ech3264_sp09_Exam2_solnkey

# ech3264_sp09_Exam2_solnkey - ECH 3264 Elementary Transport...

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Unformatted text preview: ECH 3264: Elementary Transport Phenomena Spring 2009 Exam #2 March 4, 2009 Name: Show all work and box intermediate results — this will help you get partial creditl! 3 4723' 2 Relevant volume and surface areas: Vsphm = —3 Vwmer = R? L SAME” : 4a.?"2 SA = 2:34. (winder 1. 20 ts True or False False E a Iii-l:- The distribution of velocit for laminar flow in a n i e varies - arabolicall with the radius The Reynolds number is a measure of the ratio of inertial forces to viscous forces Reversibility phenomena can be observed for Re -) 0 If two immiscible liquids A and B are ﬂowing in the x-direction between two parallel plates, both the velocity v, and shear stress I)“ are continuous at the interface between A and B, where the coordinate y is normal to the plates A force is equivalent to a rate of transfer of momentum A propeller with a rudder that incorporates back and forth motion will not be effective under inertial ﬂuid ﬂow conditions. For horizontal ﬂow ofa liquid in a rectangular duct between parallel plates, the shear stress varies from zero at the plates to a maximum at the centerline At a liquid-gas interface the shear stress is approximately zero. For laminar steady state flow in a horizontal pipe, the viscous force from the pipe on the liquid must equal the force due to the pressure drop. For ﬂows in ducts and pipes, the volumetric ﬂow rate can be obtained by differentiating the velocity proﬁle 2. (30 pts) Lubricating flow in a circular tube In the Trans-Alaska Pipeline System (TAPS), large quantities of oil must be pumped under sometimes freezing conditions. Under these conditions the oil is very viscous and pumping the ﬂuid can be expensive due to the large pressure drops required. A suggestion is made that the pressure drop may be decreased by adding a small lubricating layer of less viscous ﬂuid (water) in an annular ring. Assume that both ﬂuids are Newtonian and immiscible. Let the more viscous fluid, A, have a viscosity pa and the second ﬂuid, B, have. a viscosity 041A with a < 1 and has a thickness of BR, where R is the radius of the pipe (see ﬁgure below). The pipe length is L and you may ignore entrance effects and assume the ﬂow is laminar and steady state. (a) Using shell balances derive the governing differential equations to determine the velocity proﬁle in both ﬂuids. Note: Make sure that in your solution you use clear and consistent notation to distinguish between fluid A (oil) and ﬂuid B (water). (5 pts) (b) State the boundary conditions. (5 pts) 0493 PM» 1:. (Dim 6% V 2&0 “WW Cg?“ 0 \$0 \$01me 5‘“ Z'MOW‘“ M L)! .90“; \AKer'LéwX-k ——j> Conn. (30 emA ¥O~\O\m£ (a 2' £\~A.\c)5 . ?\‘e. 0353 5&0“ aﬁkﬁvﬁsk Egbeem‘ N" ¢K2\( #- A(¢<Z’\ wrbr *- Aa éﬂik a AE¢ZE\ :0 z=o Z’L “dc '_ W3) Daro54\ At 5 JIM/L- AB = 2"“- pr 7‘0») DC Cor-— u~(\\-t_ <12wa <95: RV»an p. A _}_, 65 “AVaVz V041 »( cw : av L. B 3N\$ *9 2 m J. “‘1’”? F am, Y M 1. Lb) BU; A ( ?A g k 9A4 \Clo :: gnA-L D! V; =_ \m L 6! Yak:w ﬂi=OJclﬂ> av Y= (km («ck v:- m). k B #2, V; a V2 03(— r— (\_/g)q{ (QUE) 3 1:3 at: = (213 V5 V=R V2 :0 ...
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ech3264_sp09_Exam2_solnkey - ECH 3264 Elementary Transport...

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