The area of two holes `A` and `B` are `2a` and `a`, respectively, The holes are at height `(H//3) and (2H//3)` from the surface of water. Find the correct option(s):

Options

A. the velocity of efflux at hole B is 2 times the velocity of efflux at hole A
B. The velocity of efflux at hole B is `sqrt(2)` times the velocity of efflux at hole A
C. the discharge is same through both the holes
D. the discharge through hole A is `sqrt(2)` times the discharge through hole B.

Answer

B, D

Explanation

`V_(A)j=(2g.(H)/(3))^(1//2),V_(B)=((4gH)/(3))^(1//2)`
`=sqrt(2)((2gH)/(3))^(1//2)=sqrt(2)V_(A),Q_(A)=V_(A)(2a)`
and `Q_(B)=V_(B)(a)=V_(A)sqrt(2)a,(Q_(A))/(Q_(B))=sqrt(2)`