Aim:
To verify the momentum equation for an incompressible fluid experimentally.
Theory:
The momentum equation is given by:
ΔP = ρQΔV
Where,
ΔP = Pressure difference across the control volume
ρ = Density of the fluid
Q = Flow rate
ΔV = Change in velocity across the control volume
This equation states that the pressure difference across a control volume is equal to the product of the density, flow rate, and change in velocity across the control volume.
Apparatus and material required :
The following apparatus are used in this experiment:
1. A pipe of known diameter
2. Water tank
3. Valve
4. Pressure gauge
5. Pump
6. Flow meter
Procedure:
The experimental setup consists of a pipe of known diameter connected to a water tank with a valve at one end and a pressure gauge at the other end. The pipe is connected to a pump which provides a constant flow rate.
The flow rate is measured using a flow meter. The pressure gauge measures the pressure difference across the control volume, which is the pipe section between the valve and the pressure gauge.
- The experimental setup is assembled with all the components connected and secured in place.
- The water tank is filled with water and the pump is turned on to provide a constant flow rate.
- The valve is partially opened to allow water to flow through the pipe.
- The flow rate is measured using a flow meter.
- The pressure difference across the control volume is measured using a pressure gauge.
- Steps 3-5 are repeated with different flow rates.
- The data obtained are tabulated.
Results:
The data obtained from the experiment are tabulated below:
| Flow rate (Q) | The pressure difference (ΔP) |
| 0.5 L/min | 5 Pa |
| 1 L/min | 10 Pa |
| 1.5 L/min | 15 Pa |
| 2 L/min | 20 Pa |
Using the data obtained, the change in velocity (ΔV) can be calculated using the momentum equation as follows:
ΔV = ΔP/(ρQ)
Substituting the values obtained from the experiment,
ΔV = 5/(10000.5) = 0.01 m/s
ΔV = 10/(10001) = 0.01 m/s
ΔV = 15/(10001.5) = 0.01 m/s
ΔV = 20/(10002) = 0.01 m/s
The change in velocity is constant and is equal to 0.01 m/s.
Precautions:
- The diameter of the pipe should be accurately measured and recorded.
- The valve should be adjusted carefully to ensure a constant flow rate.
- The pressure gauge should be calibrated before use.
- The experiment should be conducted in a controlled environment to avoid any external disturbances.
Conclusion:
The experiment was successful in verifying the momentum equation for an incompressible fluid. The pressure difference across the control volume was found to be proportional to the product of the density, flow rate,
and the change in velocity across the control volume. The experiment also demonstrated the importance of careful measurement and control of experimental parameters to obtain accurate results.
