A mouthpiece is a short tube attached to an orifice provided in the side or bottom of a tank through which a liquid flows under pressure. Generally, the length of a mouthpiece is about two to three times its diameter.

A simple orifice allows liquid to discharge directly into the atmosphere, whereas a mouthpiece modifies the flow pattern of the issuing jet. As the liquid enters the mouthpiece, the jet initially contracts and forms a vena contracta. Beyond this section, the jet expands and may completely fill the mouthpiece before leaving the outlet.

The pressure at the vena contracta becomes lower than atmospheric pressure, creating a partial vacuum inside the mouthpiece. This effect increases the discharge through the opening compared to a simple orifice operating under the same head.

The Mouthpieces experiment studies this phenomenon and determines the coefficient of discharge of the mouthpiece.

Everyday Intuition

The principle of a mouthpiece can be observed in many practical situations.

• Water flowing through a short nozzle attached to a tank.
• Garden irrigation outlets.
• Industrial discharge pipes.
• Hydraulic control valves.

Adding a short tube to an opening changes the flow pattern and can increase the amount of liquid discharged without increasing the available head.

The Mouthpieces experiment demonstrates this practical hydraulic behaviour under controlled laboratory conditions.

Experimental Relevance

The objective of the Mouthpieces experiment is to study the discharge of water through a cylindrical mouthpiece and determine its coefficient of discharge.

The experiment involves:

• Maintaining a constant head of water,
• Measuring the actual discharge,
• Calculating the theoretical discharge,
• Comparing the two values,
• Evaluating the coefficient of discharge.

The experiment also illustrates the formation of the vena contracta and the development of a partial vacuum inside the mouthpiece, which distinguishes mouthpiece flow from simple orifice flow.

Mathematical Formulation

Applying Bernoulli's theorem between the free surface of the tank and the outlet of the mouthpiece,

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

For a large tank open to the atmosphere,

• Pressure at the free surface and outlet is atmospheric,
• Velocity at the free surface is negligible,
• The difference in elevation equals the head of water, $H$.

The theoretical velocity of discharge is

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

The theoretical discharge is

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

where

• $Q_t$ = Theoretical discharge,
• $A$ = Cross-sectional area of the mouthpiece.

Because of friction and other practical effects,

$$Q_a<CQ_t,$$

and the actual discharge is

$$Q_a=C_dQ_t.$$

The coefficient of discharge is

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

where

• $Q_a$ = Actual discharge,
• $Q_t$ = Theoretical discharge.

For an external cylindrical mouthpiece running full, the coefficient of discharge is generally higher than that of a simple sharp-edged orifice because of the partial vacuum formed inside the mouthpiece.

Application to the Mouthpiece Apparatus

The experimental apparatus consists of

• A water tank,
• An external cylindrical mouthpiece,
• A head measuring arrangement,
• A measuring tank for collecting water.

Water is maintained at a constant head and allowed to flow through the mouthpiece.

As the water enters the mouthpiece,

• The jet contracts,
• A vena contracta is formed,
• The pressure at the vena contracta falls below atmospheric pressure,
• The jet expands and fills the mouthpiece,
• Water emerges from the outlet with increased discharge.

The actual discharge is determined experimentally by collecting water over a known period of time.

The theoretical discharge is calculated using Bernoulli's theorem, and the coefficient of discharge is obtained by comparing the theoretical and actual values.

A mouthpiece may operate in two modes:

Running Free

The jet contracts and does not completely fill the mouthpiece.

Running Full

The jet expands after the vena contracta and fills the entire mouthpiece, producing a greater discharge.

The present experiment generally considers the running-full condition.

Engineering Significance

Mouthpieces are widely used where controlled discharge of liquids is required.

Important applications include:

• Reservoir outlets,
• Storage tanks,
• Water distribution systems,
• Hydraulic machinery,
• Irrigation structures,
• Industrial flow-control systems,
• Laboratory hydraulic equipment.

The Mouthpieces experiment demonstrates how a simple modification to an orifice can significantly influence discharge characteristics and provides practical insight into the design of hydraulic flow-control devices.