Question

A pump is used to circulate hot water in a home heating system. Water enters the well-insulated pump operating at steady state at a rate of 0.42 gal/min. The inlet pressure and temperature are 14.7 lbf/in.² , and 180°F, respectively; at the exit the pressure is 60 lbf/in.² The pump requires 1/25 hp of power input. Water can be modeled as an incompressible substance with constant density of 60.58 lb/ft³ and constant specific heat of 1 Btu/lb·°R.

Neglecting kinetic and potential energy effects, determine the temperature change, in °R, as the water flows through the pump.

Answer 1

To determine the temperature change, calculate the specific work done by the pump on the water and the specific volume of the water. Then, use the formula to calculate the temperature change.

Step-by-step explanation:

To determine the temperature change, we need to calculate the specific work done by the pump on the water.

The specific work done can be calculated using the formula:

Specific Work = (Pressure Change * Specific Volume) / (Density)

The pressure change can be calculated by subtracting the exit pressure from the inlet pressure. The specific volume can be calculated using the formula:

Specific Volume = 1 / Density

Plugging in the given values, we can calculate the specific work done by the pump. From there, we can calculate the temperature change using the formula:

Temperature Change = Specific Work / (Specific Heat * Flow Rate)

Using the given flow rate of 0.42 gal/min and converting it to cubic feet per minute, we can calculate the temperature change in °R.