System Components of a Cooling System

Exercise 1-1: Work Done by Air Flowing Through a Turbine

• High-pressure air at 1300 K flows into an aircraft gas turbine and undergoes a steady-state, steady-flow, adiabatic process to the turbine exit at 660 K.
• The work done per unit mass of air flowing through the turbine is calculated using the conservation of energy equation: Wout = ṁ (h1 - h2).
• The work done by the air per unit mass flow is equal to the enthalpy decrease of the air.
• Using the air tables, the work done is calculated as wout = 103.9 kJ/kg.

Exercise 1-3: Steam and Cold Water Flow Rates

• Steam at 0.2 MPa, 300°C, enters a mixing chamber and is mixed with cold water at 20°C, 0.2 MPa, to produce 20 kg/s of saturated liquid water at 0.2 MPa.
• The conservation of mass equation is applied: ṁ1 + ṁ2 = ṁ3.
• The conservation of energy equation is applied: ṁ1h1 + ṁ2h2 = ṁ3h3.
• The required steam and cold water flow rates are calculated as ṁ1 = 2.82 kg/s and ṁ2 = 17.18 kg/s.

Exercise 1-4: Air and Water Flow Rates in a Heat Exchanger

• Air is heated in a heat exchanger by hot water, with a 20°C drop in temperature.
• The conservation of mass equation is applied: ṁair,1 + ṁw,1 = ṁair,2 + ṁw,2.
• The conservation of energy equation is applied: ṁair(hair,1 - hair,2) = ṁw(hw,2 - hw,1).
• The ratio of mass flow rate of air to mass flow rate of water is calculated as ṁair / ṁw = 3.33.