Question

A rectangular plate casting has dimensions 200mm x 100mm x 20mm. The riser for this sand casting mold is in the shape of a sphere. The casting takes 3.5mins to solidify. Calculate the diameter of the riser so that it takes 20% longer for the riser to solidify

Answer 1

Diameter of riser =6.02 mm

Step-by-step explanation:

Given that

Dimensions of rectangular plate is 200mm x 100mm x 20mm.

Volume of rectangle V= 200 x 100 x 20
`mm^3`

Surface area of rectangle A

A=2(200 x 100+100 x 20 +20 x 200)
`mm^2`

So V/A=7.69

We know that

Solidification times given as

`t=K\left((V)/(A)\right)^2` -----1

Lets take diameter of riser is d

Given that riser is in spherical shape so V/A=d/6

And

Time for solidification of rectangle is 3.5 min then time for solidificartion of riser is 4.2 min.

Lets take
`(V)/(A)=M`

`(M_(rac))/(M_(riser))=(7.69)/((d)/(6))`

Now from equation 1

`(3.5)/(4.2)=\left((7.69)/((d)/(6))\right)^2`

So by solving this d=6.02 mm

So the diameter of riser is 6.02 mm.