Question

The figure shows a pouring arrangement for casting of a metal block. Frictional losses are negligible. The acceleration due to gravity is 9.81 $m/s^2$. The time (in s, round off to two decimal places) to fill up the mould cavity of size (40 cm × 30 cm × 15 cm) is

• A. 28.92

Answer 1

The correct option is A 28.92
$\text{Volume of mould cavity = 40 × 30 × 150}c{m}^3$

$\text{= 18000}c{m}^3$

$\text{Apply Bernoulli's equation at point 1 and 3}$

$\frac{P_{atm}}{\rho g}+\frac{V_1^2}{2g}+z_1=\frac{P_{atm}}{\rho g}+\frac{V_3^2}{2g}+0$

$\text{Assume}{V}_1=0$

$V_3=\sqrt{2g{z}_1}=\sqrt{2\times 981\times 20}=198.09cm/s$

$\text{Moulding filling time}\left(t_1\right)=\frac{\text{Volume}}{V_2\times A_2}$

$=\frac{18000c{m}^3}{198.09cm/s\times \frac{\pi }{4}{\left(2\right)}^{2}c{m}^2}=28.92\sec$