Prof. Scalo Prof. Vlachos Prof. Ardekani Prof. Dabiri 08:30 09:20 A.M 10:30 11:20 A.M. 1:30 2:20 P.M. 3:30 4:20 P.M.


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1 Page 1 Neatly print your name: Signature: (Note that unsigned exams will be given a score of zero.) Circle your lecture section (1 point if not circled, or circled incorrectly): Prof. Scalo Prof. Vlachos Prof. Ardekani Prof. Dabiri 08:30 09:20 A.M 10:30 11:20 A.M. 1:30 2:20 P.M. 3:30 4:20 P.M. Please note the following: 1. The exam is closed notes and closed book. You may use only the formula sheet provided with the exam, a pen/pencil/eraser, and a calculator fitting the policy stated in the course syllabus. 2. Show all of your work in order to receive credit. An answer without supporting work will not receive a full score. Also, write neatly and organized and clearly box your answers. 3. Clearly state your assumptions, draw control volumes and coordinates systems, and include other significant information in order to receive full credit. 4. Only turn in those pages you wish to have graded. Do not turn in your formula sheets. 5. The honor code is in effect. 6. Write only on one side of the paper. Work on the backside of a page will not be graded. 7. Only the first solution approach encountered when grading will be scored. (2 points if the following instruction is not followed) SCORE: Write your name on all pages that are to be considered for grading. If you do not write your name, that page will NOT be graded TOTAL (out of 100):
2 Page 2 1. Describe the following terms (1 pts each, negative points if wrong apply for some questions, as indicated): a) Fullydeveloped flow: b) (2 pts) Laminar flow: c) (2 pts) Turbulent flow: d) (2 pts) Inviscid flow: e) Viscous sublayer: f) Major losses: g) Minor losses: h) Kinematic similarity: i) Dynamic similarity: j) Separated flow:
3 Page 3 2. (4 pts) On the following figures, draw the velocity profiles for laminar and turbulent flow through a pipe, and describe how they are different. Be sure to draw carefully. Laminar Turbulent 3. (4 pts) On the following figures, draw the velocity profiles for a critical and a separated boundary layer flow over a flat plate, and describe how they are different. Be sure to draw carefully. Critical Separated 4. (4 pts) On the following figures, draw the shear stress profiles for laminar (parabolic) and linear velocity profiles. Be sure to draw carefully. Laminar (parabolic) Linear
4 Page 4 5. (5 pts) Explain in words or drawings what the following quantities represent for a boundary layer: a) (1 pts/3 pts) Disturbance / boundary layer thickness, δ : b) (2 pts) Displacement thickness, u δ = 1 0 dy : U c) (2 pts) Momentum thickness, u u θ = 1 0 dy : U U 6. (1 pts) What is the approximate value of the critical Reynolds number for transition from laminar to turbulent regime for flow over a smooth flat plate, based on the distance from the leading edge of the plate? 7. (4 pts) Write four (4) independent boundary conditions that are always valid for a boundary layer. a) b) c) d)
5 Page 5 8. (5 pts) In a pipe with a rectangular crosssection (not circular), with crosssection height H and width W such that H/W=9 you measure the pressure drop between two points separated by distance L such L=20H. What is the average wall shear stress along this pipe if the pressure drop ΔP=100 Pa? 9. The pressure drop, Δp, for steady, incompressible viscous flow through a straight horizontal pipe depends on the pipe length, l [L], the average velocity, V [L/T], the fluid viscosity, µ [M/LT], the pipe diameter, D [L], the fluid density, ρ [M/L 3 ], and the average roughness height, e [L]. Δp = f ( ρ, V, D, l, µ, e ) (Hint: Δp is defined in N/m 2 and force is defined as!mass acceleration) i. (2 pts) How many dimensionless groups can be obtained according to the Buckingham pi theorem? ii. (2 pts) Find the piterm containing Δp by using ρ, V and D as repeating variables. iii. (1 pts/ 5 pts if wrong) Find the piterm containing µ, and using ρ, V, D, as repeating variables. What is the name and the physical meaning of this dimensionless number?
