Fluid Dynamics Midterm Exam #2 November 10, 2008, 7:00-8:40 pm in CE 110

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1 CVEN Fluid Dynamics Midterm Exam #2 November 10, 2008, 7:00-8:40 pm in CE 110 Name: UIN: Instructions: Fill in your name and UIN in the space above. There should be 11 pages including this one. The exam is closed book, and only two double-sided sheets of notes and a calculator are permitted. No collaboration with others! For multiple choice questions, choose the single, best answer and mark your answer on the sheets provided. For short answer and workout problems, write down all general equations used and intermediate algebraic steps. Show all your work. Failure to do so will result in a lower score. Write the solutions to workout problems on separate pages from this booklet; record all other answers on the pages provided. You have 100 minutes to complete the exam. Grading: Problems Points Possible Points Earned Multiple Choice (1-15) 60 Workout (16-17) 40 Certification: I certify by my signature below that the work I am submitting is my own. An Aggie does not lie, cheat or steal, or tolerate those who do. Grade: / 100 Signature: 1

2 Properties of Water Property Symbol SI Units BG Units Density ρ 1000 kg/m slug/ft 3 Gravity g 9.81 m/s ft/s 2 Dynamic viscosity µ Pa s lb s/ft 2 Specific weight γ 9810 N/m lb/ft 3 Useful Equations F R = γ h c A (1) y R = I xc y c A + y c (2) D v! Dt =! v t + v! v! (3) p out γ! v ( ρ v! ˆn )da = F (4) CS + v 2 out 2g + z out = p in γ + v 2 in 2g + z in + h Q + h S h L (5) W h S =! γ Q (6) Geometric Properties of Some Common Shapes 2

3 Multiple Choice Questions (4 points each for total of 60 points) For each of the following questions, circle the answer that is most appropriate or closest numerically to your answer. Be sure to clearly mark only one answer. Multiple selections will be graded as zero. 1. The pressure drop over a 300 m long section of 4 cm diameter pipe is measured to be 120 kpa. If the elevation drops 25 m over that length of pipe, calculate the head loss in units of m. a b c d e The dynamic viscosity has dimensions of a. FT 2 /L b. F/TL 2 c. L 2 /T d. M/LT e. M/LT 2 3. Arrange the pressure p, flow rate Q, diameter D, and density ρ into a dimensionless group. a. pq 2 /ρd 4 b. p/ρq 2 D 4 c. pd 4 /ρq 2 d. pd 4 ρ/q 2 4. If the density of the air in the figure below is 1.2 kg/m 3, find the force F in Newtons needed to hold the plate in place. a. 3.6 b. 7.6 c. 2.4 d. 9.7 e

4 For problems 5 and 6, refer to the figure of the nozzle below 5. What is the flow rate Q through the nozzle in m 3 /s? Assume no head losses. a. 10 b. 23 c. 16 d What reaction force R x in Newtons is necessary to hold the nozzle in place if the velocity in the larger pipe is 5 m/s? Assume losses are present and the pressure gauge still reads 800 kpa. a b c d A pressure rise of 500 kpa is needed across a pump in a pipe with a flow rate of 0.2 m 3 /s. If the pump is 85% efficient, what is the power in kw needed to satisfy the design? a. 52 b. 65 c. 85 d. 100 e Which of the following statements is true about any control volume a. A control volume cannot change shape or size over time b. A control volume is an arbitrarily defined region of space through which fluid may pass in and out c. Control volumes move with a fixed set of fluid particles such that the control volume always contains the same fluid particles d. Control volume analysis can only be used to solve steady flow problems e. A control volume is always equivalent to a material system 4

5 For problems 9 through 11 refer to the following horizontal pipe section 9. Determine the head loss in ft and the direction of flow between points 1 and 2. The magnitude of the velocity at point 1 is 5 ft/s. a. 80 ft; from 2 to 1 b. 30 ft; from 2 to 1 c. 80 ft, from 1 to 2 d. 30 ft, from 1 to 2 e. The flow direction cannot be determined from the given data 10. Determine the x-component of the anchoring force in kips (kilo-pounds) if the flow rate in the pipe is 25 ft 3 /s and α is 30. a b c d If the angle alpha in the figure were 90 and the pressure drop remained unchanged, which of the following statements would be true? a. There would be no net force on the section since the fluid does not change direction b. Bernoulli s equation would be valid along a streamline c. The net force would be to the left d. The net force would be to the right e. Cavitation would begin at point 2 5

12. The hydraulic dredge shown in the figure below is used to dredge sand from a river bottom. Estimate the thrust (force in Newtons) needed from the propeller to hold the boat stationary.

