A cylinder with a diametertoheight ratio of 1 solidifies in

A cylinder with a diameter-to-height ratio of 1 solidifies in four minutes in a sand casting operation. What is the solidification time if the cylinder height is tripled? What is the time if the diameter is tripled?

Solution

ANSWER:-

Cylinder volume V = D 2 L/4

Cylinder area A = 2D 2 /4 + DL

T TS = C(V/A) 2 = C((D 2 L/4)/ (2D 2 /4 +DL)) 2 = C((DL)/ (2D+4L)) 2

Because height-to-diameter ratio is unity, so L=D

T TS = C(V/A) 2 = C(D/6) 2 = CD 2 /36=4 min C=144/ D 2

When height is doubled, L’=2L, D’=D

T TS = C((D’L’)/ (2D’+4L’)) 2 = (144/ D 2 )(D/5) 2 =5.