midterm_1_solu

midterm_1_solu - ME 1523 Winter 2 009 First Mldterm Name...

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Unformatted text preview: ME 1523 Winter 2 009 First Mldterm Name SO‘ u jfi‘ UK; Problem 1 / 10 Problem 2 / 10 Problem 3 / 10 Problem 4 /10 TOTAL /40 Problem 3. [10 pts) Bud is driving to Fresno to see his mother. He drives to Paso Robles and then turns iniand at twilight. The atmosphere between Paso and Kettleman City is cooling at a uniform rate of 2 K/hour. But Kettleman City is hotter than Paso and at that time of day, the average temperature gradient is 0.04 K/miie. He drives toward Ket’deman City and notices that there is no change in the outside temperature. How fast is he driving? GQUYEI»: if. r. " ‘ at O ME 1528 - First midterm Problem g. [10 pts.) Consider-the motion ofa pendulum in a viscous fluid where there is a drag force on the bob ofthe pendulum due to the fluid flow around it. l gate l Assuming the drag force is proportionai to the square of the speed of the bob, the equation ofmotion for the angular displacement E), is: m L 8” + u (8’ )2 .4. m g sin[8) "2 0: 8(0) = 80, BIG] 2 0. Here to is the mass, L the length of the connecting rod, g the acceleration of gravity, u, the coefficient of drag, and the prime is differentiation with respect to time. i. (5 pts.) What are the dimensions of u? How many Pi groups can be made from the parameters {m, g, L and u}? Note: The problem does not ask you to form any Pi groups, only to give a number. ‘ L All’l-‘QV‘MS WujL-WL 5?:th filmmrlom} o‘f‘ ML/"E game \@il1=~’"’l§- ,lgéw‘kl lWJ‘WW/‘l‘ 4 fwwsLm lmvelw‘jg {widened-J Wilt, £5993 4‘3 "EX ii. [5 pts.) Using the characteristic time scale of an undamped pendulum, (L/g) 1/2, make the equation dimensionless and identify the one dimensionless parameter that describes the effect of the drag force on the motion. Lel Wit/(L11? ti migmwiwkgg lite/”L- ME 15213 - First midterm Pgoblem 3. [10 pts.) Consider steady 2D incompressible flow in a hyperbolic contraction as shown. An approximation to the velocity field is found to be u m a x, v = — ay where u and v are the x and y components of the velocity at any point [icy]. i. [5 pts.) Show, using the 2D continuity equation, that this velocity field conserves mass. Bflkgiuo e37 D\.~'C\_:Q "/ ax 9:: ii. [5 pts.) These velocity fields satisfy neither the no—slip nor the no-penetration condition. Explain where boundary layers will form in this flow. Do you think this mathematical expression for the flow field is a good approximation to the true flow for high or for low Reynolds numbers? Expiain. "Regulus by. mans}vs~m~3 WM 3a aw; Q‘WWK EM ‘ l' fling: . Wm $01M“ wew Mae wlfcl Well—l~ ME 1523 — First midterm Problem 4. [10 pts.) No one could fail to notice that the sprinkler system in Engr. II is being upgraded. The primary pipe is approximately 0.2m in diameter, [which is‘then manifolded to the labs and then to the sprinkler heads]. We are 91111: interested in flow in the straight section at the main supply; pipe. During low pressure testing with water, the following data were recorded for flow in a straight run of pipe of length 70 m. D = 0.2m, L :. 70m, V = 5 m/s, Ap = 5.25 x 104 Pascal. For water, use v = 10'6 1112/5, and p = 103 kg/mB. How rough is the pipe? Express the roughness in microns. U lo’!’ JP 23??) CzX‘H-WO) ””0 .. 0 ma .- .. W +— ‘7‘“? a 330:)“ L—f Q1030” ”.- r“. f: USP-3 a: Q 33$?» .. m 2% ‘ 5. 7| .lTsiirar .Wmm t;,.w:ua.l.,rli:w€w «WJMT fl _ 0‘ C 3 m m.m0 minmou 383.. mm m guano: ME. 93» 3.3: Wow. 4 in: 333323 ill}! “.4 A: . I;,{I1:r...|YIL “ . _ allimliw} w w M M 711. L .17 I V . it“? 0.808 #mm ...
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