First slide

Fluid dynamics

Question

A cylindrical drum, open at the top, contains 30 liters of water. It drains out through a small opening at the bottom. 10 liters of water comes out in time t₁, the next 10 liters in further time t₂ and the last 10 liters in further time t₃. Then,

Moderate

A

t₁ = t₂= t₃
B

t₁ > t₂> t₃
C

t₁ < t₂< t₃
D

t₂ > t₁= t₃

Solution

Velocity of efflux through of water through the opening, $\large u=\sqrt {2gh}$ . If 'a' be the area of opening, then rate of volume flow of water through the opening $\large Q=a \sqrt {2gh}$ . As water is drained out of the tank, 'h' decreases and hence 'Q' decreases. Hence t₁ < t₂< t₃

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