A 100mm thick square plate and right circular cylinder with

A 100-mm thick square plate and right circular cylinder with a radius of 100-mm and a height of 25-mm have the same volume. Which shape will take more time to solidify? Use n = 2. If each is to be cast with the use of a cylindrical riser, will each part require the same size riser to ensure proper feeding? Explain.

Solution

First note that it is important for the riser to solidify after the casting has solidified. A casting that solidifies rapidly would be expected to require a smaller riser than one that solidifies over a longer period of time. Let’s now calculate the relative solidification times. For the cylindrical part, we have

V = r2h = (4)2 (2) = 100.5 in3

A = 2r2 + 2rh = 2(4)2 + 2(4)(2) = 150.8 in2

Thus

  tcylinder = C(100.5/150.8)2 = 0.444C

For a square plate with sides L and height h, we have

V = 100.5 = L 2h = L 2 (4), or L = 5.0 in.

A = 2L 2 + 4Lh = 130 in2

Thus

  tplate = C(100.5/130)2 = 0.59C

Therefore, the cylindrical casting will take less time to solidify and hence will require a smaller riser.

( convert mm to inch ------ 100mm=4inch )