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To verify the Bernoulli’s theorem

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Aim:- To verify the Bernoulli’s theorem.
Apparatus required:-
Portable package system Bernoulli's Theorem Apparatus.
Description about Apparatus:-


Part names:
1-9: Piezo meters (A transparent tube with scale) are connected at various cross sections of the Duct(in $mm^2$).
10: Stainless Steel duct (for low friction).
11: Single Phase motor with pump(pump capacity is 0.5 HP, single phase 20 volts, 2800 RPM and pump of size 25 mm to discharge about 15 LPM at 30 Meter total head).
12: Flow control ball valve.
13: Supply tank with piezo meter.
14: Delivery Tank with piezo meter.
15: Supply tank drain control valve.
16: Out flow Control valve.
17: Drain valve from discharge tank.
18: Discharge measuring tank (0.3m X 0.3m Area).
19: Water storage tank.
The closed circuit self sufficient portable package system Bernoulli's theorem Apparatus does not require any Foundation, trench work, etc., so that you can conduct experiment with keeping the unit anywhere.
The unit consists of supply chamber experimental duct made out of SS sheet. The interlinking duct is smoothly varying in cross-section so that the velocity of flow changes gradually for the purpose of experiments with minimum of friction loss and loss the due to turbulence. Piezometer tubes are provided at suitable intervals along with duct for the measurement of pressure head at various points. A flow control valve is provided at the exit of the Duct for adjusting and keeping different flow rate through the Apparatus. A collecting tank is provided for measurement of rate of flow. Piezometer tubes are provided at suitable intervals along with duct for measurement of pressure head at various points. A flow control valve is provided at the exit of the duct for adjusting and keeping different flow rate through the Apparatus. A collecting tank is provided for the measurement of rate of flow.

Verification of Bernoulli's theorem
Proposition 1: Bernoulli's theorem: A steady, continuous, in-compressible, non-viscous fluid flow, the total energy or total head remains constant at all the sections along the fluid flow provided there is no loss or addition of energy.
$\frac{P}{\gamma} + \frac{V^2}{2g} + Z$ = Total head = constant
Where,
$\frac{P}{\gamma}$ = Pressure head (m)
$\frac{V^2}{2g}$ = velocity or Kinetic head (m), ($V= \frac{Q}{A}$), ($Q=\frac{Volume of water collected}{Time taken to collect that much water}$)
$Z$ = potential head (Height above some assumed datum level.
Preposition 2: application of Bernoulli's theorem
Bernoulli's equation is based on Euler's equation of motion. It is applicable to flow of fluid through pipe and channel. In Euler's equation the force of viscosity is neglected. Bernoulli's equation is required to be modified if the flow is compressible & unsteady.
Concept structure

Principle
The apparatus is fitted with Piezometer tubes and scales at 9 cross sectional points, along the experimental duct at suitable intervals for measurement of pressure head. The area of flow section is written on each one of these nine sections. The velocity of flow(V) can be calculated at each of these sections from the flow rate(Q) obtained from the measuring tank that is $V=\frac{Q}{A}$ from this velocity head $\frac{V^2}{2g}$ can be calculated for each section.
For the verification of Bernoulli's Theorem, the velocity head when superposed over the hydraulic gradient gives the energy gradient must be a level line. However, in the flow of need fluid, contain losses of energy is inevitable ad this can be readily seen by plating energy gradient. Such sets of readings can be taken for different flow rated by adjusting the valve kept at the outlet.

For each set of readings:
Area of measuring tank A= Length X Breadth; time for head 100mm rise of water in seconds; Rate of flow
$Discharge = \frac{A*h}{t} \frac{m^3}{sec}$
where,
A = Area of the measuring tank in metres (0.3 m x 0.3 m)
h = Rise of water level (say 10 cm) in metres.
T = Time in seconds for rise of water level (say 10 cm).

Observation table

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