Time of emptying a square, rectangular or circular tank through an orifice at its bottom
Key FactsGyroscopic 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.
OverviewConsider a square, rectangular or circular tank of uniform cross-sectional area, containing some liquid and having an orifice at its bottom. Let,
- A = Surface area of the tank
- = Initial height of the liquid
- = Final height of the liquid
- a = Area of the orifice
The value of dh is taken as negative, as its value will decrease with the increase in discharge.We know that the volume of liquid that has passed through the orifice in time dt, = Coefficient of discharge Area Theoretical velocity Time 2) and (3)
4) between the limits to i.e.,
Taking minus out from the bracket (as is greater than )
If the tank is to be completely emptied, then putting = 0 in this equation, we get
Example - Time of emptying circular tank through an orifice at its bottom
A circular water tank of 4m diameter contains 5m deep water. An orifice of 400mm diameter is provided at its bottom. Find the time taken for water level fall from 5m to 2m. Take = 0.6
- Diameter of circular tank, = 4m
- Diameter of orifice, = 400mm = 0.4m
- = 5m
- = 2m
- = 0.6
and the area of orifice,
Time taken to fall the water level,
Time taken to fall the water level = 61.9 s