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.
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 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
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,