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# Submerged Orifice

Discharge through a submerged orifice
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### Key Facts

Gyroscopic Couple: The rate of change of angular momentum () = (In the limit).
• = Moment of Inertia.
• = Angular velocity
• = Angular velocity of precession.

Blaise Pascal (1623-1662) was a French mathematician, physicist, inventor, writer and Catholic philosopher.

Leonhard Euler (1707-1783) was a pioneering Swiss mathematician and physicist.

## Discharge Through A Wholly Drowned Orifice

When the outlet side of an orifice is beneath the surface of liquid it is known as a wholly submerged orifice as shown in fig.1. In such orifices, the coefficient of contraction is equal to one.

Consider a wholly drowned orifice discharging water as shown in fig.1.

Let,
• = Height of water (on the upstream side) above the top of the orifice
• = Height of water (on the upstream side) above the bottom of the orifice
• = Difference between the two water levels on either side of the orifice
• = Coefficient of discharge
• = Coefficient of velocity
• = Coefficient of contraction

Area of orifice =

We know that the theoretical velocity of water through the strip =

Actual velocity of water =

From the relation of hydraulic coefficients we know that,

Since coefficient of contraction is 1 in this case, therefore

Actual velocity of water =

Now the discharge through the orifice,

= Area of orifice Actual velocity

If depth of the drowned orifice (d) is given instead of and , then in such cases the discharge through the wholly drowned orifice is:

Example:
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##### Example - Discharge through a wholly drowned orifice
Problem
A drowned orifice 1.5m wide and 0.5m deep is provided in one side of a tank. Find the discharge in liters/s through the orifice, if the difference of water levels on both the sides of the orifice be 4m. Take  = 0.64.
Workings
Given,
•  = 1.5m
•  = 0.5m
•  = 4m
•  = 0.64




Solution
Discharge = 4250 liters/s