(a) To determine The inlet and exit velocity of the air. Explanation Write the expression for density of the air at inlet of the pipe. ρ 1 = P 1 R T 1 (I) Here, the density of the air at inlet of the pipe is ρ 1 , the pressure of the air at inlet of the pipe is P 1 , the gas constant is R , the temperature of the gas at the inlet of the pipe is T 1 . Write the expression for density of the air at outlet of the pipe. ρ 2 = P 2 R T 2 (II) Here, the density of the air at outlet of the pipe is ρ 2 , the pressure of the air at outlet of the pipe is P 2 , and the temperature of the gas at the outlet of the pipe is T 2 . Write the expression for the continuity equation for the flow of air in the pipe. ρ 1 A V 1 = ρ 2 A V 2 ρ 1 V 1 = ρ 2 V 2 (III) Here, the cross-sectional area of the pipe is A , the diameter of the pipe is d , the inlet and outlet velocities of the air is V 1 and V 2 . Write the expression for the Bernoulli equation for the horizontal pipe. P 1 ρ 1 g + V 1 2 2 g = P 2 ρ 2 g + V 2 2 2 g (IV) Conclusion: Substitute 600 kPa for P 1 , 0.287 kJ / kg K for R and 330 K for T 1 in Equation (I). ρ 1 = 600 kPa ( 0.287 kJ / kg ⋅ K ) ( 330 K ) = 600 kPa 94.71 kJ / kg = 6.3351 kg / m 3 Substitute 120 kPa for P 2 , 0.287 kJ / kg K for R and 300 K for T 2 in Equation (II). ρ 2 = 120 kPa ( 0.287 kJ / kg ⋅ K ) ( 300 K ) = 120 kPa 86.1 kJ / kg = 1.39 kg / m 3 Substitute 6.3351 kg / m 3 for ρ 1 , 1.39 kg / m 3 for ρ 2 and 0.287 kJ / kg K for R in Equation (III) (b) To determine The mass flow rate of the air in the pipe in kg / s . (c) To determine The rate of entropy production in kW / K .

Fundamentals of Engineering Thermodynamics

8th Edition

ISBN: 9781118832318

Author: MORAN

Publisher: WILEY

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Chapter 6.13, Problem 90P

(a)

To determine

The inlet and exit velocity of the air.

(b)

To determine

The mass flow rate of the air in the pipe in kg/s.

(c)

To determine

The rate of entropy production in kW/K.

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Chapter 6.13, Problem 89P

Chapter 6.13, Problem 91P

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