A client has asked you to find the pressure change in a pumping station. The outlet from the pump is 20 ft above the inlet. A Newtonian fluid is being pumped at steady state. At the inlet to the pump where the diameter is 6 in., the temperature of the fluid is 80°F, the viscosity is 1.80 × 10^-3 lb_m/ft s, the density is 50 lb_m/ft³, the heat capacity is 0.580 Btu/lb_m °F, and the kinematic viscosity is 3.60 × 10^-5 ft²/sec. At the outlet to the pump, where the diameter is 4 in., the temperature of the fluid is 100°F, the viscosity is 1.30 × 10^-3 lb_m/ft sec, the density is 49.6 lb_m/ft³, the heat capacity is 0.610 Btu/lb_m °F, and the kinematic viscosity is 2.62 × 10^-5 ft²/sec. The flow rate through the system is constant at 20 ft³/sec. The pump provides work to the fluid at 3.85 × 10⁸ lb_m ft²/s³, and the heat transferred is 2.32 × 10⁶ Btu/h. You may neglect viscous work in your analysis. Under these circumstances, please calculate the pressure change between the inlet and the outlet of the pumping station.