This article provides an overview of how to measure discharge using a mouthpiece? in fluid mechanics, covering fundamental principles and practical applications.
A mouthpiece is a short length of pipe or tube attached to the tank or vessel, used to find 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.
This guide covers 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:
- Classification based on the position of the mouthpiece
- Classification based on the shape of the mouthpiece
- 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.
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 can be expressed as:
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 because of sudden enlargement is eliminated. The coefficient of discharge of a convergent-divergent mouthpiece is unity.
Actual discharge through mouthpiece can be expressed as,
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:
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.