Question

A cylinder with a height-to-diameter ratio of unity solidifies in 10 minutes in a sand casting operation. What is the solidification time if the cylinder height is doubled? What is the time if the diameter is doubled? Use n=1.5.

Answer 1

a) 13 mins

b) 18 mins

Step-by-step explanation:

solidification time = 10 minutes

height-to-diameter ratio = 1

applying the expression for calculating solidification time

t = B
`((V)/(A) ) ^n` --------- ( 1 )

n = 1.5

B = ?

t = 10 minutes

V =
`(\pi d^2)/(4) H`

A =
`(\pi d^2)/(2) + \pi dH`

back to equation 1

making B subject of the formula ; B =
`(147)/(d^(1.5) )`

a) Determine the solidification time if the cylinder height is doubled

t = B
`((V)/(A) ) ^n`

substitute : B =
`(147)/(d^(1.5) )` , H = 2D , V =
`(\pi d^2)/(4) H` , A =
`(\pi d^2)/(2) + \pi dH` , n = 1.5

therefore ; t ( solidification time when height is doubled ) ≈ 13 mins

b) Determine the time if the diameter is doubled

t = B
`((V)/(A) ) ^n`

substitute ; B =
`(147)/(h^(1.5) )` , D = 2H , n = 1.5 , V =
`(\pi d^2)/(4) H`, A =
`(\pi d^2)/(2) + \pi dH`

therefore ; t ( solidification time when diameter is doubled ) ≈ 18 mins