The discharge through a convergent mouthpiece is __________ the d

SOLUTION

Concept:

Mouthpiece:

A mouthpiece is an attachment in the form of a short length of the tube or pipe.

It is two or three times its diameter in length.

It is fitted to the tank containing fluid, through which liquid is discharged.

Classification of mouthpiece

1.According to the position of the mouthpiece

• External mouthpiece: If the pipe projects outward from the wall of the reservoir, then it is called external mouthpiece.
• Internal mouthpiece: If the pipe projects inside the tank (i.e. fixed internally), then it is called internal mouthpiece. The internal mouthpiece is also called Borda’s mouthpiece or reentrant mouthpiece.

2.According to the shape of the mouthpiece

• Cylindrical mouthpiece: If the mouthpiece has a uniform circular cross-section area, then it is called cylindrical mouthpiece.
• Convergent mouthpiece: If the flow area of the mouthpiece decreases from inlet to outlet, then it is called convergent mouthpiece.
• Divergent mouthpiece: If the flow area of the mouthpiece increases from inlet to outlet, then it is called divergent mouthpiece.

3.The classification based on the nature of discharge is only for the internal mouthpiece.

• Mouthpiece running free: If the jet after contraction doesn't touch the sides of the orifice, then it is called mouthpiece running free.
• Mouthpiece running full: If the jet after contraction expands and fill the whole mouthpiece, then it is called mouthpiece running full.

Calculation:

Discharge through convergent mouthpiece is given by:

\({Q_c} = a\sqrt {2gH}\)

where, a = area of the orifice, H = height of the liquid above the mouthpiece

Discharge through internal mouthpiece is given by:

\({Q_i} = 0.5a\sqrt {2gH}\)

∴ Q_c = 2Q_i