A large open tank has two holes in the walls. One is a square hole of side L at a depth y from the top and 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 holes are the same. then, R is equal to:

Question

A  large open tank has two holes in the walls. One is a square hole of side L      at a depth y      from the top and  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 holes are the same. then, R      is equal to:

Infinity Learn · Accepted Answer

Velocity of efflux when the hole is at depth h     , $$v=2gh$$       Rate of flow of water from square hole,$$Q1=a1v1=L22gy$$     Rate of flow of water from circular hole,$$Q2=a2v2=$$π$$R22g(4y)$$     According to problem,$$L22gy=$$π$$R22g(4y)$$     or $$R=L2$$π

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