Question

(SI units) Molten metal is poured into the pouring cup of a sand mold at a steady rate of 400 cm3/s. The molten metal overflows the pouring cup and flows into the downsprue. The cross section of the sprue is round, with a diameter at the top = 3.4 cm. If the sprue is 20 cm long, determine the proper diameter at its base so as to main- tain the same volume flow rate.

Answer 1

diameter of the sprue at the bottom is 1.603 cm

Step-by-step explanation:

Given data;

Flow rate, Q = 400 cm³/s

cross section of sprue: Round

Diameter of sprue at the top
`d_(top)` = 3.4 cm

Height of sprue, h = 20 cm = 0.2 m

acceleration due to gravity g = 9.81 m/s²

Calculate the velocity at the sprue base

`V_(base)` = √2gh

we substitute

`V_(base)` = √(2 × 9.81 m/s² × 0.2 m )

`V_(base)` = 1.98091 m/s

`V_(base)` = 198.091 cm/s

diameter of the sprue at the bottom will be;

Q = AV = (π
`d_(bottom)^2`/4) ×
`V_(base)`

`d_(bottom)` = √(4Q/π
`V_(base)`)

we substitute our values into the equation;

`d_(bottom)` = √(4(400 cm³/s) / (π×198.091 cm/s))

`d_(bottom)` = 1.603 cm

Therefore, diameter of the sprue at the bottom is 1.603 cm