(a) To determine The velocity of air at the inlet and exit of air, in m/s . Explanation Here, the air flows at steady state through the pipe whose diameter is constant at inlet and exit. Hence, the inlet and exit mass flow rates are equal. m ˙ 1 = m ˙ 2 (I) Write the formula for inlet mass flow rate in terms of ideal gas equation. m ˙ 1 = A 1 V 1 p 1 ( R ¯ / M ) T 1 (II) Write the formula for exit mass flow rate in terms of ideal gas equation. m ˙ 2 = A 2 V 2 p 2 ( R ¯ / M ) T 2 (III) Here, the cross sectional area is A , the velocity is V , the pressure is p , universal gas constant is R ¯ , the molar mass of the air is M , the temperature is T and the suffixes 1 and 2 indicates the inlet and exit states. Substitute A 1 V 1 p 1 ( R ¯ / M ) T 1 for m ˙ 1 and A 2 V 2 p 2 ( R ¯ / M ) T 2 for m ˙ 2 in Equation (I). A 1 V 1 p 1 ( R ¯ / M ) T 1 = A 2 V 2 p 2 ( R ¯ / M ) T 2 (IV) Here, the inlet and exit cross sectional areas are equal i.e. A 1 = A 2 . Substitute A 1 for A 2 in Equation (IV). A 1 V 1 p 1 ( R ¯ / M ) T 1 = A 1 V 2 p 2 ( R ¯ / M ) T 2 V 1 p 1 T 1 = V 2 p 2 T 2 (V) Rearrange the equation (V) to obtain the inlet velocity ( V 1 ) . V 1 = ( p 2 p 1 ) ( T 1 T 2 ) V 2 (VI) Write the energy rate balance equation. 0 = Q ˙ cv − W ˙ cv + m ˙ [ ( h 1 − h 2 ) + ( V 1 2 − V 2 2 ) 2 + g ( z 1 − z 2 ) ] (VII) Here, the rate of heat transfer is Q ˙ cv , rate of work transfer is W ˙ cv , rate of mass flow is m ˙ , the enthalpy is h , velocity is V , gravitational acceleration is g , the elevation is z and the suffixes cv, 1 and 2 indicates control volume, initial and final state of the system respectively. Here, the air operates in steady state. The inlet, exit of the pipe is at same elevation and the pipe is insulated well. Hence, neglect the potential energy and heat transfer rate and i.e. g ( z 1 − z 2 ) = 0 and Q ˙ cv = 0 respectively; the work done is also zero in control volume i (b) To determine The mass flow rate of air, in kg/s .

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 4.12, Problem 27P

(a)

To determine

The velocity of air at the inlet and exit of air, in m/s.

(b)

To determine

The mass flow rate of air, in kg/s.

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Chapter 4.12, Problem 26P

Chapter 4.12, Problem 28P

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Fundamentals of Engineering Thermodynamics

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