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. 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: 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 (100 out of 110 points available):
1. (3pts) Describe in a short sentence how the buoyancy force around a body is generated? 2. (3pts) What condition must be met to avoid cavitation in a pump? 3. (3pts) Is it better to locate a pump upstream or downstream of a valve in order to avoid cavitation? Why? 4. (2pts) Are major losses always larger than minor losses? 5. (3pts) Why are golf balls dimpled? 6. (2 pts) Give a physical description (not the equation) of what the Reynolds number represents.
7. (a) (4 pts) For boundary layer flow developing over a flat plate with no pressure gradient, sketch qualitatively the wall shear stress as a function of distance from the leading edge of the plate, x. x (b) (2pts) Now assume that there is a favorable pressure gradient. Which would separate earlier: a laminar or a turbulent boundary layer?
8. (12 pts) Velocity field components are given by u x =tx 2, u y =-2txy. a. (2 pt) Is the flow one-, two-, or three-dimensional? b. (2 pts) Is the flow incompressible? c. (2 pt) Is the flow steady? d. (3 pts) Determine the acceleration of a fluid particle. e. (3 pts) Calculate the streamline passing through the point (1,1) at time t=1.
9. (6 pts) Consider two smooth pipes. The first pipe has a length, diameter, and flow rate of L, D, and Q, and the second pipe has 2L, 2D, and 4Q, respectively. The same fluid flows inside both pipes. The flow is laminar and fully developed. Circle the type of similarities that apply between the two flows. a. Kinematic similarity b. Geometric similarity c. Dynamic similarity d. Kinematic and geometric similarity e. Kinematic and dynamic similarity f. Dynamic and geometric similarity g. Dynamic and kinematic similarity h. Dynamic, geometric and kinematic similarity 10. (6 pts) In the previous question, what would be the ratio of p 1 / p 2 where p is the pressure drop over the entire length of the pipe? 11. (6 pts) In the previous questions, if both pipes have turbulent flow with the same friction factor, what would be the p 1 / p 2?
12. (6 pts) Sketch the pressure distribution along a converging-diverging nozzle for when the flow first becomes choked. Mark on your sketch the stagnation pressure, critical pressure, and back pressure. P x 13. (6 pts) The specific gravity of the manometer fluid shown below is SG=1.4. Determine the volume flowrate, Q, if the flow is inviscid and incompressible and the flowing fluid is water.
14. (6 pts) What is the friction factor inside the pipe shown below if the average velocity of the flow is 4 m/s? What is the Reynolds number if the pipe is smooth? 15. (6 pts) The velocity profile in a circular pipe of radius R is given by the following equation. Calculate the average velocity in the pipe. u r U 1 r R 4
16. (6 pts) Water flows in the branching pipe shown below with uniform velocity at each inlet and outlet. At each of three inlets and outlets, determine the sign of the mass flux and y-momentum flux (give your answers in terms of positive, negative, or zero). Mass flux y-momentum flux (1) (2) (3) 17. (12 pts) Air at standard conditions enters an elbow with a uniform speed of 10 m/s as shown to the right. The elbow has a square cross-section of 1m 1m. At the exit of the elbow the velocity profile is not uniform. In fact, there is a region of separation or reverse flow and the velocity profile is linear. Assume that the pressure at the entrance and the exit are the same and close to atmospheric. Calculate the forces on the elbow in the horizontal and vertical directions.
18. (11 pts) When a spherical drop of diameter D [L] is deformed, it oscillates at a frequency f [1/T] which depends on D, surface tension [M/T 2 ], density [M/L 3 ], and viscosity [M/LT]. f = fcn(d, ) a) (2 pts) How many dimensionless groups describe this relation according to the Buckingham Pi theorem? b) (9 pts) Find all the Pi-terms and express the final function in terms of dimensionless parameters using D, as repeating parameters. 19. (5 pts) A water pump is to produce a 200 ft head rise at a flow rate of 900 gpm. If the motor to drive the pump runs at 1200 rpm, what type of pump (axial, radial, or mixed) would be the best option for this application.