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5. A pump operating at steady state receives 1.2 kg/s of liquid water at 50o C, 1.5 MPa. The pressure of the water at the pump exit is 15 MPa. The magnitude of the work required by the pump is 21 kW. Stray heat transfer and changes in kinetic and potential energy are negligible. Determine the work required by a reversible pump operating with the same conditions, in kW, and the isentropic pump efficiency. Determine the work required by a reversible pump operating with the same conditions, in kW. Determine the isentropic pump efficiency.

Respuesta :

nuhulawal20

Answer:

the work required by a reversible pump operating with the same conditions, in kW is 16.39 kW

the isentropic pump efficiency is 78%

Explanation:

Given that;

m = 1.2 kg/sec

T = 50 degree Celsius   { Vf = 0.001012 m^3/kg}

P1 = 1.5 Mpa

P2 = 15  Mpa

W-actual = 21 kw  

W reversible = m*Vf (p2 - p1)

= 1.2 * 0.001012 * ( 15*10^3 - 1.5*10^3)

= 1.2 * 0.001012 * 13500

= 16.39 kW

the work required by a reversible pump operating with the same conditions, in kW is 16.39 kW

Isentropic Pump efficiency = W-reversible / W-actual

= 16.39 / 21 = 0.78

= 78%

the isentropic pump efficiency is 78%

A) The work required by a reversible pump operating with the same conditions, in kW is; 16.39 kW

B) The Isentropic pump efficiency for the given work condition is;

η_p ≈ 78%

Isentropic Efficiency

We are given;

  • Mass transfer; m' = 1.2 kg/sec
  • Temperature; T = 50 °C  
  • Pressure at entry; P₁ = 1.5 Mpa = 1500 kPa
  • Pressure at exit; P₂ = 15  Mpa = 15000 kPa
  • Work required by pump; W_actual = 21 kw  

From steam tables online, at a temperature of 50 °C, the specific volume of saturated liquid is;

υ_f = 0.001012 m³/kg

A) Formula for work required by the reversible pump is;

W_reversible = m' × υ_f × (P₂  - P₁)

W_reversible = 1.2 × 0.001012 × ( 15000 - 1500)

W_reversible = 1.2 × 0.001012 × 13500

W_reversible ≈ 16.39 kW

B) The formula for the isentropic pump efficiency is;

η_p = (W_reversible/W_actual) * 100%

η_p = (16.39/21) * 100%

η_p = 78.05%
η_p ≈ 78%

Read more about Isentropic Efficiency at; https://brainly.com/question/16014998

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