An orifice is a small opening of regular shape provided in the side or bottom of a tank through which a liquid flows under the action of gravity. The pressure exerted by the liquid above the opening causes the fluid to emerge as a free jet.

As the liquid passes through the orifice, its pressure energy is converted into kinetic energy. The velocity and discharge of the jet depend on the head of liquid above the orifice and the characteristics of the opening.

In practice, the jet contracts after leaving the orifice and experiences energy losses due to friction and turbulence. Consequently, the actual flow differs from the ideal theoretical prediction.

The Orifices experiment studies these effects and determines the coefficients that describe the behaviour of the flowing jet.

Everyday Intuition

The flow through an orifice can be observed in many common situations.

• Water flowing from a hole in a storage tank.
• Leakage through a small opening in a pipe.
• Water emerging from a reservoir outlet.
• Flow through irrigation outlets.

In each case, a greater water level above the opening produces a higher velocity of the issuing jet. The jet initially contracts to a smaller cross-section before gradually expanding as it moves through the air.

This contraction and subsequent expansion are characteristic features of orifice flow.

Experimental Relevance

The objective of the Orifices experiment is to study the discharge of water through an orifice under a constant head and to determine the coefficients governing the flow.

The experiment involves:

• Measuring the actual discharge through the orifice,
• Calculating the theoretical discharge using Bernoulli's theorem,
• Studying the trajectory of the issuing jet,
• Determining the coefficient of velocity,
• Determining the coefficient of contraction,
• Determining the coefficient of discharge.

The experiment demonstrates that the actual flow is influenced by the contraction of the jet and energy losses occurring during discharge.

Mathematical Formulation

Applying Bernoulli's theorem between the free surface of the tank and the centre of the orifice,

$$\frac{P_1}{\rho g} + \frac{V_1^2}{2g} + Z_1 === \frac{P_2}{\rho g} + \frac{V_2^2}{2g} + Z_2.$$

For a large tank,

• The free surface and the orifice are exposed to atmospheric pressure,
• The velocity at the free surface is negligible,
• The difference in elevation equals the head of liquid, $H$.

The equation simplifies to

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

which is known as Torricelli's theorem.

Here,

• $V_t$ = Theoretical velocity,
• $H$ = Head above the centre of the orifice.

The theoretical discharge is

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

where

• $A$ = Area of the orifice.

The actual discharge is

$$Q_a=C_dQ_t.$$

The coefficient of discharge is

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

The coefficient of velocity is

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

where

• $V_a$ = Actual jet velocity,
• $V_t$ = Theoretical jet velocity.

The coefficient of contraction is

$$C_c=\frac{A_c}{A},$$

where

• $A_c$ = Area of the jet at vena contracta,
• $A$ = Area of the orifice.

These coefficients are related by

$$C_d=C_cC_v.$$

Application to the Orifice Apparatus

The experimental apparatus consists of a water tank fitted with an orifice on one side.

Water is maintained at a constant head above the orifice and allowed to discharge freely into the atmosphere.

As the water leaves the opening,

• The jet contracts,
• The minimum cross-section occurs at the vena contracta,
• The jet then follows a parabolic trajectory under gravity.

The actual discharge is determined by collecting water in a measuring tank over a known time interval.

The trajectory of the jet is observed to determine the actual velocity of flow.

Using these measurements, the coefficients of velocity, contraction, and discharge are evaluated.

Engineering Significance

The study of orifice flow is important in many hydraulic engineering applications.

Important applications include:

• Reservoir outlets,
• Water tanks,
• Irrigation structures,
• Spillways,
• Flow-measuring devices,
• Hydraulic control structures,
• Industrial storage systems.

Knowledge of the coefficients of orifice flow enables engineers to accurately predict discharge and design hydraulic structures involving the controlled release of fluids.

The Orifices experiment provides a practical demonstration of the conversion of pressure energy into kinetic energy and the influence of contraction and friction on real fluid flow.