Mem 220 Mock Final Exam

A

FINAL EXAMINATION

MEM 220: BASIC FLUID MECHANICS March 20, 2007

NAME _____________________________________

Multiple Choice:

____________

points of 20

Problem 1

____________

points of 50

Problem 2

____________

points of 30

____________

points of 100

Solve:

TOTAL

Please remember to: 1. Write your units at all steps and especially in the answer! 2. Show all work and explain steps 3. List all assumptions 4. Write neatly 5. Only exams in non-erasable ink will be eligible for re-grade 6. Box the answer

A

Multiple Choice and Short Answer (circle the correct answer) 1. You want to increase the speed of sound through a fluid-filled tank. Which of the following would increase the speed of sound? (Select all that apply) A. Increase fluid bulk modulus Ev B. Increase fluid density C. Increase fluid temperature D. Increase fluid pressure

2. Why does supersonic flow get choked at the throat?

3. The plug for a sink drain is designed to seal at a gage pressure of 0.1 psi. How deep must the water in the sink be for the plug to seal? A. 6.25 inches B. 2.75 inches C. 0.02 inches D. 9.1 inches 4. What is the pressure difference between points 1 and 2, if ρf = 912 kg/m3, ρm = 13,600 kg/m3, a = 10 cm, and b = 5 cm? A. P1 – P2 = 6223 N/m2 B. P1 – P2 = 20407 N/m2 C. P1 – P2 = -6344 N/m2 D. P1 – P2 = 8011 N/m2

A

5. A 0.5 m x 0.5 m x 0.5 m block of unknown material is lowered into the water. If the tension on the rope is 1594 N when the block is in water, what is the density of the block material? A. ρblock = 300 kg/m3 B. ρblock = 1000 kg/m3 C. ρblock = 1300 kg/m3 D. ρblock = 2300 kg/m3

6. In the following equation, clearly label the static, stagnation, and total pressures.

P+

1 ρV 2 + ρgz = Co 2

7. A turbulent boundary layer is _________ than a laminar boundary layer. A. Thicker B. Thinner C. The same thickness

8. A fire hydrant is opened on a hot day, resulting in a vertical water jet. If the gage pressure just inside the fire hydrant is 400 kPa, and water is assumed to be inviscid, what is the maximum height that the water jet can obtain (h)? A. 30.4 m B. 10.4 m C. 40.8 cm D. 40.8 m

A

9. As you go up in the atmosphere, A. Pressure increases and temperature decreases B. Pressure increases and temperature increases C. Pressure decreases and temperature decreases D. Pressure decreases and temperature increases

10. The acceleration field is given by the material derivative of the velocity vector. For a 2dimensional velocity field, the acceleration in the x direction is:

ax =

∂u ∂u ∂u +u +v ∂y ∂t ∂x

For the velocity field described by u = 1 + 3x – y and v = 1 – 2x – 3y, what is the acceleration in the x direction at (x, y) = (2, -3)? A. 16 B. 24 C. 44 D. 4

11. Which of the following will increase lift on an airfoil? (circle all that apply) A. increase the angle of attack B. maintain a laminar boundary layer C. induce separation at the rear of the airfoil D. use wing flaps to increase airfoil curvature

12. Circle each of the following statements that is true: A. The Reynolds transport theorem is used to transform conservation equations from their naturally occurring control volume form to a system form. B. The Reynolds transport theorem is applicable only to non-deforming control volumes. C. The Reynolds transport theorem can be applied to both steady and unsteady flow. D. The Reynolds transport theorem can be applied to vector and scalar quantities.

A

13. When using the control volume formulation for the conservation of momentum, which of the following do you need to consider: (circle all that apply) A. Pressure at inlets and outlets B. Mass flow at inlets and outlets C. Velocity at inlets and outlets D. Forces applied to the control volume

14. List two boundary conditions that can be applied in the integration of the Navier-Stokes equations for viscous, incompressible flow. A.

B.

15. True or False: If a Reynolds number is small, the viscous effects are relatively strong. A. True B. False

16. Which of the following quantities are conserved in fluid mechanics? (circle all that apply) A. Mass B. Vorticity C. Momentum D. Energy E. Pressure

17. For which cases would you want turbulent pipe flow? (circle all that apply) A. When you want a lot of heat transfer B. When you want a lot of mixing C. When you want a small pressure drop D. When you want a long entrance length

A

18. If water is added to a bathtub (6 ft long x 3 ft wide x 2 ft high) at Q = 15 gallons/minute, how fast is the water in the bathtub rising? (7.5 gallons = 1 ft3) A. dh/dt = 0.83 inches/min B. dh/dt = 1.33 inches/min C. dh/dt = 6.25 inches/min D. dh/dt = 10 inches/min

19. How does velocity through a diverging duct (increasing area) vary for subsonic and supersonic flow? A. Velocity increases for subsonic flow; velocity decreases for supersonic flow B. Velocity decreases for subsonic flow; velocity increases for supersonic flow C. Velocity decreases for subsonic flow; velocity decreases for supersonic flow

20. Which area would you use to calculate the friction drag from the skin friction coefficient? A. Cross section area B. Planform area C. Wetted surface area

A

Solve I. You are testing a new space shuttle design with a 1:50 scale model in a wind tunnel. NASA is concerned about the lift the shuttle will generate when operating at slow speeds upon landing. A. You think that lift (/) is a function of shuttle velocity (V), air density (ρ), air viscosity (μ), wing chord length (c) and wing length (l). Use dimensional analysis to develop the Pi terms.

B. Your boss tells you that Reynolds number similarity is important for your tests. If the space shuttle landing speed is 220 mph, and your wind tunnel uses air, what air velocity do you need in your wind tunnel? (1 mph = .447 m/s)

C. If this velocity is not possible in your wind tunnel, how could you modify the system to still achieve Reynolds number similarity?

