A liquid having area of free surface A and has an orifice at a depth of h with an area a, below the liquid surface, then find the velocity v of flow through the orifice

Options

A. `v=sqrt(2gh)`
B. `v=sqrt(2gh)sqrt((A^(2))/(A^(2)-a^(2)))`
C. `v=sqrt(2gh)sqrt((A)/(A-a))`
D. `v=sqrt(2gh)sqrt((A^(2)-a^(2))/(A^(2)))`

Explanation

Appliying Bernoulli's therorem,
`(p)/(rho)+(1)/(2)(v')^(2)+gh=(p)/(rho)+(1)/(2)v^(2)+0`
wher v' is velocity of all surface of liquid and v is velocity of efflux.
From equations of continuity
`Av'avrArrv'=(av)/(A)`
`(1)/(2)((av)/(A))^(2)+gh=(1)/(2)v^(2)`
`v=sqrt(2gh)sqrt((A^(2)-a^(2))/(A^(2)))`