me 309 – fluid mechanics last name (print): spring … 309 – fluid mechanics last name (print):...

ME 309 – Fluid Mechanics LAST NAME (print): ___________________________________ Spring 2015 FIRST NAME (print): __________________________________ 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 Mr Berdanier 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) 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 SCORE: TOTAL (100 out of 100 points available ):

ME 309 – Fluid Mechanics LAST NAME (print): ___________________________________ Spring 2015 FIRST NAME (print): __________________________________

Part 1 (40 pts) SCORE:

Problem 1-1 (10 pts)

The inverted U-tube manometer shown in the figure contains oil with SG=0.9 and water. If pA-pB=-5 kPa, find h.

ME 309 – Fluid Mechanics LAST NAME (print): ___________________________________ Spring 2015 FIRST NAME (print): __________________________________ Problem 1-2 (20 pts)

In the wind tunnel shown above, the fan is producing a constant wind speed of 40-m/s. The tunnel pipes are 3-m in diameter and can be considered smooth. The four bends are all the same with a loss coefficient k=0.3. The tunnel is all at the same elevation, gravity effects are ignored. Determine:

a) The total minor losses b) The total major losses c) The head that the fan generates d) The power that the fan adds to the air.

ME 309 – Fluid Mechanics LAST NAME (print): ___________________________________ Spring 2015 FIRST NAME (print): __________________________________ Problem 1-3 (10 pts)

A viscous fluid is contained between infinitely wide parallel plates spaced a distance h apart. The upper plate is fixed and the bottom plate oscillates harmonically with a velocity amplitude U and frequency ω. The differential equation for the velocity distribution between the plates is:

where u is the velocity, t is time and ρ, µ, are the density and dynamic viscosity of the fluid respectively.

a) Rewrite this equation in non-dimensional form using h, U and ω as reference parameters.

b) Identify the dimensionless number that appears and state what ratio of forces does this number represent

ρ ∂u∂t

= µ ∂2u∂y2

ME 309 – Fluid Mechanics LAST NAME (print): ___________________________________

Spring 2015 FIRST NAME (print): __________________________________

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SCORE:

Problem III-1 (6 points)

You are told that a boundary layer velocity profile is “parabolic,” such that:

��

(a) [2 pts] Is this boundary layer laminar or turbulent?

(b) [2 pts] You are told the displacement thickness for this velocity profile is �� .

Describe using words and/or drawings what the displacement thickness represents.

(c) [2 pts] You want to use the Momentum Integral Equation (MIE) to calculate boundary

layer information:

��

��

If you have a zero pressure gradient (ZPG) flow, what simplification can you make to the

above equation, and why?



(d) [3 points] For this parabolic velocity profile, the skin friction coefficient is defined by:

�� !�"#$%

If the free-stream (inviscid) velocity is U, the density is �, and the dynamic viscosity is �,

determine the value of the wall shear stress at a position x on a flat plate using the above

equation.




[6 pts] Fairings are attached to the front and back of a cylindrical body to make it look more

streamlined. What is the effect of this modification on the (i) friction drag, (ii) pressure drag, and

(iii) total drag? Assume the Reynolds number is high enough so that the flow is turbulent for

both cases.

Circle the correct answer:

(i) Friction drag will: increase decrease

(ii) Pressure drag will: increase decrease

(iii)Total drag will: increase decrease




Stagnation conditions in a solid propellant rocket motor are

To = 727 ºC and Po = 10 MPa (absolute). At maximum thrust

conditions, the exit (throat) of the rocket nozzle is “choked.”

(a) [3 pts] Using complete sentences (no equations), define the meaning of “choked” flow in

terms of the mass flow rate through the nozzle.

(b) [4 pts] Using the information provided, evaluate the value of the Mach number at the exit

of the nozzle.

(c) The exiting combustion products are not air, so you can assume that R = 323 J/(kg·K)

and k = 1.2.

(i) [4 pts] Calculate the pressure, P, at the nozzle exit.

[2 pts] Clearly define any required assumptions to allow your calculations.

(d) [2 pts] For space applications, your employer wants to test this rocket nozzle in different

conditions, such that the nozzle exhausts to vacuum (Pb = 0 MPa). How will the flow in

the nozzle change?

Po

To

Nozzle exit


Part 2 (30 points) SCORE:

Problem 2-1 (3 points) Consider the following steady state velocity distribution between two horizontal plates. Which direction the plates are moving? A) Both plates are moving together B) Both plates are stationary C) Upper plate is stationary and lower plate is moving to left D) Upper plate is stationary and lower plat is moving to right E) Plates are moving in the opposite direction (2 points) For the velocity profile above, which statement is correct?

A) Pressure gradient is zero, dp/dx=0 B) Pressure gradient is positive, dp/dx>0 C) Pressure gradient is negative, dp/dx<0 D) None of the above

ME 309 – Fluid Mechanics LAST NAME (print): ___________________________________ Spring 2015 FIRST NAME (print): __________________________________ Problem 2-2 (10 points) Consider the flow field given by:

V ̂ y ȷ̂ .

Determine: (a) the number of dimensions of the flow, (b) if it is an incompressible flow, and (c) the acceleration of a fluid particle at point (x, y, z) = (1, 2, 3).

ME 309 – Fluid Mechanics LAST NAME (print): ___________________________________ Spring 2015 FIRST NAME (print): __________________________________ Problem 2-3 (3 points) What is the momentum flux of the jet in the x-direction? (The width of the jet into the screen is w)

A) ρV2bw

B) ρV2bw cosθ

C) ρV2bw cos2θ

D) ρV2bw/cosθ

E) None of the above

(3 points) What is the momentum flux of the jet in the x-direction? (The width of the jet into the screen is w)

A) ρV2bw

B) ρV2bw cosθ

C) ρV2bw cos2θ

D) ρV2bw/cosθ

E) None of the above

V

b

x θ

CS

CV

V

b

x θ

CS

CV

ME 309 – Fluid Mechanics LAST NAME (print): ___________________________________ Spring 2015 FIRST NAME (print): __________________________________ Problem 2-4 (9 points) To check the machining accuracy of a long shaft with radius Ri, it is vertically inserted into a sleeve block (inner radius Ro) concentrically. Oil (density , dynamic viscosity ) is filled in the gap between shaft and sleeve block. The shaft is kept stationary and the sleeve block slides in the vertical direction at a constant speed V. The gravity acting on the oil film can be neglected. The edge effects near both ends of the sleeve block can be neglected too. Assume the oil flow is axisymmetric and fully developed in the gap, and there is NO pressure variation in the oil film.

a. Without solving any equations, cancel all the terms of the Navier-Stokes equations as appropriate:

2 2 2

2 2 2 2

2 2

2 2 2 2

1 1 2

1 1 1 2

r r r r r rr z r r

rr z

u u uu u u u u upu u ru g

t r r r z r r r r r z r

u u u u u u u u u upu u ru

t r r r z r r r r r z r

2 2

2 2 2

1 1

r

z z z z z z zr z z

g

uu u u u u u upu u r g

t r r z z r r r r z

b. Which statement is correct for the velocity profile in the oil film if (Ro-Ri) ≪ Ro:

A) Velocity linearly changes with r B) Velocity is a parabolic function of r C) Velocity changes as ln(r) D) Velocity changes as 1/r

r

z

me 309 – fluid mechanics last name (print): spring … 309 – fluid mechanics last name (print):...

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