Properties Of Solids And Liquids Question 245
Question: A large open tank has two holes in the wall. One is a square hole of side L at a depth y from the top and the other is a circular hole of radius R at a depth 4y from the top. When the tank is completely filled with water, the quantities of water flowing out per second from both the hole are the same. Then R is equal to
Options:
A) $ 2\pi L $
B) $ \frac{L}{\sqrt{2\pi }} $
C) $ L $
D) $ \frac{L}{2\pi } $
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Answer:
Correct Answer: B
Solution:
[b] Velocity of efflux when the hole is at depth h. $ v=\sqrt{2gh} $
Rate of flow of water form square hole $ Q _{1}=a _{1}v _{1}=L^{2}\sqrt{2gy} $
Rate of flow of water from circular hole $ Q _{2}=a _{2}v _{2}=\pi R^{2}\sqrt{2g(4y)} $
According to problem, $ Q _{1}=Q _{2} $
$ \Rightarrow L^{2}\sqrt{2gy}=\pi R^{2}\sqrt{2g(4y)}\Rightarrow R=\frac{L}{\sqrt{2\pi }} $
