Signature: (Note that unsigned exams will be given a score of zero.)

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Abner Webster
5 years ago
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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. Dabiri Prof. Wassgren Prof. Vlachos Mr. Mishra 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. SCORE: 1. (25 pts) 2. (25 pts) 3. (25 pts) 4. (25 pts) 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):

Problem 1 SCORE: 1. (25 pts) Part A: 3 pts each, no partial credit. 1) Which one of these statements about a Newtonian fluid is correct? a. The shear stress is proportional to the velocity gradient in the flow direction.

2 Problem 1 SCORE: 1. (25 pts) Part A: 3 pts each, no partial credit. 1) Which one of these statements about a Newtonian fluid is correct? a. The shear stress is proportional to the velocity gradient in the flow direction. b. The shear stress is proportional to the velocity of the fluid. c. The shear stress is proportional to the velocity gradient perpendicular to the flow direction. d. None of the above 2) Two identical tanks A and B have holes with round corners at the bottom. The hole on tank B is fitted with a pipe with the same cross-sectional area. If viscous effects are negligible, which tank will have a larger flow rate (Q)? a. Q A > Q B b. Q A < Q B c. Q A = Q B d. Insufficient data for an answer 3) If a uniform solid body weighs 50 N in air and 30 N in water, its specific gravity is a. 1.5 b c. 2.5 d. 3.0 e. 5.0

4) To apply the linear momentum equation, the fluid in the control volume must satisfy one or more of the following assumptions: a. Flow is steady b. Flow is irrotational c. Flow is inviscid d.

3 4) To apply the linear momentum equation, the fluid in the control volume must satisfy one or more of the following assumptions: a. Flow is steady b. Flow is irrotational c. Flow is inviscid d. Flow is incompressible e. None of the above 5) Two tanks filled with air are connected by water-filled tubes as shown. What is the gage pressure of the air in tank A in terms of inches of water? a. +4 of water b. +3 of water c. 0 d. +2 of water e. None of the above 6) The velocity of a two-dimensional flow field is given by V=ayi+bxyj where a and b are non-zero constants. What is the equation for streamlines? 7) Is the flow in the question 6) incompressible? a. Yes b. No c. It depends on the values of a and b.

4 Part B: 4 pts. Different flows can be classified following the chart shown below: The picture below shows an off-shore wind farm. Use the chart above to list all the correct classification relevant to this flow:

5 Problem 2 SCORE: 1. (25 pts) (25 points) Consider the rectangular gate AB shown in the figure above. The width of the gate into the page is L and the gate is pivoted at the hinge B. The specific weight and depth of the fluid are and a, respectively, and the weight of the gate is negligible. The gate makes a =30º angle with the horizon. Develop an analytic expression for the force F required to keep the gate closed.

8 Problem 3 SCORE: 1. (25 pts) 1 V 1 P 1 P v Water jets 2 (25 points) A two-dimensional, planar body is placed in a two-dimensional water tunnel. At low pressures the incoming flow splits into two jets with a vapor cavity in between the jets and behind the body. The density of the vapor is negligible compared to the water s density and its pressure is the vapor pressure P v (P v <P 1 where P 1 is the static pressure of the incoming flow). At point 2 the jets thicknesses no longer change downstream, the velocity across the jets is constant, and the pressure is P v. Also assume that the flow is inviscid and the effect of gravity is negligible. Give the answer for these questions in terms of V 1, P 1, h, and P v. (a) (5points) What is the velocity of the two jets, V 2? (b) (5points) What is the thickness of each jet? (c) (15points) What is the drag force on the body per unit depth?

10 Problem 4 SCORE: 1. (25 pts) When a small stone is dropped in a calm pond, surface waves are generated that travel at a velocity of V. The wave velocity V is assumed to be a function of the water s density, wavelength, pond s depth h, gravity g, and surface tension. (a) (15 pts) Find all of the dimensionless groups and write the relationship between the dimensionless groups describing this problem. (b) (5 pts) Assume that is negligible and the pond is so deep that h is not important anymore. What are the dimensionless groups in this case? (c) (5 pts) Using your results from part (b), what is the ratio of the velocity of a wave with wavelength 2 to the velocity of a wave with wavelength? h g

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.