Aim:

This lab activity aims to determine the coefficient of discharge of a mouthpiece and understand its importance in measuring the flow rate of fluids.

Theory:

A mouthpiece is a device used to measure the rate of flow of fluids such as water, air, or gas. It is a convergent divergent tube that reduces the cross-sectional area of the fluid flowing through it,

increasing its velocity. The flow rate is related to the head of fluid above the mouthpiece, and the coefficient of discharge.

The coefficient of discharge is the ratio of the actual flow rate to the theoretical flow rate for a given head. This activity aims to determine the coefficient of discharge of a mouthpiece and to understand its significance in fluid mechanics.

Apparatus & Materials Required:

1. Mouthpiece
2. Water tank
3. Measuring cylinder
4. Stopwatch
5. Vernier calliper
6. Spirit level
7. Ruler
8. Thermometer

Procedure:

1. Mount the mouthpiece vertically in the water tank and connect it to a constant head supply.
2. Level the tank to ensure accurate measurements.
3. Measure and record the diameter of the inlet and outlet of the mouthpiece using a vernier calliper.
4. Record the temperature of the water in the tank using a thermometer.
5. Adjust the constant head supply until the head of water above the mouthpiece is at a specific height.
6. Allow the water to stabilize and note the initial level of water in the measuring cylinder.
7. Collect the water flowing through the mouthpiece in the measuring cylinder for a known time (usually 30 seconds) and record the volume.
8. Repeat the above steps for different heads of water.
9. Calculate the discharge for each head by dividing the volume collected by the time.
10. Calculate the theoretical flow rate using the formula Q = A√(2gh) where Q is the flow rate, A is the area of the mouthpiece, g is the acceleration due to gravity, and h is the head of water above the mouthpiece.
11. Calculate the coefficient of discharge using the formula Cd = Q/(A√(2gh)).
12. Plot a graph of the discharge coefficient versus the head of water.
13. Determine the average coefficient of discharge and compare it with the theoretical value.

Results:

The experiment results show that the coefficient of discharge decreases as the head of water above the mouthpiece increases. The graph of the coefficient of discharge versus the head of water is a curve. The curve is not a straight line, indicating that the coefficient of discharge is not constant.

The average coefficient of discharge is calculated and compared with the theoretical value. If the average coefficient of discharge is close to the theoretical value, the mouthpiece is calibrated and can be used to measure the flow rate of fluids in the future.

Precautions:

1. The tank should be level to ensure accurate measurements.
2. The mouthpiece should be mounted vertically to avoid any turbulence.
3. The diameter of the inlet and outlet of the mouthpiece should be measured accurately using a vernier calliper.
4. The constant head supply should be adjusted accurately to ensure a specific head of water above the mouthpiece.
5. The volume of fluid collected should be measured accurately using a measuring cylinder.
6. The time should be measured accurately using a stopwatch.
7. The experiment should be repeated several times to ensure accuracy.
8. The temperature of the fluid should be recorded to account for any changes in fluid density.

Conclusion:

Determining the coefficient of discharge of a mouthpiece is an essential activity in measuring the flow rate of fluids. The coefficient of discharge is a critical parameter in the calibration process, and its determination requires accurate measurements of the head of fluid above the mouthpiece and the volume of fluid