# Experimental Verification of Bernoulli’s Theorem Reading time: 1 minute

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 - 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.

H = P/w + V2 / 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 of tapered pipe at points where piezometer tubes are located.
• Now, take the stopwatch 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

Area of cross section of tapered pipe under piezometer tubes = A1, A2, A3…….

Area of Measuring tank, A =

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

## 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 v1 = Q/A1,

v2 = Q/A2,

v3 = Q/A3………

Velocity head = v2 / 2g

Total Head = P/w + V2 / 2g + Z

 S.no Discharge, Q  (cm3/sec) Area of c/s under each piezometer (cm2) Velocity of flow under each piezometer (cm/sec) Pressure Head, P/w (cm) Velocity Head, v2 / 2g (cm) Elevation Head, Z (cm) Total Head (cm) 1 A1 v1 2 A2 v2 3 A3 v3 4 A4 v4 5 A5 v5

## Result

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