To determine The highest average flow velocity of the air in the duct. Explanation Write the expression for the energy balance equation for the closed system. E ˙ in − E ˙ out = ( d E d t ) system (I) Here, rate of net energy transfer in to the control volume is E ˙ in , rate of net energy transfer exit from the control volume is E ˙ out and rate of change in internal, kinetic and potential energies of system is ( d E / d t ) system . For steady state, the rate of change in internal, kinetic and potential energies of the system is zero. ( d E / d t ) system = 0 Substitute 0 for Δ E ˙ system in Equation (I). E ˙ in − E ˙ out = 0 W ˙ in + m ˙ ( P v ) in − m ˙ ( P v ) out = 0 W ˙ in = m ˙ [ ( P v ) out − ( P v ) in ] = m ˙ [ ( P ) out − ( P ) in ] v (II) Here, rate of power input is W ˙ in , mass flow rate is m ˙ , inlet pressure is ( P ) in , outlet pressure is ( P ) out and volume of air is v . Use volume flow rate to rewrite the rate of power input. W ˙ in = [ ( P ) out − ( P ) in ] V ˙ Here, volume flow rate is V ˙

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Chapter 2.8, Problem 49P

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The highest average flow velocity of the air in the duct.

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