Name ______
ME363 Exam 3/Fall 2006
Honor Statement:
Signed:______
Concept Questions: /40
Problem 1: ______/10
Problem 2: /15
Problem 3: ______/19
Problem 4: /16
Total: /100
For the Concept Questions, please the correct answer.
“Reynolds number 2”
Reynold’s number is considered to be the ratio of inertial forces to viscous forces. Because of this:
a. At specific Re regions, the flow transitions from laminar to turbulent flow.
b. At low Re, i.e. laminar flow, viscous effects dominate the flow behavior
c. At high Re, i.e. turbulent flow, viscous effects do not dominate the flow behavior
d. all of the above
e. a and b above
“pitot-static probe”
Imagine you are using a pitot-static probe to measure the speed of your bicycle at sea level. What is the value of the static pressure that you would measure?
a. A pressure equal to the total pressure.
b. A pressure below atmospheric
c. A pressure above atmospheric
d. A pressure equal to atmospheric
e. a and e above
“Continuity II”
The “continuity equation” is given as Eq. 5.1a in your text:
The authors obtained this equation…
a. by taking the derivative of the conservation of mass equation
b. by applying the integral conservation of mass equation to a differential element
c. using Taylor series expansions to calculate fluid properties at the faces of a differential element
d. all of the above
e. b and c above
“reading the conservation of mass equation”
Consider the conservation of mass equation:
In words, this equation reads:
a. The mass flow into the control volume is equal to the mass flow out of the control volume
b. The accumulation of mass in the control volume is balanced by the net rate at which mass flows into the control volume
c. The rate of change of the amount of mass in the control volume is balanced by the net rate at which mass flows out through the control surface
d. The fixed amount of mass in the control volume is balanced by the mass that leaves or enters the control volume.
e. b and c above
“identifying extensive properties”
Which of the following are extensive properties?
a. mass
b. temperature
c. entropy
d. pressure
e. internal energy
f. specific internal energy
g. density
h. a and e above
i. a, c, and e above
j. a, c, and d above
“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. The density is a function of position even though this is a steady flow
b. The density of the gas is uniform
c. The density is not a function of time
d. all of the above
e. a and c above
“manometers”
Two manometers are shown below. One manometer with a single “U-tube” is connected between tanks “A” and “B”. The other manometer has two U-tubes and is connected between tanks “C” and “D”. The four tanks contain air. The liquid in both manometers is water. Circle the letter of the correct statement.
A (PA – PB) = 4(PC – PD)
B (PA – PB) = (PC – PD)/2
C (PA – PB) = (PC – PD)/4
D (PA – PB) = (PC – PD)
E (PA – PB) = 2(PC – PD)
“figure 1.1 question 4”
Given the following diagram for the definition of a fluid:
This figure is a depiction of the behavior of a fluid element under the action of a constant shear force.
Given this, if the viscosity of the fluid is somehow made to be zero, which of the following are true?
a. The magnitude of the fluid force on the lower plate is zero
b. All of the fluid has a velocity of 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. a and c above
“clothes dryer”
If you go outside and feel the exhaust of the dryer in my house the flow feels “weak”. Which of the following are likely to increase the mass flow rate of air leaving the house through the dryer vent:
a) Installing a new hose with a smoother surface finish
b) Cleaning the hose connecting the dryer to the outside world.
c) Increasing the inside diameter of the hose.
d) Lengthening the hose.
e) all of the above
f) a-c above
g) b and c above
“fluids magnitudes 1”
Later we will learn about buoyancy, a concept that may already be familiar to you. A consequence: when you weigh yourself on a scale, you underestimate your true weight by the weight of the air you displace.
Typically, what is this error (how many pounds does a volume of ordinary air the size of an average person weigh)?
a) 0.0015 pounds
b) 0.015 pounds
c) 0.15 pounds
d) 1.5 pounds
Problem 1 {10 points}: In a diesel engine, high-pressure diesel fuel is delivered from a large-diameter (10 mm) supply line through a small (0.1 mm diameter) hole. This is done to form a high-speed jet that comes out of the hole and produces a fuel spray which burns. The supply line pressure is P. Diesel fuel properties: density ρ = 843 kg/m3, viscosity μ = 2.53 x 10-3 kg/m-s. Also note: 1 bar = 100,000 Pa ≈ 1 atm.
a) {4 points} Find a symbolic expression for Vjet, the fuel velocity in the spray emerging from the hole.
b) {3 points} If P = 400 bar, what is Vjet in m/s?
c) {3 points} If P = 1600 bar, what is Vjet in m/s?
Problem 2: {15 points} Consider the flow in the fuel supply line described in problem 1.
a) {3 points} For the P = 1600 bar case, what is the flow velocity in this line when fuel is being sprayed? [m/s]
b) {3 points} What is the Reynolds number of the flow in the supply line?
c) {2 points} Is the flow laminar or turbulent?
d) {3 points} What is the entrance length for this flow? [mm]
e) {4 points} Assume a straight piece of fuel supply line 1 m long containing fully-developed fuel flow. What is the pressure drop in this 1-m section [Pa]?
Problem 3: {19 points} The time it takes for a commuter to make it to work, ttot, is expected to be a function of the maximum speed of the commute vehicle, Vmax, the distance to work, D, and the time twait spent waiting for stoplights or to board the bus or whatever.
a) {3 points} How many pi groups characterize this problem?
b) {4 points} Identify the pi group(s):
c) {4 points} Fill in the table below – only fill in as many pi group columns as you need:
Name / ttot [hr] / Vmax [mi/hr] / D [mi] / twait [hr] / Π1 / Π2 / Π3 / Π4‘Perfect’ commute / 0.3 / 15 (cycle) / 4.5 / 0
Undesirable commute / 2 / 65 (car) / 45 / 1
d) {8 points} Use the information you entered in (c) to predict the commute time ttot for ‘Susie’. You may have to make one or more assumptions/extrapolations/interpolations in this process, please explain your work.
Name / ttot [hr] / Vmax [mi/hr] / D [mi] / twait [hr] / Π1 / Π2 / Π3 / Π4Susie’s commute / 18 (cycle) / 4.5 / 0.18
Problem 4: {16 points} Consider an air flow with a velocity field given by , with a = 1 [s-1] and b = 1 [ft∙s-2] . For air, ρ = 0.00234 slug/ft3 = 0.0753 lbm/ft3and μ = 3.79 x 10-7 lbf∙s/ft2.
a) {3 points} Sketch velocity vectors at each of the 9 points in the plots below for t=0 and t = 1s. The points below are on a 1 ft x 1 ft grid.
t = 0 s t = 1 s
b) {3 points} Does this field satisfy conservation of mass? (show your work)
c) {5 points} Write a vector equation that describes the acceleration anywhere in this velocity field.
d) {5 points} Assuming gravitational forces are unimportant, estimate ΔP [psi], where ΔP = P1 – PO, where P1 is the pressure at the point (x,y) = (0,1) and PO is the pressure at the point (0,0).
Some extra work space:
______
Appendix: Moody Chart; note Friction factor
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