Question

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

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

Applying Bernoulli's theorem,

$\frac{P}{\rho }+\frac{1}{2}(v^{\prime }{)}^2+gh=\frac{P}{\rho }+\frac{1}{2}{v}^2+0$

Where $v^{\prime }$ is velocity of all surfaces of liquid and v is velocity of efflux.

From equation of continuity

$\Rightarrow v^{\prime }=\frac{av}{A}$

Av' = av

$\therefore \frac{1}{2}{\left(\frac{av}{A}\right)}^2+gh=\frac{1}{2}{v}^2$

$\Rightarrow v=\sqrt{2gh}\sqrt{\left(\frac{A^2}{A^2-a^2}\right)}$