Question

A mould having dimensions 100 mm × 90 mm × 20 mm is filled with molten metal through a gate with height h and C.S. are A, the mould filling time is $t_1$. The height is now quadrupled and the cross-sectional area is halved. The corresponding filling time is $t_2$. The ratio $t_2/t_1$ is

• A. $2$
• B. $1/\sqrt{2}$
• C. $1$
• D. $\sqrt{2}$

Answer 1

The correct option is C $1$

$t_1=\frac{\text{Volume of cavity}}{\text{Flow rate}}=\frac{V}{A\times \sqrt{2gh}}$

$\text{For}{t}_2$
$h_2=4h,A_2=\frac{A}{2}$

$t_2=\frac{V}{\frac{A}{2}\times \sqrt{2\times g\times 4h}}$

$t_2=\frac{V}{A\sqrt{2gh}}=t_1$

$\frac{t_1}{t_2}=1$