The orifice is a small opening in the wall or base of a vessel through which the fluid flows. A mouthpiece is an attachment in the form of a small tube or pipe fixed to the orifice. Its length is usually two or three times the diameter of orifice. It is used to increase the amount of discharge.

### Hydraulic coefficients

- Coefficient of contraction :- It is defined as the ratio of area of jet at vena contracta (the points at which the streamlines first become parallel is called vena contracta) to the area of orifice.
- Coefficient of velocity :- It is defined as the ratio of the actual velocity of the jet at vena contracta to the theoretical velocity.
- Coefficient of discharge(C
_{d}) :- It is defined as the ratio of the actual discharge through the orifice to the theoretical discharge. The coefficient of discharge is equal to the product of coefficient of contraction and coefficient of velocity. - Coefficient of resistance :- It is defined as the ratio of loss of head in the orifice to the head of water available at the exit of orifice.

### Important expressions used in Orifices and Mouthpieces\

#### a) Discharge through a large rectangular orifice

#### b) Discharge through a wholly submerged orifice

#### c) Time required to empty the tank completely through an orifice at the bottom

#### d) Time required to empty the hemispherical tank through an orifice at the bottom

#### e) Discharge through an external mouthpiece

#### f) Discharge through the internal mouthpiece when it is running free

#### g) Discharge through the internal mouthpiece is an internal mouthpiece

NOTE:-- The re-entrant or Borda's mouthpiece is an internal mouthpiece.
- If the jet of the liquid after contraction does not touch the sides of the mouthpiece, then the mouthpiece, is said to be running free. In this case, the length of mouthpiece is equal to diameter of the orifice.
- If the jet of the liquid after contraction expands and fills up the whole mouthpiece, then the mouthpiece is said to be running full. In this case, the length of mouthpiece is more than three times the diameter of orifice

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