What is Measured?

During the experiment, the following quantities are recorded:

• Volume of water collected in the measuring tank,
• Time required for collection,
• Pressure head at different tapping points,
• Diameter of the test section at each tapping location.

These measurements provide the information required to determine the flow characteristics of the fluid through the converging-diverging channel.

Why are these Measurements Important?

Each measurement helps evaluate one aspect of the energy of the flowing fluid.

Collected Volume and Time

These measurements are used to determine the discharge through the apparatus. Knowing the discharge ensures that the flow conditions are the same throughout the experiment.

Diameter of the Test Section

The diameter determines the cross-sectional area available for flow. Since the area changes along the channel, the fluid velocity also changes.

Pressure Head

The pressure head measured by the piezometer tubes represents the pressure energy of the flowing water. Comparing the pressure head at different sections shows how pressure changes as the flow area changes.

Velocity and Velocity Head

Using the measured discharge and cross-sectional area, the velocity of flow and the corresponding velocity head can be determined. The velocity head represents the kinetic energy of the fluid.

Total Head

Combining the pressure head and velocity head allows the total mechanical energy of the flowing water to be evaluated. If Bernoulli's theorem is valid, the total head should remain nearly constant throughout the apparatus, except for small losses due to friction.

Sequential Calculations

1. Measure collected volume.
2. Measure collection time.
3. Calculate discharge.

$$Q=\frac{V}{t}$$

4. Calculate area of each section.

$$A=\frac{\pi d^2}{4}$$

5. Calculate velocity.

$$v=\frac{Q}{A}$$

6. Calculate velocity head.

$$\frac{v^2}{2g}$$

7. Record pressure head from piezometer.

8. Calculate total head.

$$H=h_p+\frac{v^2}{2g}$$

9. Compare total head at all sections.

Solved Numerical Example

Collected volume:

$$V=0.02\ m^3$$

Time:

$$t=20\ s$$

Discharge:

$$Q=\frac{0.02}{20}=0.001\ m^3/s$$

Pipe diameter:

$$d=0.03\ m$$

Area:

$$A=7.07\times10^{-4}\ m^2$$

Velocity:

$$v=\frac{0.001}{7.07\times10^{-4}}=1.41\ m/s$$

Velocity head:

$$\frac{1.41^2}{2\times9.81}=0.101\ m$$

Pressure head from piezometer:

$$0.85\ m$$

Total head:

$$H=0.85+0.101=0.951\ m$$

Similar calculations are carried out for all tapping points.

Observation Table

Section	Diameter (m)	Pressure Head (m)	Velocity (m/s)	Velocity Head (m)	Total Head (m)
1	0.050	0.95	0.51	0.013	0.963
2	0.040	0.92	0.80	0.033	0.953
3	0.030	0.85	1.41	0.101	0.951
4	0.040	0.91	0.80	0.033	0.943
5	0.050	0.93	0.51	0.013	0.943

Interpretation

The observations show that as the flow area decreases, the velocity increases and the pressure head decreases. In the diverging section, the velocity decreases and the pressure head increases.

The total head remains nearly constant throughout the apparatus, with small reductions due to frictional losses and experimental uncertainties.

The experiment therefore verifies Bernoulli's theorem and demonstrates the conversion between pressure energy and kinetic energy in flowing fluids.