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f11_12_ps04_s04 - Spring 2004 Unified Engineering Fluids...

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Unformatted text preview: Spring 2004 Unified Engineering Fluids Problems F11–F14 F11+12. Air is drawn at high speed out of a large reservoir through a duct of constant area ˙ A, which contains a radiator delivering a known Q to the flow (in Watts). The heating and friction of the duct walls are negligible. . Q h o 1 � 1 p 1 V1 h o �o po h o 2 � 2 p 2 V2 The known flow quantities are: ho = ho1 reservoir total enthalpy �o reservoir total density po reservoir total pressure p2 outlet pressure (drives the flow) The remaining six unknown quantities inside the duct are: ho2 outlet total enthalpy V1 inlet velo city V2 outlet velo city �1 inlet density �2 outlet density p1 inlet pressure A total of six equations are needed to solve for the six unknowns. One of these equations is the isentropic relation b etween the reservoir and station 1, p1 = po � ho1 − 1 V12 2 ho �� /(� −1) and two additional ones are the state equations at stations 1 and 2. �−1 1 �1 ho1 − V12 2 � � �−1 12 = � 2 ho 2 − V 2 2 � p1 = p2 � Write down the remaining three equations by constructing a suitable control volume and applying the integral mass, momentum, energy equations. (Do not try to solve the six equations — it gets very messy!) ...
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