Answer :
Answer:
d = 2.711
H = 4.06 inch
Explanation:
Given Data:
length = 1.5 times of diameter of cylinder
square plate side = 12 inch, thickness = 1.1 inch
mold constant = 13.0 min/in^2
Casting volume
[tex]V= tl^2[/tex]
t is thickness and L is length
substitute t = 1.1 inch, L =12 inch
[tex]v = 1.1\times 12^2 = 158.4 inc^3[/tex]
casting area
[tex]A = 2L^2 + 4Lt[/tex]
[tex]A = 2\times 12^2 + 4\times 12\times 1.1[/tex]
A = 340.8 in^2
Ratio between casting volume and area
[tex]\frac{v}{A} = {158.4}{340.8} = 0.464[/tex]
Total solidification time TST using chvorinov rule
[tex]TST = Cm [\frac{V}{A}]^2[/tex]
Cm is mold constant
[tex]TST = 13\times 0.464^2[/tex][/tex]
TST = 2.798 min
TST for riser
riser [tex]TST = 1.30\times2.798 = 3.63[/tex]
Riser volume [tex]v = \frac{\piD^2 H}{4}[/tex]
[tex]v = 0.25\pi\times D^2(1.5D)[/tex]
[tex]v = 0.375\pi D^3[/tex]
Riser area
[tex]A =\frac{2\pi D^2}{4} + \pi DH[/tex]
[tex]A = 0.5\pi D^2 +1.5\pi D^2[/tex]
[tex]A = 2\pi D^2[/tex]
RATIO of riser volume and area
[tex]\frac{v}{A} = \frac{0.375\piD^3}{2.0\pi D^2} = 0.1875 D[/tex]
TST for riser
[tex]TST = Cm [\frac{v}{A}]^2
[tex]TST= 13 \times (0.1875 D)^2 [/tex]
[tex]3.36 =13\times (0.1875 D)^2[/tex]
d = 2.711
[tex]H = 1.5 \times 2.711 =4.06 inc[/tex]
H = 4.06 inch