This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: MB or BME Class? DULUU a N 3 NAME f’oL» on <3 M5 Fluid Mechanics _ {/i Q3551 fat/«emwawgr
Exam 9, Spring 2007 Km ; There are 6 problems on this exam for a total of 107 points Problem 1: 16 points
Problem 2: 14 points
Problem 3: 15 points
Problem 4: 32 points
Problem 5: 16 points
Problem 6: 14 points By signing below 1 agree to abide by the following honor code: As a member of the Northwestern community, I will not take unfair advantage of any other
member of the Northwestern community. I speciﬁcally agree not to reveal to any other student
the contents of this exam. Si gnature: Date: Page 1 ol‘ ll) MB or BME Class? NAME Problem 1: 16 points Water (density p, assumed inviscid) ﬂows steadily from a right—angle elbow as
shown. It emerges with an initial velocity V0 and an area A0. Its initial velocity is entirely in the
positive Xdirection. (A) 4 points. Find the (x, y) location where the ﬂuid hits the ground.
Hint for part (A): In addition to a value for x and a value for y, there is something you need to
indicate, either in the drawing or in words, in order for us to give you credit for your answer: r \z
i x“ mama) (B) 12 points. Find the force (magnitude and direction) of the ground on the water pit“; ‘r‘ Warning: There will be little or no partial credit given on this problem
0 One way to check your answer is to be certain your units work out correctly
0 Double check to be certain that you have correctly determined sin(0) and 005(9). Write your ﬁnal, correct answers in this box: (Q T”: " Page 2 of 10 MB or BME Class? NAME You can usethis page to work on problem 1 MB or BME Class? NAME Problem 2. (14 points) For the problems below, do NOT assume steady flow. Do NOT assume
constant density unless otherwise stated A) Write the Reynold’s Transport Theorem F) Write conservation of mass in differential form, writing out each vector component and assuming
constant density. r} x m
32‘ r r: w»! {~1an
WWW. (mm was“
We _ an”; ,«3 \ G) Does the equations you wrote in (F) hold for steady flow, unsteady ﬂow, or both? 94 t n: H) What is another name for the equation that expresses conservation of mass in differential form? I) Write conservation of momentum in integral form Page 4 ol’lO MB or BME Class? NAME Problem 3) 15 points The following equation expresses conservation of momentum in differential form: wig?“ ﬂ: p§ + ,uV2V DZ Term 1 Term 2 Term 3 Term 4 ,0 (A) Draw horizontal lines over every variable in the equation that is a vector. (B) Which term(s) do you need to leave out of the equation in order to obtain Euler’s equations? (C) l7 ill in the blanks. (mass)* (acceleration) of the system is reﬂected 111 term number(s)
t; reg. 22W :22» , iiimw? M“ wwwﬁrmw 4‘ 1.: 6,6»: energy is reﬂected in term number(s) The energy is reﬂected in term number(s) energy is reﬂected in term number(s) WM“ ,e musovum :4 Mm W. WWW», MN, Wﬂmwwbmmw m o N Na (iii) Working in Cartesian coo1dinates and assuming that grav1tymhﬁgvswa”)gompwonentmonly 1.9.3132?
write out all components ol the conservation of momentum equation in differential form. Be
very ca1eful to indicate which of your terms contain partial derivatives; and which contain full derivatives. Also be sure you indicate which component is which. 'We cannot give you credit unless
you make it clear! ‘~ MB or BME Class? NAME Problem 4. 32 points) A rectangula1 plate is ﬁxed at the ground and a second parallel plate with a1ea 4
m2 moves above it at a distance of 10 mm with a speed of 2 m/s. The shear stress developed 15 4O N/m2.
Assuming steady ﬂow of a constant density Newtonian ﬂuid and that edge— effects are negligible,
please do the following: (A) Sketch a plot of velocity as a function of distance y between the plates after the ﬂow is fully
developed. Indicate the origin, label the axes, and indicate the numerical value of the slope at each region of the curve you have sketched. (B) Here are six assumptions needed to derive the sketch that you drew in part (A) from the
conservation of momentum equations. In the blanks next to each assumption write down the mathemancal ex' ‘ ss (l) Steady ﬂow (4) No pressure gradient (2) Constant density (5) Fully developed ﬂow (3) Newtonian fluid (6) TWOdimensional flow {hwﬁés W if? 411) Page (1 of m ME or BME Class? NAME D. Write down the x—component of the conservation of momentum equation (note: you already wrote it
down in the previous problem). Cross out each term of the conservation of momentum equation that is zero and indicate which assumption you used to state that it is zero: {a (E) Rewrite the equation you wrote in part (D) as a differential equation you can solve. Clearly
list all assumptions you are making in this step (G) Use the information given in the first part of the problem to apply appropriate boundary
conditions to get a full solution ME or BME Class? NAME Problem 5 The drawing below shows a tank that contains two incompressible liquids. The liquids
have speciﬁc weights VA and VB. ya” << “(A and VA < YB The top of the tank is open to the atmosphere. Side View A. Write an expression for the pressure P as a function of y between heights hl and 112. Work in
absolute pressure, and assume that that atmospheric pressure is Palm B. Write an expression for the pressure P as a function of V between heights 0 and hi, Wor< in
absolute pressure, and assume that that atmospheric pressure is Pm C. Now assume that Pam = 0. Find the magnitude of the force due to ﬂuid pressure acting on the side
of the tank . Please put a box around your ﬁnal answer. Page 8 of ill NAME 01' BME Class? ‘ MP .1 Blank page. 5 You can use this page to work on problem xwwdzs MB or BME Class? NAME Problem 6: 14 points Water (density p, assumed inviscid) ﬂows steadily from a pipe with initial velocity V0, area A0 and
angle of emergence 8. It pools up on the ground without splashing and rolls smoothly away into the
page. Find the force (magnitude and direction) of the water on ground Warning: There will be little or no partial credit given on this problem
0 One way to check your answer is to be certain your units work out correctly
0 Double check to be certain that you have correctly determined sin(9) and 008(9). Write your final, correct answer in this box: LA, x
If?” y“
w " {V Page ll) ol‘ 10 g _i r w ﬁﬂwﬂw XE:
,a w § w M3 4 4 4
2/;qu «a “m «W ...
View
Full Document
 Spring '08
 HARTMANN

Click to edit the document details