A

D. The space shuttle wings are shaped as shown in the diagram. Experiments by your predecessors have demonstrated that the pressure drag coefficient follows the chart at right. Calculate the pressure drag at an angle of attack (α) = 5º for a wing of length (b) = 9 m, chord length (c) = 3 m, and height (h) = 0.5 m, where the aspect ratio (A) = b/c.

E. The transition from a laminar to a turbulent boundary layer occurs at a Reynolds number of 5 x 105. At what distance from the leading edge does the boundary layer transition occur?

F. Find the skin friction coefficient at the middle of the wing (x = 4.5 m) and use this value to estimate the skin friction drag on one shuttle wing.

A

II. For your next coop, you are to recreate a rain forest exhibit at the zoo. The zoo directors want your system to produce both a light and a heavy rain, which correspond to the minimum and maximum head generated by the pump. Your system pumps water from a large tank at atmospheric pressure up 15 m and for a total length of 50 m. The pipe is 5 cm diameter stainless steel (surface roughness ε = .045 mm). 1. For light rain, the flow rate is Q = 44 cm3/s. How much head should your pump generate?

2. For heavy rain, the flow rate is Q = 5500 cm3/s. How much head should your pump generate?

Equation Sheet for Final Exam 1. − ∇P − ρgkˆ = ρaˆ

V2 14. P + ρ ∫ dn + ρgz = C o ℜ

∂p ˆ ∂p ˆ ∂p ˆ i+ j+ k 2. ∇P = ∂x ∂y ∂z

∂p ρV 2 15. − = ∂n ℜ

3. −

∂p = ρg ∂z

16. τ = μ

du dy

4. p 2 − p1 = ρgh

17.

r ∂ ρ d ∀ + ρ V ∫ ∫CS ⋅ nˆdA = 0 ∂t CV

5. p = ρRT

18.

r r r ∂ Vρd∀ + ∫ VρV ⋅ nˆdA = ∑ F ∫ ∂t CV CV CS

6. FR = ρghc A

19.

r r r r r r r ∂ ˆ r × V ρ d ∀ + r × V ρ V ⋅ n dA = r ×F ∑ ∫ ∫ ∂t CV CV CS

20.

r ∂ e ρ d ∀ + e ρ V ∫ ∫CS ⋅ nˆdA = Q& net ,in +W& net ,in ∂t CV

21.

P2 P 1 2 1 2 + V2 + z 2 = 1 + V1 + z1 + h p − hL ρg 2 g ρg 2 g

7. y R =

I xc + yc yc A

8. FB = ρg∀ 9.

(

)

r

⎛ ∂v z ∂ (rvθ ) ⎞ eˆr ⎛ ∂v r ∂v z − − ⎟ +⎜ ∂z ⎠ r ⎝ ∂z ∂r ⎝ ∂θ

ξ = ∇ ×V = ⎜ ∂z rω 2 = g ∂r

11.

∫

12.

dp

1 + V 2 + gz = C o ρ 2

dp

∫ρ

13. P +

+∫

V2 dn + gz = C o ℜ

1 ρV 2 + ρgz = C o 2

)

(

)

r ⎛ ∂w ∂v ⎞ ⎛ ∂u ∂w ⎞ ⎛ ∂v ∂u ⎞ 22. ξ = ∇ × V = ⎜⎜ − ⎟⎟iˆ + ⎜ − ⎟ ˆj + ⎜⎜ − ⎟⎟kˆ ∂ y ∂ z ∂ z ∂ x ⎝ ⎠ ⎝ ∂x ∂y ⎠ ⎝ ⎠

ay ∂z =− ∂y g + az

10.

(

23.

⎛ ∂ (rvθ ) ∂v r ⎞ − ⎟eˆθ + ⎜ ∂θ ⎠ ⎝ ∂r

⎞ eˆ z ⎟ ⎠ r

r ∂ρ + ∇ ⋅V = 0 ∂t

r ∂u ∂v ∂w 1 ∂ (rv r ) 1 ∂vθ ∂v z 24. ∇ ⋅ V = + + = + + r ∂θ ∂z ∂x ∂y ∂z r ∂r

25. Q =

πR 4 ΔP 8μl

26. Patm = 14.7 psi = 101300 Pa, g = 9.81 m/s2 = 32.2 ft/s2

27.

le = 0.06 Re (laminar) D

28. Q =

29.

1

le = 4.4 Re 6 D

(turbulent)

ρVD μ

Re =

πD 4 ΔP 128μl

τ=

DΔP 4l

30.

⎛D⎞ ΔP⎜ ⎟ 64 ⎝ l ⎠ = 8τ w = f = 1 Re ρV 2 ρV 2 2

31.

hL =

2 4lτ w ⎛ l ⎞⎛ V ⎞ ⎟⎟ = f ⎜ ⎟⎜⎜ ρgD ⎝ D ⎠⎝ 2 g ⎠

⎛V 2 ⎞ ⎟⎟ 32. hL ,min or = K L ⎜⎜ ⎝ 2g ⎠

33.

CL =

34. C D =

35. c =

L 1 ρU 2 A 2 D 1 ρU 2 A 2

Ev

ρ

= kRT

Laminar δ

Boundary layer thickness

x

δ*

=

=

5 Re x

δ

1.721 Re x

δ*

Displacement thickness

x

Momentum thickness

Θ 0.664 = x Re x

Skin friction coefficient

C f ,x =

Turbulent

0.664 Re x

x

x

0.16

=

1

Re x 7 =

0.020 1

Re x 7

Θ 0.016 = x Re 17 x C f ,x =

0.027 1

Re x 7