The procedure of Laboratory experiment to verify Bernoulli’s

theorem, required apparatus and calculations to be done are explained in this

article.

Bernoulli’s theorem states that, for a continuous, steady

and frictionless flow the total head (which is the sum of pressure head,

velocity head and elevation head) at any section remains constant.

Total Head = pressure head + velocity head + elevation head

H = P/w + V^{2} / 2g + Z

According to Bernoulli’ theorem, Total head at any two sections is expressed as

## Apparatus required

Apparatus required to conduct Bernoulli’s experiment are

- Supply tank
- Tapered inclined pipe with piezometer tubes at

different points. - Measuring tank
- Stop watch
- Scale

## Test Procedure

Test procedure to verify Bernoulli’s experiment is as

follows

- Open the inlet valve and allow the water to flow from the supply tank to the receiving tank through a tapered inclined pipe.
- Adjust the flow using an outlet valve to make the head constant in the supply tank. At the constant head, head causing inflow and outflow are equal.
- After adjusting the flow, Note down the readings of the water level of each piezometer tube which are nothing but pressure heads at different points of tapered tube.

- Compute the area of
cross section of tapered pipe at points where piezometer tubes are located. - Now, take the stop watch and measure the height of water collected for a particular time interval.
Also Note down the measuring tank dimensions.- Repeat the same procedure for different discharges for at least two more times.

## Observations

Pressure head or Piezometer readings, P/w =

Area of cross section of tapered pipe under piezometer tubes = A_{1}, A_{2}, A_{3}…….

Area of Measuring tank, A =

Height of water collected for “t” interval of time =

Elevation head, Z =

## Calculations

Volume of water Collected in measuring tank (V) = Area of measuring tank (A) X height of water collected for “t” interval of time (h)

Discharge Q = volume / time = V/t

Velocity of flow, v = Discharge / Area of cross section of

tapered pipe

Velocities under each piezometer tube are v_{1} = Q/A_{1},

v_{2} = Q/A_{2},

v_{3} = Q/A_{3}………

Velocity head = v^{2} / 2g

Total Head = P/w + V^{2} / 2g + Z

S.no | Discharge, Q (cm^{3}/sec) |
Area of c/s under each piezometer (cm^{2}) |
Velocity of flow under each piezometer (cm/sec) | Pressure Head, P/w (cm) |
Velocity Head, v^{2} / 2g(cm) |
Elevation Head, Z (cm) |
Total Head (cm) |

1 | A_{1} |
v_{1} |
|||||

2 | A_{2} |
v_{2} |
|||||

3 | A_{3} |
v_{3} |
|||||

4 | A_{4} |
v_{4} |
|||||

5 | A_{5} |
v_{5} |

## Result

Hence, Bernoulli’s theorem is proved and It can be expressed as,