name (-1 point, if missing): id (-1 point, if missing): no
TRANSCRIPT
AE301
Your solution must be less than total 2-pages for each problem. (Page 1 of 14) Write your name and student ID on all pages.
ID (-1 point, if missing): NAME (-1 point, if missing):
NO PARTIAL CREDITS FOR YOUR WORK, IF THESE GENERAL REQUIREMENTS ARE NOT SATISFIED
Show all steps of your work and list all assumptions. Explain, in your own words, full details of your work. Clearly show your
conclusion (box your answer) associated with proper units specified for each problem. Show all engineering units for all your values.
THIS IS QUIZ: Absolutely no external help of any kind. You MUST solve problems using your own fluid mechanics notes ONLY.
PROBLEM 1a (1 point each = 5 points total)
This is the review of fluid mechanics (Dr. Hayashibara's Fluid Mechanics Unit A: Fundamental Concepts)
Basic dimensions in engineering (units)
An automobile tire (with an internal volume of 100 gallons: note that 1 ft3 = 7.48 gallons) was inflated to the gage pressure of 32 psi
of air at a car mechanic at Phoenix (the atmospheric pressure at Phoenix was happened to be the standard sea-level value, that was:
14.7 psi). The gravity was happened to be NOT the standard value, but 31.9 ft/s2 at Phoenix at that time (note: this is hypothetical).
If the air temperature inside the tire was 120 F, calculate the followings:
(a) What was the air density, in “pounds per cubic inches,” in the tire (at Phoenix)?
(b) What was the weight of air, in “pounds,” in the tire (at Phoenix)?
(c) What was the mass of air, in “pounds,” in the tire (at Phoenix)?
Suppose, you drive this vehicle back to Prescott (a “mile-high” atmospheric pressure: 12.8 psi at Prescott). The temperature inside the
tire is then changed to 20 F (very cold weather). Also, the gravity at Prescott is now 30.9 ft/s2 (note: this is hypothetical). Although
there is absolutely no leak of air from the tire, you notice a slight volume change of the tire (internal volume of the tire is now 90
gallons). Under these conditions, calculate the followings:
(d) What is the specific weight of air, in “pounds per cubic inches,” in the tire (at Prescott)?
(e) What is the gage pressure, in “psi,” of the tire (at Prescott)? Does this activate “low tire pressure” warning indicator of your car?
Note that the “low tire pressure” warning is set for 32 psi or less tire air pressure as a manufacturer default.
AE301
Your solution must be less than total 2-pages for each problem. (Page 2 of 14) Write your name and student ID on all pages.
ID (-1 point, if missing): NAME (-1 point, if missing):
AE301
Your solution must be less than total 2-pages for each problem. (Page 3 of 14) Write your name and student ID on all pages.
ID (-1 point, if missing): NAME (-1 point, if missing):
NO PARTIAL CREDITS FOR YOUR WORK, IF THESE GENERAL REQUIREMENTS ARE NOT SATISFIED
Show all steps of your work and list all assumptions. Explain, in your own words, full details of your work. Clearly show your
conclusion (box your answer) associated with proper units specified for each problem. Show all engineering units for all your values.
THIS IS QUIZ: Absolutely no external help of any kind. You MUST solve problems using your own fluid mechanics notes ONLY.
PROBLEM 1b (1 point each = 5 points total)
This is the review of fluid mechanics (Dr. Hayashibara's Fluid Mechanics Unit A: Fundamental Concepts)
Basic dimensions in engineering (units)
An automobile tire (with an internal volume of 3,200 L) was inflated to the gage pressure of 265 kPa of air at a car mechanic at
Phoenix (the atmospheric pressure at Phoenix was happened to be the standard sea-level value, that was: 101 kPa). The gravity was
happened to be NOT the standard value, but 9.79 m/s2 at Phoenix at that time (note: this is hypothetical).
If the air temperature inside the tire was 70 C, calculate the followings:
(a) What was the air density, in “kilograms per cubic meters,” in the tire (at Phoenix)?
(b) What was the weight of air, in “kilograms,” in the tire (at Phoenix)?
(c) What was the mass of air, in “kilograms,” in the tire (at Phoenix)?
Suppose, you drive this vehicle back to Prescott (standard “mile-high” atmospheric pressure: 84 kPa at Prescott). The temperature
inside the tire is then changed to 5 C (very cold weather). Also, the gravity at Prescott is now 9.59 m/s2. Although there is absolutely
no leak of air from the tire, you notice a slight volume change of the tire (internal volume of the tire is now 3,000 L). Under these
conditions, calculate the followings:
(d) What is the specific weight of air, in “kilograms per cubic meters,” in the tire (at Prescott)?
(e) What is the gage pressure, in “kPa,” of the tire (at Prescott)? Does this activate “low tire pressure” warning indicator of your car?
Note that the “low tire pressure” warning is set for 250 kPa or less tire air pressure as a manufacturer default.
AE301
Your solution must be less than total 2-pages for each problem. (Page 4 of 14) Write your name and student ID on all pages.
