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A mouthpiece is a short length of pipe or tube attached to the tank or vessel, used to determine the rate of flow of fluid. It is an extended form of an orifice with a length equal to 2 to 3 times the diameter of the orifice.

Mouthpiece in Fluid Mechanics
Figure-1: Mouthpiece used in Fluid Mechanics

This article explains the discharge equation for a fluid passing through different types and conditions of mouthpieces.

Classification of Mouthpiece

The mouthpieces can be classified based on the following categories:

  1. Classification based on the position of the mouthpiece
  2. Classification based on the shape of the mouthpiece
  3. Classification based on the nature of discharge at the outlet of the mouthpiece

1. Based on Position of Mouthpiece

1.1 Internal Mouthpiece

Internal mouthpieces are pipes fixed inside the tank or the vessel to measure the rate of flow.

1.2 External Mouthpiece

External mouthpieces are pipes that are fixed externally and project out of the vessel or tank walls.

 Internal and External Mouthpiece
Figure-2: Internal and External Mouthpiece

2. Based on Shape of Mouthpiece

When the jet of liquid enters the mouthpiece as shown in Figure-1, it contracts and reaches a point where the area is minimum. This point is called the vena-contracta. Based on the shape, mouthpieces can be classified as:

2.1 Cylindrical Mouthpiece

When the jet of liquid enters a cylindrical mouthpiece as shown in Figure-3, it contracts and forms vena-contracta at section c-c. Beyond the section c-c, the jet of fluid expands and fills the mouthpiece.

Here, the actual discharge is given by:

 Cylindrical Mouthpiece
Figure-3: Cylindrical Mouthpiece

2.2 Convergent-Divergent Mouthpiece

In the case of a convergent-divergent mouthpiece, the jet of fluid converges up to vena-contracta and then diverges as shown in Figure-4. Here, just like in the cylindrical mouthpiece, the loss of energy due to sudden enlargement is eliminated. The coefficient of discharge of a convergent-divergent mouthpiece is unity.

Convergent-Divergent Mouthpiece
Figure-4: Convergent-Divergent Mouthpiece

Actual discharge through mouthpiece is given by,

3. Based on Discharge at Outlet

An internal mouthpiece is a short cylindrical tube that projects inwardly towards the tank. It is also called as Re-entrant or Borda’s mouthpiece. Based on the condition of discharge at the outlet, it is classified as:

Re-entrant or Borda’s mouthpiece
Figure-5: Re-entrant or Borda’s mouthpiece

3.1 Borda’s Mouthpiece Running Free

A Borda’s mouthpiece is said to run free when the jet of water coming out of the mouthpiece after the formation of vena-contracta does not touch the sides of the mouthpiece.

For an internal mouthpiece running free, the coefficient of discharge, Cd = 0.5

3.2 Borda’s Mouthpiece Running Full

A Borda’s mouthpiece is said to run fully when the jet of water coming out of the mouthpiece after vena-contracta touches the sides of the mouthpiece.

For an internal mouthpiece running full, the coefficient of discharge, Cd = 0.707.

FAQs

What is a mouthpiece in fluid mechanics?

Mouthpiece is a short length of pipe or tube attached to the tank or vessel containing the fluid. It is used to determine the rate of flow or discharge of a fluid.

What is a convergent-divergent mouthpiece?

In a convergent-divergent mouthpiece, the jet of fluid initially diverges to form vena-contracta and then diverges. This process eliminates the loss of energy due to the sudden enlargement, unlike cylindrical mouthpiece. The coefficient of discharge of a convergent-divergent mouthpiece is unity.

What is a re-entrant mouthpiece?

A re-entrant mouthpiece or Borda’s mouthpiece is an internal mouthpiece which is a short cylindrical tube that is projected inwardly towards the tank.

What is coefficient of discharge of an internal mouthpiece?

The coefficient of discharge of an internal mouthpiece running free is, Cd = 0.5
The coefficient of discharge of an internal mouthpiece running full is, Cd = 0.707

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