Download Exam1Fall06_final

Name _______________________________________
ME363 Exam 1/Fall 2006
Honor Statement:
Signed:_____________________________________________
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Concept Questions:
Problem 1:
/40
______/30
Problem 2:
/30
Total:
/100
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For the Concept Questions, please circle the correct answer.
“definition of fluid”
A fluid is:
a) A substance that fills the volume of the container in which it is placed.
b) A substance in liquid phase.
c) A substance that deforms continuously under the action of a shear stress.
d) a & c above
“figure 1.1 question 3”
Given the following diagram for the definition of a fluid:
Constant F
t0
t1
t2
This figure is a depiction of the behavior of a fluid under the action of a constant shear force.
Given this, if the viscosity of the fluid is somehow made to be infinite and the fluid slip at the top plate is
somehow made to be infinite, which of the following are true?
a. All of the fluid has a velocity of zero
b. The magnitude of the horizontal fluid force on the lower plate is zero
c. The upper plate will continue to accelerate while a force is applied, regardless of how long the force is
applied.
d. All of the above
e. b & c above
“what’s a basic equation?”
The basic equations governing fluid mechanics:
a) include conservation of momentum and the Ideal Gas Equation
b) include conservation of energy and the 2nd law of thermodynamics
c) include conservation of mass and Newton’s Law of viscosity
“skydiver 1”
Consider a skydiver in free fall. Which of the basic laws apply to this situation?
a. The conservation of energy
b. The second law of thermodynamics
c. The principle of angular momentum
d. The conservation of momentum
e. The conservation of mass
f. All of the above
g. b, d, and e above
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“ideal gas equation”
The ideal gas equation is:
a. a fundamental equation similar to the conservation of mass equation
b. a model of real gas behavior.
c. used to describe the behavior of ideal gases
“Brett Favre 1”
Consider Brett Favre playing football. I am interested in knowing how many footballs are on the field of
play at any instant in time. Then I am interested in the:
a. LaGrangian or particle view of the football
b. Eulerian view of the field
c. Control Volume Equations applied to the football field
d. System Equations applied to the football that has just left Brett’s hand
e. All of the above
f. Neither System nor Control Volume Equations
g. a & d above
h. b & c above
“differential vs. integral”
Which of the following are true regarding the difference between the integral and differential approach.
Again consider the football in flight:
a. The integral approach is not useful because it does not retain sufficient detail of the flow pattern around
the football.
b. The differential approach allows us to determine flow at any point on the football at any point in the
flight of the football.
c. The combined integral-differential approach is always the best method.
“uniform vs constant”
Imagine we are viewing the pipe from an Eulerian perspective. For the gas inside the pipe, involved in this
steady flow situation, which is/are true?
a.
b.
c.
d.
e.
f.
The density is not a function of time
The density of the gas is uniform
The density is a function of position even though this is a steady flow
all of the above
a and c above
b and c above
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“implications of continuum assumption 2”
For a real fluid (which could be different than the ideal continuum we will use in this course):
a. all of the below
b. The density is defined between the two limits defined in b. and c.
c. Below a certain volume of fluid, the density can fluctuate irregularly.
d. Above a certain volume of fluid, the density can increase or decrease due to large-scale effects.
“System form of basic equations”
The following is true of the system form of the basic equations (mass, momentum, angular momentum,
energy, and entropy):
a. The equations apply to a fixed quantity of mass
b. The equations are formulated in extensive properties
c. There is a general method to convert the system form to control volume equations
d. All the basic equations are vector equations.
e. All of the above
f. a-c above
g. a and c above
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A hollow cube 1m x 1m x 1m made by welding together six square metal panels. It is filled completely with oil
through a vent hole in the top panel. It is then placed on a cooled surface in a heated room. After reaching
thermal equilibrium, oil density varies from ρh = 900 kg/m3 at the top of the cube to ρc = 1100 kg/m3 at the
bottom. Note that the variation of oil density with vertical position is  = 200 kg/m4 (200 kg/m3 for every

vertical m) Assume the oil density varies linearly from top to bottom. Use g = + 9.81 m/s2 ĵ , and use g = 9.81

m/s2 to note the magnitude of g . Note: edge A-D is closest to you, edge B-C is on the back side of the cube.

a) {10 points} Starting from p  g , show that the pressure distribution in the cube is given by
gy 2

. Hint: you need to first reduce p  g to a simpler scalar equation, then separate variables
p   h gy 
2
and integrate. Sketch this pressure distribution on the right side panel here:
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b) {15 points} Obtain a symbolic expression for the moment on the right side panel, due to the oil pressure,
about axis A-B. Your expression should contain only g ,  h ,  , w, h .
c) {5 points} Solve (b) for a numeric answer with units and a direction.
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Name _______________________________________
Problem 2: {30 points} A rectangular channel system is shown below. (Everything is rectangular, nothing is
round). Water enters from the left. The velocity profile is shown at section C-D, with a = 2 ft -1 and b = 1 ft -2.
The flow is uniform at the exit on the right. For both the entrance and exit flows, Umax = 0.5 ft/s.
a) {25 points} Obtain a symbolic expression for the rate of change of the height of water in the accumulator,
d d 2 
. The expression should contain only Umax, a, b, d1, d3, and L.
dt
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b) {5 points} Solve (a) for a numerical answer with units.
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