6 Page 6! 10. Bernoulli s Equation is as follows: +!! +!" =!"#$%&#%!! a) (4 pts) Bernoulli s 1738 treatise Hydrodynamica contains many excellent sketches of flow patterns related to his frictionless relation. One, however, redrawn below, seems physically misleading. Identify what is wrong with the figure and explain why. Assume flow to be frictionless. b) (3pts) Look at the Figure 2 (a) for an inviscid flow in a pipe with variable cross section. Can you say that!!!! =!"h? Provide an explanation for your answer. c) (3pts) In Figure 2 (b), flow is moving from point 1 to point 2. Can you apply Bernoulli s Equation between point 1 and point 2? Justify your answer. Q Q h 1 2 g h!!!!!! 1 2 g Figure 2(a) Figure 2(b)
7 Page (10 pts) Below is a cylinder in a viscous flow, the fluid flows from left to the right. a) (5 pts) Draw the streamlines around the cylinder qualitatively. In your drawing, you need to label the stagnation points, locations of flow separation & indicate wake structure behind cylinder.!direction of Flow! b) (5 pts) In the plot below, plot the pressure coefficient distribution as a function of the angle around the cylinder for the following 3 cases (i) inviscid flow, (ii) laminar separated flow and (iii) turbulent separated flow. Note, for inviscid flow the pressure coefficient C p =14sin 2 (Θ) U" Θ!
8 Page 8! Ax 12. (10 pts) Given the velocity field V = x 2 + y 2 î + Ay x 2 + y 2 ĵ, A = constant. a) (1 pts) Is the flow field is one, two, or threedimensional, and why? b) (3 pts) For incompressible flow, is this velocity field physically feasible? Yes/No and Why? (Hint: show with equations) c) (2 pts) What is the equation for the acceleration in the xdirection d) (4 pts) Determine the equation of the streamlines and plot a few representative streamlines.
9 Page (5 pts) Liquid is moving in a vertical pipe. The fluid has γ = 10 kn/m 3 and dynamic viscosity µ = 1x103 Nm/s 2. The pipe length is L=10 m, the diameter is D = 0.01 m. Assume that the flow is laminar. If the pressure drop is 100 kpa along the length of the pipe, what is the mean velocity? 14. (5 pts) For a pipe flow, if relative roughness is k/d=0.002, using the Moody diagram (shown below), what is the Reynolds number for: a) (1 pts) transition to turbulence: b) (2 pts) complete turbulence : c) (2 pts) the friction coefficient to be independent of the Re number:
10 Page Air flows from a reservoir through a converging nozzle as the one shown in the figure (top). a) (1 pts) What is the definition of choked flow? b) (1 pts) Where in the nozzle will the flow be choked? (describe with words and show on the figure) c) (1 pts) In that location, what is the Mach number, M? d) (3 pts) The pressure distribution inside the converging nozzle for different back pressures is shown in the figure. Which case(s) for the back pressure corresponds to choked flow? (check all that apply): Select your answer(s) : (4 pts) Air flows through the geometries shown below. Identify for each one, which one is a nozzle and which one is a diffuser a) b) c) d) (a)$ (c)$ (b)$ (d)$
11 Page As shown in the figure an irregularly shaped object weighs 1000 kn when in air. 1000#kN#?### a) (3 pts) What is the specific weight γ object of the object if the volume of the object is 0.1 m 3? b) (4 pts) How much will the object weight when fully submerged in water. (For water, γ water = 10 kn/m 3.) c) (1 pts) What is the specific gravity of the object? d) (1 pts) Circle the correct answer: Based on above results, the object is, ( positively / negatively / neutrally )* buoyant. (*) see note at the bottom of the page e) (1 pts) Circle the correct answer: If the shape of the object becomes spherical and everything else stays the same, then the object will be ( positively / negatively / neutrally )* buoyant. (*) see note at the bottom of the page Note: positively buoyant = floats up negatively buoyant = sinks down neutrally buoyant = stays in place
Signature: (Note that unsigned exams will be given a score of zero.)
Neatly print your name: Signature: (Note that unsigned exams will be given a score of zero.) Circle your lecture section (1 point if not circled, or circled incorrectly): Prof. Dabiri Prof. Wassgren Prof.
More informationPage 1. Neatly print your name: Signature: (Note that unsigned exams will be given a score of zero.)
Page 1 Neatly print your name: Signature: (Note that unsigned exams will be given a score of zero.) Circle your lecture section (1 point if not circled, or circled incorrectly): Prof. Vlachos Prof. Ardekani
More informationSignature: (Note that unsigned exams will be given a score of zero.)
Neatly print your name: Signature: (Note that unsigned exams will be given a score of zero.) Circle your lecture section (1 point if not circled, or circled incorrectly): Prof. Dabiri Prof. Wassgren Prof.
More informationSignature: (Note that unsigned exams will be given a score of zero.)
Neatly print your name: Signature: (Note that unsigned exams will be given a score of zero.) Circle your lecture section (1 point if not circled, or circled incorrectly): Prof. Dabiri Prof. Wassgren Prof.
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