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Consider casting sand mold of the piece shown in the figure. The dimensions are in centimeters.

(i) The molten metal overflows the pouring cup of the mold and flows down the sprue (downsprue) at a constant rate of 2000 cm3/s. The cross section of the sprue is circular, with a diameter of 6 cm at the top. If the sprue has a length of 50 cm, what is the appropriate diameter in the lower part of the sprue, so as to maintain a constant flow rate of molten metal?

(ii) Calculate the time needed to fill the cavity in the mold with molten metal.

(iii) If the mold constant is 3.5 min/cm2, calculate the solidification time necessary to melt the part.

(iv) For a cylindrical riser of 15 cm radius, calculate the critical height of the riser. That is the height at which the solidification time of the metal in the riser is equal to the solidification time of the metal in the mold cavity.

(v) What should be the height of the riser so that the solidification time of the metal in it is 25% longer than that of the metal in the mold cavity?

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