What is Measured?

During the experiment, the following quantities are measured:

• Head of water above the orifice,
• Volume of water collected,
• Time of collection,
• Horizontal and vertical coordinates of the jet,
• Diameter of the orifice.

These measurements are used to determine the theoretical and actual characteristics of the jet and to evaluate the coefficients of orifice flow.

Why are these Measurements Important?

Head of Water

The head provides the pressure energy that drives the flow through the orifice and determines the theoretical velocity of the jet.

Collected Volume and Time

These measurements determine the actual discharge through the orifice.

Jet Coordinates

The horizontal and vertical positions of the jet are used to calculate the actual velocity of the issuing water and study the trajectory of the jet.

Orifice Diameter

The diameter determines the area of the opening, which is required for calculating the theoretical discharge.

Flow Coefficients

Comparing the theoretical and actual behaviour of the jet allows the coefficients of velocity, contraction, and discharge to be evaluated.

Sequential Calculations

Step 1

Calculate the area of the orifice.

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

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

Determine the coefficient of discharge.

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

Step 6

Calculate the actual jet velocity from the trajectory observations.

$$C_v=\frac{V_a}{V_t}$$

Step 7

Determine the coefficient of contraction.

$$C_c=\frac{C_d}{C_v}$$

Solved Numerical Example

Given,

Head,

$$H=0.50\ m$$

Orifice diameter,

$$d=0.02\ m$$

Collected volume,

$$V=0.02\ m^3$$

Time,

$$t=12\ s$$

Theoretical velocity,

$$V_t=\sqrt{2\times9.81\times0.50}=3.13\ m/s$$

Actual discharge,

$$Q_a=\frac{0.02}{12}=0.00167\ m^3/s$$

Theoretical discharge,

$$Q_t=0.00192\ m^3/s$$

Coefficient of discharge,

$$C_d=0.87$$

Measured coefficient of velocity,

$$C_v=0.97$$

Coefficient of contraction,

$$C_c=\frac{0.87}{0.97}=0.90$$

Observation Table

Trial	Head (m)	Actual Discharge ($m^3/s$)	Theoretical Discharge ($m^3/s$)	$C_v$	$C_d$	$C_c$
1	0.30	0.00125	0.00145	0.96	0.86	0.90
2	0.40	0.00147	0.00169	0.97	0.87	0.90
3	0.50	0.00167	0.00192	0.97	0.87	0.90
4	0.60	0.00185	0.00212	0.98	0.87	0.89
5	0.70	0.00201	0.00232	0.98	0.87	0.89

Interpretation

The observations show that increasing the head above the orifice increases both the jet velocity and the discharge.

The actual discharge is smaller than the theoretical discharge because of jet contraction and frictional losses. The issuing jet contracts to form the vena contracta, where the velocity is maximum.

The experimentally determined coefficients of velocity, contraction, and discharge account for these practical effects and enable accurate prediction of orifice flow.

The experiment demonstrates the practical application of Bernoulli's theorem and Torricelli's theorem to the discharge of fluids through small openings.