Question

Water is filled in a cylindrical container to a height of 3 m. The ratio of the cross-section area of the orifice and the beaker is 0.1. The square of the speed of the liquid coming out from the orifice is

• A. 60.6
• B. 50.5
• C. 51
• D. 52

Answer 1

The correct option is A

60.6

(a) Applying continuity equation at 1 and 2, we have $A_1{V}_1$ = $A_2{V}_2$

Furthur applying Bernoullis equation at these two points, We have

$p_{\circ }+\rho gh+\frac{1}{2}\rho V_1^2=p_{\circ }+0+\frac{1}{2}\rho V_2^2$

Solving eqs. (i) and (ii),

$v_2^2=\frac{2gH}{1-\frac{A_2^2}{A_1^2}}$

We have

Substituting the values

We have

$v_2^2=\frac{2\times 10\times 3}{1-(0.1{)}^2}=60.6m^2/s^2$