Exam2_2008_Solutions

# Exam2_2008_Solutions - NAME L U \ \Q Ofﬁcially Enrolled...

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Unformatted text preview: NAME L U \ \Q Ofﬁcially Enrolled in MB or BME? Fluid Mechanics Exam 2, Spring 2008 There are 4 problems on this exam: Problem 1: 10 points Problem 2: 12 points Problem 3: 10 points Problem 4: 12 points By signing below I 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. Signature: Date: Front Page Exam 2., Spring 2008 page 1 Problem 1. 10 points Consider the vector ﬁeld Fand the scalar function CD F=(x3+y4+z)(i+}+li) CD=6x2+2y4+3z3 If it is possible, ﬁnd the quantities requested below. If it is not possible to ﬁnd the quantity, write "not possible" in the box Exam 2, Spring 2008 You can use this page to work on problem 1. V F 7 Vlu’zh Wig/5 + Viv to KL: CVJ :. x3+xfl£+} 1m 1': ’ 31:35 .93; Q V M A 331* ML 393: '2 QJ : 3%; ’39: : “L33 E9— 6 9—8 9%; 1 ML 5. (0% u r 1 1 at»: I BEL—la g3 35" Z _ v“: frames??? : QZV “L”.- V F -: 2, & Q&: ’9: “x. ’V M " Jr 3' m 9% VA - 9‘85 9% k (cl “ 4— 3*+ 3-1 W); 8:39 Jr 9.262 9i? 62%?” pal—J'— (9&1; \$0 3°? 3 ax“ W a “‘1? \$9??? .224) "1 £1? 5 "f l :: :1] 3J1 Léj air? page 2 Exam 2, Spring 2008 page 3 Problem 2 (12 points) The pressure at the top of the closed manometer shown is measured and found to be Pg (measured in gage pressure). What is the speciﬁc weight «(A of the fluid in pipe A? Work in absolute pressure, and assume that atmospheric - pressure is Pam, Your answer may include some or all of the following variables: 73, the speciﬁc weight of the manometer ﬂuid hi, h2, and h3, the heights as indicated PA, the pressure in pipe A, measured in gage pressure Patm, atmospheric pressure Pg, the pressure measured at the top of the manometer Please put a box around your ﬁnal answer. -: aegpngPBa) W i y ~71 :— a-Mygap —- rah/ex Exam 2, Spring 2008 page 4 Problem 3 (10 points) (A) What are the dimensions of pressure in terms of kilograms, meters, and seconds? O’L ?'\‘5 (kg) / (m s2) du (B) If u is velocity (meters/sec) and x is position (meters), what are the dimensions of — ? dx i [Sir l/sec (C) The units of shearing stress are (kg) / (m S?) Fluids for which the shearing stress is linearly related to the rate of shearing strain (also referred to as rate of angular deformatiou) are designated as Newtonian ﬂuids. What are the dimensions of rate of shearing strain in terms of kilograms, meters, and seconds? 3 F46 l/sec (D) What are the dimensions of dynamic Viscosity p. in terms of kilograms, meters, and seconds? (Hint: you can ﬁgure it out from parts A through C). a viscosity : (shearing stress)/(du/dx) = [(kg) / (in sEJ] [sec] : kg / (m s) (E) if u is velocity (meters/sec) and t is time (seconds), what are the dimensions of it: ? lei“ (F) If F is force (Newtons) and x is position (meters), what are the dimensions of a in terms of 2 meters/ sec kilograms, meters, and seconds? \ Newton = (kg m) / 52 so dF/dx has units ofkg/ s2 (G) If F is force (Newtons) and t is time (seconds), what are the dimensions of 2—: in terms of kilograms, meters, and seconds? ( _k, Newton : (kg in) / s2 so dF/dt has units of(kg m)/ s3 Exam 2, Spring 2008 page 5 Problem 4. (12 points ) The drawing to the right shows the front View of a small tank that contains two incompressible liquids. The liquids have speciﬁc weights wt and 73- 'Yair \$< 'YA and YA < 73. A. (1 point) Indicate in the picture where you choose z = O. B. (5 points) Write an expression for the pressure P as a function of 2 between heights hl and h2. Work in absolute pressure, and assume that that atmospheric pressure is Pmm C. (6 points) Write an expression for the pressure P as a function of 2 between heights h2 and h3. Work in absolute pressure, and assume that that atmospheric pressure is Pam. Exam 2, Spring 2008 page 6 C. Write an expression for the pressure P as a function of 2 between heights h2 and h3. Work in absolute pressure, and assume that that atmospheric pressure is Palm Ifyou assumed that 113 = 0 then a?» PA ‘2 _ KEQ’EE ~ \$.23} W3) — PM '2 “\$55 (s6 4;; Pm : PL 4- 1/5)th 9‘3 And from part (A) we know that FL —: 759 otqu * Fadw 25%;. SO \ j 2 (L ‘3') 1m. qn 5L1 pen y; mum + m w, t w Ifyou assumed that hl : 0 then ...
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## This note was uploaded on 09/29/2008 for the course MECH 241 taught by Professor Hartmann during the Spring '08 term at Northwestern.

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Exam2_2008_Solutions - NAME L U \ \Q Ofﬁcially Enrolled...

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