A cylindrical blind riser with diameter d and height h,

A cylindrical blind riser with diameter d and height h, is placed on the top of the mold cavity of a closed type sand mould as shown in the figure. If the riser is of constant volume, then the rate of solidification in the riser is the least when the ratio h : d is

v =	π	D²h
	4

h =	4v	...(1)
	πD²

A_s = πDh +	π	D²
	4

A_s = πD	4v	+	π	D² =	4v	+	π	D²
	πD²		4		D		4

For min A_s ,

	dA_s	= 0
	dD

	-4v	+	π	2D = 0 ⇒	4v	=	Dπ
	D²		4		D²		2

v =	πD³	=	π	D²h
	8		4

D = 2h

⇒	h	=	1
	D		2

h : D = 1 : 2