hand-side of the above equation represent the pressure head (h), velocity
head (hv ), and elevation head (z), respectively. The sum of these terms is known as the total head
(H). According to the Bernoulli’s theorem of fluid flow through a pipe, the total head (H) at any
cross section is constant (based on the assumptions given above). In a real flow due to friction
and other imperfections, as well as measurement uncertainties, the results will deviate from the
theoretical ones.
In our experimental setup, the centerline of all the cross sections we are considering lie on the
same horizontal plane (which we may choose as the datum, z=0), and thus, all the ‘z’ values are
zeros so that the above equation reduces to:
.
+
.
=
´=const. (This is the total head at a cross section).
For our experiment, we denote the pressure head as h and the total head as
Procedure:
´.
1. Open the inlet valve slowly and allow the water to flow from the supply tank.
2. Now adjust the flow to get a constant head in the supply tank to make flow in and out
flow equal.
3. Under this condition the pressure head will become constant in the piezometer tubes.
4. Measure the height of water level “ℎ”(above the arbitrarily selected plane) in different
piezometric tubes.

Apply enough pressure so that the air trapped goes out from the venture.

When using a manometer, remove the air bubbles by using the vent cocks
provided/ or by gently taping the manometer tubes.

Use the balloon provided for adjusting the water level in the manometer tube.

Measure accurately the water level in all the piezometers h and record the values
in the observation table.
2
5. Compute the area of cross-section under the piezometer tubes.
6. Note down the quantity of water collected in the measuring tank for a given interval of
time.
7. Change the inlet and outlet supply and note the reading.
8. Take at least two reading as described in the above steps.
OBSERVATIONS:
H = ----- mm
Time “t” required to collect 10 litres of water = ___ sec
Total head = Velocity head + Pressure head
Where,
Velocity Head =
(cm)
Velocity =
Discharge =
(cm/sec)
(cm3/ sec)
OBSERVATION TABLE
Table 1
Sl
No.
Section
No.
Radius
(cm)
1
1
1.265
2
2
1.005
3
3
0.87
4
4
0.725
5
5
0.76
6
6
0.845
Area of C/S
(cm2)
Velocity of
flow
(cm/sec)
Velocity Head
cm
Pressure
Head
(cm)
Total Head
´=
+
3
7
7
0.93
8
8
1.02
9
9
1.105
10
10
1.2
11
11
1.28
Section
No.
Radius
(cm)
Table 2
Sl
No.
Area of C/S
(cm2)
Velocity of
flow
(cm/sec)
Velocity Head
cm
Pressure
Head
(cm)
1
1
1.265
2
2
1.005
3
3
0.87
4
4
0.725
5
5
0.76
6
6
0.845
7
7
0.93
8
8
1.02
9
9
1.105
10
10
1.2
11
11
1.28
Total Head
´=
+
Results and Discussion
4