Question

A mould has downsprue whose length is 20 cm and the cross sectional area at the base of the downsprue is 1 $c{m}^2$. The downsprue feeds a horizontal runner leading into the mould cavity of volume 1000 $c{m}^3$. The time required to fill the mould cavity will be

• A. $\text{5.05 s}$
• B. $\text{4.05 s}$
• C. $\text{6.05 s}$
• D. $\text{7.25 s}$

Answer 1

The correct option is A $\text{5.05 s}$

$\text{Length of sprue, h = 20 cm = 0.2 m}$

$\text{Area of down sprue, A = 1}c{m}^2={10}^{-4}{m}^2$

$\text{Volume of mould cavity = 1000}c{m}^3={10}^{-3}{m}^3$

$\text{Velocity at base of sprue,}$

$V=\sqrt{2gh}=\sqrt{2\times 9.81\times 0.2}=1.98m/s$

$\text{Let t is time of filling the mould cavity,}$

$t_f=\frac{V_m}{A_g{V}_g}=\frac{{10}^{{}^{-3}}}{{10}^{-4}\times \sqrt{2\times 9.81\times 0.2}}=5.05s$