What is Measured?

During the experiment, the following quantities are measured:

• Head of water above the mouthpiece,
• Volume of water collected,
• Time required for collection,
• Diameter of the mouthpiece.

These measurements are used to determine the theoretical discharge, actual discharge, and coefficient of discharge of the mouthpiece.

Why are these Measurements Important?

Head of Water

The head provides the pressure energy responsible for the flow through the mouthpiece and determines the theoretical velocity of discharge.

Collected Volume and Time

These measurements determine the actual quantity of water discharged through the mouthpiece.

Mouthpiece Diameter

The diameter determines the flow area and is required for calculating the theoretical discharge.

Coefficient of Discharge

Comparing the actual and theoretical discharge accounts for practical effects such as friction and the partial vacuum developed within the mouthpiece.

Sequential Calculations

Step 1

Calculate the cross-sectional area of the mouthpiece.

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

Step 2

Calculate the theoretical velocity.

$$V_t=\sqrt{2gH}$$

Step 3

Calculate the theoretical discharge.

$$Q_t=A\sqrt{2gH}$$

Step 4

Calculate the actual discharge.

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

Step 5

Calculate the coefficient of discharge.

$$C_d=\frac{Q_a}{Q_t}$$

Solved Numerical Example

Given,

Head,

$$H=0.60\ m$$

Mouthpiece diameter,

$$d=0.02\ m$$

Collected volume,

$$V=0.025\ m^3$$

Collection time,

$$t=12\ s$$

Actual discharge,

$$Q_a=\frac{0.025}{12}=0.00208\ m^3/s$$

Theoretical discharge,

$$Q_t=0.00221\ m^3/s$$

Coefficient of discharge,

$$C_d=\frac{0.00208}{0.00221}=0.94$$

Observation Table

Trial	Head (m)	Actual Discharge ($m^3/s$)	Theoretical Discharge ($m^3/s$)	Coefficient of Discharge
1	0.30	0.00146	0.00156	0.94
2	0.40	0.00168	0.00179	0.94
3	0.50	0.00189	0.00201	0.94
4	0.60	0.00208	0.00221	0.94
5	0.70	0.00225	0.00240	0.94

Interpretation

The observations show that the discharge through the mouthpiece increases with increasing head of water.

The actual discharge is slightly smaller than the theoretical discharge because of frictional and other hydraulic losses. However, the coefficient of discharge for an external cylindrical mouthpiece is generally higher than that of a simple orifice because the formation of a partial vacuum inside the mouthpiece increases the flow rate.

The experiment demonstrates the influence of mouthpiece geometry on fluid discharge and verifies the practical application of Bernoulli's theorem to hydraulic flow-control devices.