question_answer

A square hole of side length i is made at a depth of h and a circular hole of radius r is made at a depth of 4h from the surface of water in a water tank kept on a horizontal surface. If \[\ell <<h,r<<h\]and the rate of water flow from the holes is the same, then r is equal to             [JEE ONLINE 07-05-2012]

A) \[\frac{\ell }{\sqrt{2\pi }}\]         

B)      \[\frac{\ell }{\sqrt{3\pi }}\]

C) \[\frac{\ell }{3\pi }\]                   

D)      \[\frac{\ell }{2\pi }\]

Correct Answer: A

Solution :

[a] As(Principle of continuity)

or,

(Efflux velocity  )

or