Consider the casting of a block of a tin alloy of unknown dimensions. An 8 cm high pouring basin, which is filled to its top, sits on top of a 15 cm high conical sprue, which is in contact with the block through a runner and gate (see figure below). The bottom of the sprue is 2 cm in diameter. a) Estimate, by calculation, the diameter of the top of the sprue to avoid microporosity in the part. (10 points) b) Determine the Reynolds number at the bottom of the sprue. (10 points) c) Discuss your answers to (a) and (b) and what they mean in terms of the final part quality. (5 points) Material Sand Aluminum Nickel Magnesium Copper Gray cast iron Steel Tin Zinc Choke 1.16 0.90 0.44 1.02 0.385 0.441 Pouring basin 0.434 0.21 0.384 IT h Data for solid materials (room temperature) Specific heat (C) (kJ/kg-C) Ingate Casting Density (p) (kg/m) 1500 2700 8910 1740 8960 7125 7832 7280 7135 Thermal conductivity (k) (kW/m-C) 0.00060 0.222 0.092 0.156 0.394 0.0427 0.059 0.064 0.112 Material Aluminum Nickel Magnesium Copper Gray cast iron Tin Zinc Melting point (C) 660 1453 650 1083 1251 232 420 Data for liquid materials Latent heat of Specific solidification heat (C) (fusion) (Hr) (kJ/kg-C) (kJ/kg) 396 297 384 220 211 60.7 100.9 1.05 0.73 1.38 0.52 0.34 0.218 0.48 Thermal Conductivity (k) (kW/m- C) 0.094 0.053 0.139 0.166 0.026 0.0303 0.0495 Viscosity () (mPa-s) 1.3 4.9 1.25 4.0 2.25 1.85 3.85