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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
Bernoulli's Experiment Apparatus
Fig 1: Bernoulli’s Experiment Apparatus

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.
Bernoulli's Apparatus Parts
Fig 2: Bernoulli’s Apparatus Parts
  • 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,

About Sadanandam AnupojuVerified

Sadananda is a Civil Engineer and is an Author, Editor and Partner of The Constructor since 2016.