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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 + 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
cross-section 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 = A1, A2, A3…….
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 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,
