Butyl alcohol, a Newtonian fluid, is being pumped at steady state with the density of 50 Ib_m/ft³. viscosity of 1.80 × 10^-3 Ib_m/ft s, heat capacity of 0.58 Btu/lb_m °F, and kinematic viscosity of 3.60 × 10^-5 ft²/s. The inlet to the pump is a pipe with a diameter of 6 in., and the outlet is a pipe with a diameter of 2 in. The outlet is 10 ft above the inlet. The pump provides work to the fluid at 7.1 × 10⁸ Ib_m ft²/s³. The flow rate through the system is constant at 20 ft³/s. During the pumping process, the fluid undergoes a 20°F increase in temperature. Under these circumstances, please calculate the pressure change between the inlet and the outlet of the pumping station. You may neglect any heat transfer to the control volume from the surroundings and viscous work, as these are very small.