In a gating system design, a down sprue of 180 mm length has a diameter of 20 mm at its top end. The liquid metal in the pouring cup is maintained up to 60 mm height. The diameter (in mm) of the down sprue at its lower end to avoid aspiration will be:

Concept:

To avoid aspiration in a gating system, the diameter of the downsprue at its bottom should be calculated based on Bernoulli’s equation and the principle of continuity. The flow of molten metal must be such that the pressure at the bottom of the sprue remains atmospheric to prevent air entrainment.

Calculation: 

Given:

Length of downsprue = 180 mm, Diameter at top = 20 mm, Height of liquid metal in pouring cup = 60 mm

Total head (H) = 180 + 60 = 240 mm = 0.24 m

Using Bernoulli’s equation:

\(v = \sqrt{2gH} = \sqrt{2 \times 9.81 \times 0.24} = \sqrt{4.7088} \approx 2.17~\text{m/s} \)

Assuming atmospheric pressure at both ends and negligible velocity at the top due to larger cross-section area:

Apply continuity equation: \(A_2 v_2 = A_3 v_3\)

Let D₂ = 20 mm, and assume v₂ negligible, then use ratio of areas:

\(D_3 = D_2 \times \sqrt{\frac{v_2}{v_3}} = 20 \times \sqrt{\frac{1.085}{2.17}} = 20 \times \sqrt{0.5} = 20 \times 0.707 \approx 14.14~\text{mm}\)