Explanation 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 ) ] (I) 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 diffuser is at same elevation and the air flow adiabatically. Hence, neglect the potential energy i.e. g ( z 1 − z 2 ) = 0 , heat transfer i.e. Q ˙ cv = 0 and the work done is also zero in diffuser i.e. W ˙ cv = 0 . Then the Equation (I) becomes as follows to obtain the exit velocity. ( h 1 − h 2 ) + ( V 1 2 − V 2 2 ) 2 = 0 h 2 − h 1 = 1 2 ( V 1 2 − V 2 2 ) V 1 2 − V 2 2 = 2 ( h 2 − h 1 )

Fundamentals of Engineering Thermodynamics

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ISBN: 9781118832318

Author: MORAN

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Fundamentals of Engineering Thermodynamics

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

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