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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.
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,
po � ho1 − 1 V12
ho �� /(� −1) and two additional ones are the state equations at stations 1 and 2.
�1 ho1 − V12
� 2 ho 2 − V 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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- Fall '05