Name ______
ME363 Exam 2/Fall 2006
Honor Statement:
Signed:______
Concept Questions: /40
Problem 1: ______/30
Problem 2: /30
Total: /100
For the Concept Questions, please circle the correct answer.
“Vxyz”
A bus is moving to the right at U mph. You throw a water balloon at the bus at V mph after the bus passes you. A person on the bus sees the balloon hit the bus at:
a. V+U mph
b. U-V mph
c. V-U mph
d. V mph
“inertial vs non-inertial”
The difference between an inertial coordinate system and a non-inertial coordinate system is:
a. An inertial coordinate system is not moving while a non-inertial coordinate system is.
b. An inertial coordinate system is not rotating while a non-inertial coordinate system is.
c. An inertial coordinate system is not accelerating while a non-inertial coordinate system is.
“rocket problems”
Consider a rocket in flight:
a. Relative to a ground reference frame, the rocket’s exhaust can be moving in the same direction as the rocket.
b. The rocket’s velocity can never be faster than its exhaust velocity.
c. The rocket’s velocity can exceed its exhaust velocity
d. The rocket’s velocity equals its exhaust velocity at the maximum speed of the rocket.
e. a and c above
f. a and d above
“Energy”
Consider conservation of energy for a control volume:
a. Is a scalar equation.
b. In this form defines heat transfer to the control volume as positive in sign
c. Includes pressure in an important work term
d. all of the above
e. a and c above
“Angular Momentum I”
Consider conservation of angular momentum. The angular momentum of a system can be changed by:
a. The angular momentum of a system can be changed via a shaft that has a torque acting on it.
b. The angular momentum of a system can be changed via the action of a force acting at a distance.
c. A body force like gravity could result in a net change in angular momentum of a system.
d. A system is a quantity of fixed mass and therefore, fixed angular momentum. Everyone knows that!
e. all of the above
f. a-c above
“the unsteady term in the momentum equation 1”
Consider the tank that is filling in the figure below. The input flow is steady. The tank is not moving. The rate of change of the x-component of momentum in the tank is:
a.
b.
c. 0
d. Everywhere in the tank the x-component of momentum is zero, therefore, the rate of change of the x-component of momentum is zero.
e. a, c, and d above
f. a and c above
“body forces and surface forces”
Examples of a body force and a surface force are:
a. Shear is a body force, pressure is a surface force.
b. Gravity is a body force, shear is a surface force.
c. Gravity is a surface force, pressure force is a body force.
“nozzle 3”
Consider the flow from a firehose nozzle when the nozzle is in use. p1 and p2 represent the absolute pressures at the surfaces indicated. One control volume that could be used to determine the net pressure force is the following:
In this case, the net pressure force in the x-direction is given by:
a. Need to know the area of the control volume parallel to A1 and A2.
b. p1*A1-p2*A1
c. p1*A1-p2*A2
d. p1*A2-p2*A2
“comparing the mass and momentum basic equations”
When considering the basic equations, the following is/are true:
a. For conservation of mass and momentum, the rate of change of mass and momentum in the control volume is balanced by the rate at which mass and momentum are flowing out of the control surface.
b. For conservation of mass, a. is true, but for conservation of momentum, the change in the system momentum can be nonzero.
c. The system and control volume forms of the conservation of mass equation are the same, however, for the conservation of momentum equation, they are different.
“skydiver 1”
Consider a skydiver in free fall. Which of the basic laws apply to this situation?
a. The conservation of momentum
b. The conservation of energy
c. The second law of thermodynamics
d. The principle of angular momentum
e. The conservation of mass
f. all of the above
g. d and e above
Problem 1 {30 points}: A bus is traveling east on a straight highway at Vb = 60 mph in heavy rain. To make matters worse, the rain is accompanied by a Vw = 10 mph wind out of the east (blowing west). We will try to figure out how much extra gas it takes the bus to travel in this rain, compared to traveling in dry air.
The front of the bus is flat with an area A = 64 ft2. In this problem you will only consider the rain that hits the front of the bus and ignore effects of the top, sides, etc. You may assume the rain freezes to the front of the bus upon contact if it simplifies your thinking. When comparing the rainy air to dry air, the density difference is Dr = + 0.00028 lbm/ft3.
Notes: 1 mi = 5280 ft; 1 hour = 3600 s; rwater = 1.94 slug/ft3 = 62.5 lbm/ft3; rair = 0.00247 slug/ft3 = 0.0795 lbm/ft3. Make a sketch to start the problem.
a) {12 points}Using a control volume that just encloses the bus and moves with the bus, find a symbolic expression for the added propulsion force DF that is required to maintain the bus speed in the presence of the rain. DF should be zero for travel in dry air. Your expression should contain only the variables above.
b) {12 points}Using a large control volume the size of the bus (64 ft2 cross-sectional area, just like the bus) but extending for many miles in front of the bus, moving with the wind or fixed to the ground, find a symbolic expression for the added propulsion force DF.
c) {6 points}Choose one of your expressions from above and determine DF for the numbers given above. Later in class, we will convert this to gallons of gas.
Problem 2: {30 points} A hypodermic needle containing flowing water is held at the end of a syringe by glue. The needle i.d. is 694 μm. The input velocity is uniform with U = 5 m/s. The output velocity profile is parabolic as shown. The gage pressure at station 1 is P1 = 61 kPa. In this problem you will determine Fg, the force (in the x direction) that the glue must support to keep the needle attached. Notes: 1 mm = 0.001m; 1 μm = 0.000001 m; A = πR2; density of water ρw = 1000 kg/m3.
a) {24 pts} Find a symbolic expression for Fg containing only variables shown above.
b) {6 points} Solve your expression to obtain a numeric value for Fg in [N].
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