The flow rate of liquid metal into the downsprue of a mold is 500 cm3/s. The cross-sectional area at the top of the sprue is 8 cm2, and the height of the sprue is 15 cm. What should the cross-sectional area be at the base of the sprue in order to avoid separation during pouring of the molten metal

The area at the base should be 2.91cm²

Explanation:

The separation of the molten metal may occur when the pressure of the flowing liquid falls below the atmospheric pressure and the air entrapped inside the mold tries to escape but rather gets rapped inside the casting (which is solidifying) causing the liquid to separate and the casting to be porous.

The velocity at the bottom of the sprue is written as V = √ (2gh), where g is the acceleration due to gravity and h is the height of the sprue

V = √ (2 x 9.81 x 100 x 15) = 171.6 cm² (Multiplying by 100 to convert 9.81 m/s to cm/s)

The expression for flow rate is Q = VA where V is the velocity as calculated above and A is the area

500 = 171.6 x A, solving for A we get A = 500/171.6 = 2.91cm²

The cross - sectional Area at the base of the sprue should be 2.91cm² to avoid separation of the molten metal.