The transfer of liquid from one vessel into another
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.
OverviewWhen two vessels,containing liquid, are connected together by means of an orifice, the liquid will flow from the vessel with a higher level to the vessel with a lower level irrespective of their areas. In such a case the liquid level will fall in one vessel with a corresponding rise in the other. The orifice, through which the flow takes place, is a drowned one and the liquid head causing flow will be the difference between the two liquid levels. Consider two tanks connected at their bottom by a small orifice as shown in figure. Let,
- = Area of the larger vessel
- = Area of the smaller vessel
- = Area of the orifice
- = Initial difference between the liquid levels of the two vessels
- = Final difference between the liquid levels of the two vessels
- = Time, in seconds, required to bring the difference of liquid levels from to
(-) negative sign of dh is taken, as the value of h will decrease as the discharge will increase
2) and (3),
Now the total time (T)required to bring the differences of liquid levels from to may be found out by integrating the above equation between the limits and i.e.,
Taking minus sign out of the bracket as is greater than
Example - Time of Flow of Liquid from One Vessel into Another
A tank 6m long and 1.5m wide is divided into two parts, so that area of one part is 7.2m2 and that of the other is 1.8m2. The water level in the larger part is 3m higher than in the lower one. Find the time taken for difference in water levels to reach 1m if the water flows through a submerged orifice of 75mm diameter, in the partition. Assume coefficient of discharge for orifice as 0.6.
- Size of the tank = 6 1.5 = 9 m2
- = 7.2 m2
- = 1.8 m2
- = 3m
- = 1m
- = 75mm = 0.075m
- = 0.6
So, time taken for the difference of water levels,
Time taken for the difference of water level = 3 min