A flat plate is to be cast in an open mold whose bottom has

A flat plate is to be cast in an open mold whose bottom has a square shape that is 200 mm by 200 mm. The mold is 40 mm deep. A total of 1,000,000 mm3 of molten aluminum is poured into the mold. Solidification shrinkage is known to be 6.0%, which is a volumetric contraction, not a linear contraction. Table 10.1 lists the linear shrinkage due to thermal contraction after solidification. If the availability of molten metal in the mold allows the square shape of the cast plate to maintain its 200 mm by 200 mm dimensions until solidification is completed, determine the final dimensions of the plate

Solution

we are given initial volume of liquid metal = 1000000 mm^3

we know that when poured into the mold

it will take the shape of the open mold

that is is 200 mm X 200 mm = 40,000 mm^2

now, we can find the starting height of the molten metal

that would be

h= 1000000 / 40000 = 25 mm

since, we know that volumetric solidification shrinkage = 6%

so, we will get

volume after solidification = 1000000(100-6)%

=1000000(94)%=1000000*0.94

=940000

we are given that its base l measures 200 mm X 200 mm because of flow of liquid metal prior to solidification

now, we will find new height = 940000/40000 = 23.5 mm

we are given that linear shrinkage = 1.3%

so, we will get final dimensions of the plate = 200(1-0.013) X200(1-0.013) X23.5(1-0.013)

= 197.40 mm*197.40 mm*23.195 mm...........Answer