6 12. The hydraulic dredge shown in the figure below is used to dredge sand from a river bottom. Estimate the thrust (force in Newtons) needed from the propeller to hold the boat stationary. Assume the specific gravity of the sand/water mixture is SG = 1.2. a. 220 b c d The bilge pump in an ocean liner discharges water from the hull at a rate of 0.5 ft 3 /s through a 5 in diameter pipe as shown in the figure. If the head loss through the pipe is 0.8 v 2 /(2g), the minimum pump size in hp needed to achieve the design is a. 0.5 b. 1.7 c. 9.5 d A student tests a wind turbine in the laboratory using smoke to visualize the flow. The wind tunnel is turbulent so that the flow is unsteady. What line will the smoke follow? a. Timeline b. Dateline c. Pathline d. Streakline e. Streamline 6

7 15. Determine the x-component of the acceleration field,! a = D! v / Dt, for a three-dimensional flow with velocity! v = 2xyt,5x 2 t, 2yzt ( ). a. 2xy + 4xy 2 t x 3 t b. 2xy + 4xy 2 t 2 + 4y 2 zt 2 c. 2xy + 5x 2 2yz d. Undefined Work Out Problems (points as indicated for a total of 40 points) For the work out problems, please show all your work. Write down all general equations used and intermediate algebraic steps. Failure to include important steps in a solution will result in a lower score. Please do not leave any problem blank: partial credit will be awarded for correct parts of the problem solution. Submit your solution in the space provided. 16. Consider the pipe T-connection and orifice meter in the figure below. A 1 m 3 /s flow rate of water enters the large pipe from left to right and the pressure in the system is as given by the gauges in the figure. The orifice meter is a flat plate that obstructs the flow with a center ring exit. Assume that 40% of the inflow exits through the free jet. 7

8 (a) (10 points) If the inner diameter of the orifice plate is 15 cm, calculate the reaction force necessary to hold the orifice plate in place. Assume the pressure at the plate throat is that given by the 150 kpa gauge. Draw your selected control volume, label the flows and applied forces, and calculate the reaction force in Newtons. 8

9 (b) (10 points) Calculate the reaction forces on the flange holding the T-connection in place. Again, draw a new control volume, label the flows and applied forces, and calculate the reaction forces (x-, and y-direction) in Newtons. 9

10 17. A pipeline carries drinking water through the Rocky Mountains as shown in the figure below. A pump is designed to drive the flow from Reservoir 1 to Reservoir 2 over a mountain ridge. A second pipeline from Reservoir 2 to Point 3 is planned for hydroelectric power. (a) (10 points) If the maximum flow rate from Reservoir 1 to Reservoir 2 is to be 3 m 3 /s, what power pump in kw will be required to achieve the design? Assume the total head loss to be 250v 2 /2g and the pipe diameter to be 1 m. 10

11 (b) (5 points) If the discharge at Point 3 is to be 1 m 3 /s, what is the maximum power in kw that could be generated by a hydroelectric turbine? Assume 100% efficiency and no losses. Also assume the velocity at Point 3 exiting the turbine is negligible and that the pressure is atmospheric. (c) (5 points) If the vapor pressure of water is 2.0 kpa (abs), what is the maximum height h that point A can be above Reservoir 2 before cavitation will begin? Assume no losses and use the design flow of 3 m 3 /s in the 1 m diameter pipe. Atmospheric pressure is 101 kpa (abs). Bonus: Can you think of any way to increase h without cavitating? 11

Exam #2: Fluid Kinematics and Conservation Laws April 13, 2016, 7:00 p.m. 8:40 p.m. in CE 118

CVEN 311-501 (Socolofsky) Fluid Dynamics Exam #2: Fluid Kinematics and Conservation Laws April 13, 2016, 7:00 p.m. 8:40 p.m. in CE 118 Name: : UIN: : Instructions: Fill in your name and UIN in the space