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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
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
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.
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.
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,
Result
Hence, Bernoulli’s theorem is proved and It can be expressed as,
According to Bernoulli’ theorem, Total head at any two sections is expressed as :
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