Time of emptying a circular horizontal 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 circular horizontal tank, containing liquid and having an orifice at its bottom as shown in figure. Let,
- = Radius of the tank
- = Initial height of the liquid
- = Final height of the liquid
- = Area of the orifice
- = Length of the tank
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)
Substituting this value of in equation (4)
Now the total time (T) required to bring the liquid level from to may be found out by integrating the above equation between the limits to . Therefore
Example - Time of emptying a circular horizontal tank
An orifice is fitted at the bottom of a boiler drum for the purpose of emptying it. The drum is horizontal and half full of water. It is 10m long and 2m in diameter. Find out the time required empty the boiler, if the diameter of the orifice is 150mm. Assume coefficient of discharge as 0.6.
- Length of boiler, = 10m
- Diameter of boiler, = 2m
- Diameter of orifice, = 150mm = 0.15m
- = 0.6
So time required to empty the boiler,
This boiler is half full at the time of commencement, and it is to be completely emptied. Then putting and in the above equation,
Time to empty the boiler = 8 min 38 s