(a) Explanation The below figure represents the schematic diagram of the cooling tower. Figure-(1) Write the expression for the mass balance for dry air. m ˙ a 3 = m ˙ a 4 (I) Here, mass flow rates of atmospheric air inlet is m ˙ a 3 , mass flow rates of saturated moist air exit is m ˙ a 4 . Write the expression for the mass flow rate of dry air. m ˙ a = m ˙ a 3 . (II) Here, mass flow rate of dry air is m ˙ a . Write the expression for the mass balance to the water. m ˙ 1 + m ˙ 5 + m ˙ v 3 = m ˙ 2 + m ˙ v 4 (III) Here, mass flow rate of liquid water is m ˙ 1 , mass flow rate of water at exit is m ˙ 2 , mass flow rate of water vapor at inlet is m ˙ v 4 and mass flow rate of water vapor at exit is m ˙ v 5 . Write the expression for the mass flow rate of water at exit. m ˙ 5 = m ˙ a ( ω 4 − ω 3 ) (IV) Here, specific humidity of air at state 3 is ω 3 and specific humidity of air at state of 4 is ω 4 . Write the expression for the energy balance. Q ˙ + W ˙ = m ˙ 1 h w 1 + ( m ˙ a h a 3 + m ˙ v 3 h v 3 ) + m ˙ 5 h w 5 − m ˙ 2 h w 2 − ( m ˙ a h a 4 − m ˙ v 4 h v 4 ) (V) Here, specific enthalpy of air at state 1 is h a 1 , specific enthalpy of water at state 2 is h w 2 , specific enthalpy of vapor at state 5 is h v 5 , specific enthalpy of water at state of 4 is h w 4 , specific enthalpy of air at state of 4 is h a 4 , specific enthalpy of air at state of 3 is h a 3 and specific enthalpy of vapor is h v 3 . The work and heat transfer is zero from process 1 to 4. Substitute 0 for Q ˙ and 0 for W ˙ in Equation (V). 0 = m ˙ 1 h w 1 + ( m ˙ a h a 3 + m ˙ v 3 h v 3 ) + m ˙ 5 h w 5 − m ˙ 2 h w 2 − ( m ˙ a h a 4 − m ˙ v 4 h v 4 ) (VI) Simplify the energy Equation (VI). 0 = m ˙ 1 h f 1 + ( m ˙ a h a 3 + m ˙ v 3 h g 3 ) + m ˙ 5 h f 5 − m ˙ 2 h f 2 − ( m ˙ a h a 4 − m ˙ v 4 h g 4 ) (VII) Here, specific enthalpy of saturated liquid at state 1 is h f 1 , specific enthalpy of the saturated vapor at state 3 is h g 3 and specific enthalpy of the superheated vapor is h g 4 . Write the expression for the relation between mass flow rate of air and mass flow rate of vapor at state of 3. m ˙ v 3 = m ˙ a ω 3 (VIII) Write the expression for the relation between mass flow rate of air and mass flow rate of vapor at state of 4. m ˙ v 4 = m ˙ a ω 4 (IX) Substitute m ˙ a ω 1 for m ˙ v 1 and m ˙ a ω 3 for m ˙ v 3 in Equation (V). 0 = m ˙ 1 h f 1 + ( m ˙ a h a 3 + m ˙ a ω 3 h g 3 ) + m ˙ 5 h f 5 − m ˙ 2 h f 2 − ( m ˙ a h a 4 − m ˙ a ω 4 h g 4 ) m ˙ a = m ˙ 1 ( h f 1 − h f 2 ) ( h a 4 − h a 3 ) + ω 4 h g 4 − ω 3 h g 3 − ( ω 4 − ω 3 ) h f 5 (X) Write the expression for the specific humidity at state of 3. ω 3 = 0.622 ϕ 3 p g 3 p − ϕ 3 p g 3 (XI) Here, the gas pressure at state of 3 is p g 3 and the relative humidity is ϕ 3 . Write the expression for the saturation pressure. p s a t = p g 3 (XII) Write the expression for the specific humidity at state of 4. ω 4 = 0.622 ϕ 4 p g 4 p − ϕ 4 p g 4 (XIII) Write the expression for the specific enthalpy at state of 3. h T 3 = h T 1 + ( h T 2 − h T 1 ) ( T 3 − T 1 T 2 − T 1 ) (XIV) Here, the specific enthalpy at state of 3 is h T 3 , assumed temperature for interpolation are T 1 and T 2 , enthalpies with respect to the assumed temperature are h T 2 and h T 3 . Write the expression for the specific enthalpy at state of 4. h T 4 = h T 2 + ( h T 3 − h T 2 ) ( T 4 − T 2 T 3 − T 2 ) (XV) Here, the specific enthalpy at state of 4 is h T 4 , assumed temperature for interpolation are T 2 and T 3 , enthalpies with respect to the assumed temperature are h T 2 and h T 3 (b) To determine Exergy destruction in the cooling tower.

Fundamentals of Engineering Thermodynamics

8th Edition

ISBN: 9781118412930

Author: Michael J. Moran, Howard N. Shapiro, Daisie D. Boettner, Margaret B. Bailey

Publisher: WILEY

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Chapter 12.9, Problem 107P

(a)

To determine

The mass flow rate of the dry air and makeup water.

(b)

To determine

Exergy destruction in the cooling tower.

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Chapter 12.9, Problem 105P

Chapter 12.9, Problem 108P

Chapter 12 Solutions

Fundamentals of Engineering Thermodynamics

Ch. 12.9 - Prob. 1E Ch. 12.9 - Prob. 2E Ch. 12.9 - Prob. 3E Ch. 12.9 - Prob. 4E Ch. 12.9 - Prob. 5E Ch. 12.9 - Prob. 6E Ch. 12.9 - Prob. 7E Ch. 12.9 - Prob. 8E Ch. 12.9 - Prob. 9E Ch. 12.9 - Prob. 10E

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