Answer:
Optimal aspect ratio = 1
Explanation:
From Chvorinov's Rule,
[tex] T = c [\frac{volume}{surface are}]^n [/tex]
Where
T = solidification time
c = mold constant
[tex] Volume = \frac{pi D^2 h}{4}[/tex]
[tex] Surface areaA= pi Dh[\frac{2pi D^2}{4}[/tex]
For the riser to have the longest solidification time:
We have: D = h
[tex] V = \frac{pi D^3}{4} [/tex]
[tex] A = pi Dh[\frac{2pi D^2}{4}] = 1.5D^2 pi[/tex]
Therefore,
[tex] \frac{V}{A} = \frac{\frac{pi D^3}{4}}{1.5D^2 pi} [/tex]
[tex] \frac{V}{A} = \frac{D}{6} [/tex]
To have to longest solidification time, D = h
Therefore the best aspect ratio would be,
[tex] \frac{D}{h} = 1 [/tex]
