Explanation Given: The initial pressure of the steam ( P 1 ) is 1200 kPa. The initial temperature of the steam ( T 1 ) is 250 ° C . The initial velocity of the steam ( V 1 ) is 4 m/s . The final pressure of the steam ( P 2 ) is 1000 kPa. The inlet diameter of the pipe ( D 1 ) is 0.15 m. The outlet diameter of the pipe ( D 2 ) is 0.1 m. Calculation: Consider the steam flows at steady state. Hence, the inlet and exit mass flow rates are equal. m ˙ 1 = m ˙ 2 = m ˙ (I) Write the energy rate balance equation for one inlet and one outlet system. [ Q ˙ 1 + W ˙ 1 + m ˙ ( h 1 + V 1 2 2 + g z 1 ) ] − [ Q ˙ 2 + W ˙ 2 + m ˙ ( h 2 + V 2 2 2 + g z 2 ) ] = Δ E ˙ system (II) Here, the rate of heat transfer is Q ˙ , the rate of work transfer is W ˙ , the enthalpy is h and the velocity is V , the gravitational acceleration is g , the elevation from the datum is z and the rate of change in net energy of the system is Δ E ˙ system ; the suffixes 1 and 2 indicates the inlet and outlet of the system. The system is at steady state. Hence, the rate of change in net energy of the system becomes zero. Δ E ˙ system = 0 Here, the pipe is insulated, neglect the heat transfer i.e. Q ˙ 1 = Q ˙ 2 = 0 . Also neglect the kinetic and potential energy changes. No work is involved, neglect the work transfers. The Equations (II) reduced as follows. [ 0 + 0 + m ˙ ( h 1 + 0 + 0 ) ] − [ 0 + 0 + m ˙ ( h 2 + 0 + 0 ) ] = 0 m ˙ h 1 − m ˙ h 2 = 0 m ˙ h 1 = m ˙ h 2 h 1 = h 2 (III) Write the formula for inlet and outlet mass flow rates. Calculate the Inlet mass flow rate. m ˙ = m ˙ 1 = A 1 V 1 v 1 = ( π D 1 2 4 ) V 1 v 1 m ˙ = [ π ( 0.15 m ) 2 4 ] 4 m/s 0.19242 m 3 /kg = ( 0

5th Edition

ISBN: 9780078027680

Author: Yunus A. Cengel Dr., Robert H. Turner, John M. Cimbala

Publisher: McGraw-Hill Education

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Chapter 6, Problem 131RQ

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The mass flow rate of steam and its speed at the pipe outlet.

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Chapter 6, Problem 130RQ

Chapter 6, Problem 132RQ

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Chapter 6 Solutions

Fundamentals of Thermal-Fluid Sciences

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