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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 1808F, respectively; at the exit the pressure is 120 lbf/in.2 The pump requires 1/35 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 ? 8R. Neglecting kinetic and potential energy effects, determine the temperature change, in 8R, as the water flows through the pump. Comment on this change.

Answer :

Answer:

Temperature change is 0.0345 degree rankine

The change in temperature is therefore small

Explanation:

Please see attached for the workings.

The temperature change and the comment on it is; 0.1263 °R and the comment is that the change is small due to the insulated pump.

What is the temperature change?

We are given;

Rate of entry of water; A = 0.42 gal/min = 0.0009357639 ft³/s

Inlet Pressure; P₁ = 14.7 lbf/in²

Inlet Temperature; T₁ = 180 °F

Exit Pressure; P₂ = 120 lb/in²

Constant density; ρ = 60.58 lb/ft³

Mass flow rate;

m' = 60.58 * 0.0009357639

m' = 0.05669 lb/s

We are told that the pump requires 1/35 Hp of power input. Converting to Btu/s gives; Workdone = -0.0202 Btu/s

From energy balance we can write the work done equation as;

W = -m[c(T₂ - T₁) + (1/ρ)(P₂ - P₁)

Making T₂ - T₁ the subject and plugging in the relevant values with c = 1, we have; T₂ - T₁ = 0.1263 °R

The reason why the temperature change is small is because of the insulated pump.

Read more about change in temperature at; https://brainly.com/question/13439286

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