finalexam-solution1

finalexam-solution1 - ME ED 240 Fluid Mechanics Fall 2004...

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Unformatted text preview: ME ED 240 Fluid Mechanics Fall 2004 FINAL EXAM Name 50 \‘ Instructions: Show your work, partial credit will be given only if there is sufficient detail to the solutions Read all questions carefully. I. (25 pts) True or False / Short answer TorF F (a) Fluids and solids have the same relationship between stress in the material and strain. Ir , (b) The Reynolds transport theorem describes the relationship between the lagrangian and eulerian descriptions of fluid flow. F (c) The flow just upstream of a normal shock is subsonic. T (d) The Buckingham Pi theorem is used to determine dimensionless parameters that can be used to simplify the analysis of fluid flows. |-v< (e) Turbulence can help to create separation in external flows. (i) For steady inviscid flows, the continuity equation and energy equation are redundant T i (g) Friction and shocks in compressible flows are both sources of the loss of energy. l-n (h) In general, the drag produced by an external flow around a body is proportional to both the volume and weight of the body. T (i) streamlines, streaklines, and pathlines are all the same thing in steady flows F (j) Minor losses in pipes are proportional to AP2 ‘ 1. con’t Short answer 4, 7) (k) describe the nature of a boundary layer in an external flow. What is the physical interpretation of the displacement thickness? ‘ ‘ a in ,MY 'tmfimM/w/‘Z’i—m may/7) flu new ‘ M if”: ut. flamzkm w? mew/M :3]? % any/MM flwcflrnezd’ 5" M‘aM/wam l m m fay/M ital/745 mamwfzaw MM _. 63 (1) determine the fluid convection in the x and y directions for the velocity field V = x2 f — 2 x y] t + : ' K o 2 3 9“ “,9” vi“ )< (1x3 02 3C ) ’2“ 2 ‘6‘: “3¥+Vg§ 3 K2413) Jew-2x) 2 ‘2’}? ‘F “a? 3&9“— (m) in your design project, what was the theoretical basis of the connection between the pipe system @ and the given pump? @ @ (0) describe the hydrostatic variation. of pressure in a fluid. ' 4”” m m M 4m 91%st Mpwr w E7 W arwyfifigfl m. s l3 2. (20 pts) River floods are typically held back levees. During large storms temporary barriers are used in places without levees. .One manufacturer has barriers that weigh W and have a length L and have other dimensions as shown. The principle is that the barrier resists the water with the force due to dry friction between barrier and the ground. Recall, that force is given by Ff = 77 N where, N, is the net normal force and 77 is the coefficient of static friction. ' t. t ‘1 Assume the water has a density, p and that w 3;: atmospheric pressure cancels all around the ’ barrier. Considering the hydrostatic force acting on the barrier, derive an expression for the I maximum height of water h that this of“ . ~.‘ ‘ 7.. a 11),. \ vbwz‘,‘«¢ ‘ .‘ . .‘w x U “n. ) (LA F, :u "" 4'pr x 3 €9§$ w teawugmwi' W at 3mg 0 @ ‘ \.',_ L— K d! [9130 N “N "FrCO'SG'ZO firms} manufacturer’s barriers can hold back. (draw a free body diagram) Wmth “YIN >$>§Jh9 stingzo “- N f ' L M _: 69 M f3 (imagxa St 96.939 0 §a\u.c lav N w w W 9% at gaammmum (mt. fvéi, Wr_£3’l/_VL (050. in?” WZO' SNML‘QW’A. 3. (20 pts) Recall, Couette flows are an exact solution to the Navier—Stokes equations. In this case, water (,0 = 1000 kg/m3 ,,u = 0.001 N —s/m2) flows in a H = 25 mm gap between two infinitely long plates as shown. The top plate moves with a speed U a, = 0.01 m / s and the bottom plate is stationary. Two pressure gages are used to measure the static pressures at point 1 and point 2. The distance between the pressure gages is L = 0.15 m U°° -’ For steady flow between the plates, the velocity is " “ ‘ given by, u(z) = Um i+—l—(a—P)(z2 —zH) H 2;: 6x Determine the height above the lower plate at which the velocity will be maximum if, dqcv 2129; 94m edges am: 4. (20 pts) Before the Wright Brothers flew their airplane in 1903 they worked out the details of their design by flying kites. An example shown in the figure has a weight W = 220 N and is flying in a U 00 = 40 km / hr breeze. In this wind the kite line has a tension of T = 60 N and the line is at an angle of 0 = 30" relative to the ground. The properties of the air are , p =l.2 kg/m3 and ,u =1.9x10'5N—s/m2 Assume that the lifl and drag produced by the kite are both proportional to the planform area of the kite Ac = 7.5 m2. The wings of the kite have a chord length C = 1.5 m. W) Z QOW/hr> z mwis . a.) Draw a free body diagram and determine the lift and drag coefficients for the kite. L“ EQUIUBIZHMA Zazo 2' D’nge fl DZ'TCOSG’ 7” ZgazwL—w —Ts.,:,.e lel/tmfsz‘ne L19 w A D2 (90065500: 5/99” r *5 L. 2 220M + (towsmaw =2§0N OWL}: 15"“ ' 9 0.240953” if) “0 ’40 L0‘1%%>(M.l(nfs)1(7,(mz) ‘ b.) If the flow does not separate from the wings of the kite and assuming the wings can be modeled as a thin ' the dis lace t thickness of the b0 er wing at the /’9)(/0'$/N’f/V7L '>/()S J1, W M“ vay g@o.o+b$x 192:“ Wm Xac 00:3» 5. (15 pts) You are standing at sea-level and watch as a high altitude of z = 3000 m The pilot radios that he is flying temperature outside the airplane is T = 100 C (a) Under these conditions when do I e airplane? (circle (1) (2) Before it gets to above where you are standing. At the time it gets to above After it passes over where where you are standing. you are standing. @e answer to part (a) is either (1) or@ien estimate the time either before or after the plane passes directly above that you hear the plane. ~ ’I z L —~> fl 2 2% [.1 ) Ma, 4Q, ...
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finalexam-solution1 - ME ED 240 Fluid Mechanics Fall 2004...

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