Question

For sand-casting a steel rectangular plate with dimensions 80 mm × 120 mm × 20 mm, a cylindrical riser has to be designed. The height of the riser is equal to its diameter. The total solidification time for the casting is 2 minutes. In Chvorinov's law for the estimation of the total solidification time, exponent is to be taken as 2. For a solidification time of 3 minutes in the riser, the diameter (in mm) of the riser is (correct to two decimal places).

• A. 51.84

Answer 1

The correct option is A 51.84
Given: Casting size = 80 × 120 × 20 $m{m}^3$

$(t_s{)}_{casting}=2min;{\left(t_s\right)}_{riser}=3min$

${\left(t_s\right)}_{casting}=k{\left(\frac{V}{A}\right)}^2$

$2=k{\left(\frac{80\times 120\times 20}{2(80\times 120+120\times 20+20\times 80)}\right)}^2$

$k=0.040138min/n{m}^2$

$Riser:{\left(t_s\right)}_{riser}=k{\left(\frac{V}{A}\right)}^2$

$3=0.040138{\left(\frac{V}{A}\right)}^2$

$\left(\frac{V}{A}\right)=8.64$

$\frac{V}{A}=\frac{\frac{\pi }{4}{d}^{2}h}{2\frac{\pi }{4}{d}^2+\pi dh}$

For riser if h = d then $\frac{V}{A}=\frac{d}{6}$

$\frac{d}{6}=8.64$
h = d = 51.84 mm