To develop the problem it is necessary to apply the concepts of Volume calculation, area calculation and the solidification time.
The solidification time equation is given by
[tex]TST = C_m (\frac{V}{A})^n[/tex]
Where,
TST = Total solidification time
V = Volume of the casting
A = Surface area of casting
n = Exponent with typical value=2
[tex]C_m[/tex] = Mold constant
We do not have the volume or area, so we proceed to calculate them with the data we have,
Volume,
[tex]V= \frac{\pi D^2t}{4}[/tex]
[tex]V = \frac{\pi (650)^2(16)}{4}[/tex]
[tex]V = 5309292mm^3[/tex]
Area,
[tex]A= 2\pi \frac{D^2}{4}+\pi Dt[/tex]
[tex]A =\frac{\pi 650^2}{2}+\pi(650)(16)[/tex]
[tex]A = 696334mm^2[/tex]
Replacing at the previous equation we have
[tex]TST = C_m (\frac{V}{A})^n[/tex]
[tex]TST = 2.2(\frac{5309292}{696334})^2[/tex]
[tex]TST = 127.897s[/tex]
[tex]TST = 127.897s(\frac{1min}{60s})[/tex]
[tex]TST = 2.13min[/tex]
Therefore it will take the casting to solidify around to 2.13min
