?A pump operates adiabatically with liquid water entering at \(T_{1}\) and \(P_{1}\)

Chapter 7, Problem 7.44

(choose chapter or problem)

A pump operates adiabatically with liquid water entering at \(T_{1}\) and \(P_{1}\) with a mass flow rate \(\dot m\). The discharge pressure is \(P_{2}\), and the pump efficiency is η. For one of the following sets of operating conditions, determine the power requirement of the pump and the temperature of the water discharged from the pump.

(a) \(T_{1} = 25°C, \quad P_{1} = 100 kPa, \quad \dot m = 20 kg \cdot s^{−1}, \quad P_{2} = 2000 kPa, \quad η = 0.75, \quad β = 257.2 × 10^{−6} K^{−1}\).

(b) \(T_{1} = 90°C, \quad P_{1} = 200 kPa, \dot m = 30 kg \cdot s^{−1}, \quad P_{2} = 5000 kPa, \quad η = 0.70, \quad β = 696.2 × 10^{−6} K^{−1}\).

(c) \(T_{1} = 60°C, \quad P_{1} = 20 kPa, \quad \dot m = 15 kg \cdot s^{−1},\quad  P_{2} = 5000 kPa, \quad η = 0.75, \quad β = 523.1 × 10^{−6} K^{−1}.

(d) \(T_{1} = 70(°F), \quad P_{1} = 1(atm), \quad \dot m = 50(lbm)(s)^{−1}, \quad  P_{2} = 20(atm), \quad η = 0.70, \quad β = 217.3 × 10^{−6} K^{−1}\).

(e) \(T_{1} = 200(°F), \quad P_{1} = 15(psia), \quad \dot m = 80(lbm)(s)^{−1}, \quad P_{2} = 1500(psia), \quad η = 0.75, \quad β = 714.3 × 10^{−6} K^{−1}\).

Text Transcription:

T_1

P_1

dot m

P_2

T_1 = 25°C, P_1 = 100 kPa, dot m = 20 kg cdot s^−1, P_2 = 2000 kPa, η = 0.75, β = 257.2 × 10^−6 K^−1

T_1 = 90°C, P_1 = 200 kPa, dot m = 30 kg cdot s^−1, P_2 = 5000 kPa, η = 0.70, β = 696.2 × 10^−6 K^−1

T_1 = 60°C, P_1 = 20 kPa, dot m = 15 kg cdot s^−1, P_2 = 5000 kPa, η = 0.75, β = 523.1 × 10^−6 K^−1

T_1 = 70(°F), P_1 = 1(atm), dot m = 50(lbm)(s)^−1, P_2 = 20(atm), η = 0.70, β = 217.3 × 10^−6 K^−1

T_1 = 200(°F), P_1 = 15(psia), dot m = 80(lbm)(s)^−1, P_2 = 1500(psia), η = 0.75, β = 714.3 × 10^−6 K^−1