Mild steel is being cast into a cylindrical solid which is 60 cm high and has a diameter of 12 cm. The cylinder is upright in the mold. The mold is bottom-gated (see class notes for geometry). There is a vent on the top of this part which extends to the top of the mold, but is so thin that no liquid metal can enter it. You wish to fill the part with no aspiration. The pouring basin is 2 cm tall and is completely filled during pouring. The height from the bottom of the pouring basin to the top of the part is 8 cm. The sprue is conical; the gate and runner are cylindrical. Determine the following: a) diameter of the gate b) diameter of the runner c) diameter of the top of the sprue d) diameter of the bottom of the sprue e) the filling time of the mold Material Properties Data for solid materials (room temperature) Density (p) Thermal conductivity Material Specific heat (C) (kJ/kg-C) (kg/m) (k) (W/m-C) Sand 1.16 1500 0.60 Aluminum 0.90 2700 222 Nickel 0.44 8910 92 Magnesium 1.02 1740 156 Copper 0.385 8960 394 Gray cast iron 0.441 7125 53 Steel (mild) 0.434 7832 59 Tin 0.21 7280 64 Zinc 0.384 7135 112 Data for liquid materials Material Melting Latent heat of Specific heat Thermal Viscosity (u) point (C) solidification (C) (kJ/kg-C) Conductivity (mPa-s) (fusion) (Hf) (k) (W/m- (kJ/kg) C) Aluminum 660 396 1.05 94 1.3 Nickel 1453 297 0.73 53 4.9 Magnesium 650 384 1.38 139 1.25 Copper 1083 220 0.52 166 4.0 Gray cast 1251 211 0.34 26 2.25 iron Steel (mild) 1450 247 0.47 41 5 Tin 232 60.7 0.218 30.3 1.85 Zinc 420 100.9 0.48 49.5 3.85