ID (-1 point, if missing): NAME (-1 point, if missing):
AE301
Your solution must be less than total 2-pages for each problem. (Page 5 of 14) Write your name and student ID on all pages.
ID (-1 point, if missing): NAME (-1 point, if missing):
NO PARTIAL CREDITS FOR YOUR WORK, IF THESE GENERAL REQUIREMENTS ARE NOT SATISFIED
Show all steps of your work and list all assumptions. Explain, in your own words, full details of your work. Clearly show your
conclusion (box your answer) associated with proper units specified for each problem. Show all engineering units for all your values.
THIS IS QUIZ: Absolutely no external help of any kind. You MUST solve problems using your own fluid mechanics notes ONLY.
PROBLEM 2 (2 point each = 6 points total)
This is the review of fluid mechanics (Dr. Hayashibara's Fluid Mechanics Unit B: Fluid Statics)
Atmospheric pressure variation models from hydrostatic equation
A mountain rises to a height ( )z of approximately 9,000 ft. Determine the ratio of the pressure at the top of the mountain (p2) and the
pressure at its base (p1), meaning: p2/p1, in the following different methods. For each case, you must start from the governing equation
(hydrostatic equation: dp gdz= − ) and derive appropriate equation first, and then determine the ratio for each case.
For simplification, assume that the gravity is being constant (standard sea-level value). Also, assume that the pressure at its base (p1)
is standard sea-level atmospheric pressure.
(a) What is p2/p1, if air is assumed to be incompressible gas (density is constant, standard sea-level value: 2 1 = = )?
(b) What is p2/p1, if air is assumed to be isothermal gas (temperature is constant, standard sea-level value: 2 1T T T= = )?
(c) What is p2/p1, using the U.S. standard atmosphere model (temperature is a variable from sea-level to 36,000 ft altitude)? The
lapse rate is given as: o0.00357 R ft = . Do not use U.S. standard atmospheric data from the table. Use the equation you derived
(gradient region from sea-level to 36,000 ft), assuming that the gravity is constant.
AE301
Your solution must be less than total 2-pages for each problem. (Page 6 of 14) Write your name and student ID on all pages.
ID (-1 point, if missing): NAME (-1 point, if missing):
AE301
Your solution must be less than total 2-pages for each problem. (Page 7 of 14) Write your name and student ID on all pages.
ID (-1 point, if missing): NAME (-1 point, if missing):
NO PARTIAL CREDITS FOR YOUR WORK, IF THESE GENERAL REQUIREMENTS ARE NOT SATISFIED
Show all steps of your work and list all assumptions. Explain, in your own words, full details of your work. Clearly show your
conclusion (box your answer) associated with proper units specified for each problem. Show all engineering units for all your values.
THIS IS QUIZ: Absolutely no external help of any kind. You MUST solve problems using your own fluid mechanics notes ONLY.
PROBLEM 3 (2 point each = 4 points total)
This is the review of fluid mechanics (Dr. Hayashibara's Fluid Mechanics Unit C: Fluid Dynamics)
Application of Bernoulli's equation and wind tunnel testing
Consider a through-flow type wind tunnel, as shown in the figure. Assume
standard sea-level atmospheric condition for operation. Specific gravity of oil in
the U-tube manometer is 0.9. An automobile model is placed into the wind tunnel
to be tested.
(a) If the manometer reading (h) is 10 inches, calculate the test section airspeed
(in “mph”).
(b) Calculate the stagnation pressure (developed at the front face of the
automobile), in “psig.”
(0) (1) (2)
AE301
Your solution must be less than total 2-pages for each problem. (Page 8 of 14) Write your name and student ID on all pages.
ID (-1 point, if missing): NAME (-1 point, if missing):
AE301
Your solution must be less than total 2-pages for each problem. (Page 9 of 14) Write your name and student ID on all pages.
ID (-1 point, if missing): NAME (-1 point, if missing):
NO PARTIAL CREDITS FOR YOUR WORK, IF THESE GENERAL REQUIREMENTS ARE NOT SATISFIED
Show all steps of your work and list all assumptions. Explain, in your own words, full details of your work. Clearly show your
conclusion (box your answer) associated with proper units specified for each problem. Show all engineering units for all your values.
THIS IS QUIZ: Absolutely no external help of any kind. You MUST solve problems using your own fluid mechanics notes ONLY.
PROBLEM 4 (1 point each = 5 points total)
This is the review of fluid mechanics (Dr. Hayashibara's Fluid Mechanics Unit C: Fluid Dynamics)
Limitations of Bernoulli's equation
Consider a converging duct flow. Conditions are given as below:
(Station 1)
- Air velocity (magnitude) = 50 m/s
- Cross-sectional area = 1.8 m2
- Air pressure = 1 atm (standard sea-level value)
- Air temperature = 280 K
(Station 2)
- Air pressure = 0.95 atm (standard sea-level value)
Determine the followings:
(a) Air flow Mach number at inlet (station 1)
(b) Mass flow rate of air, in kg/s, through this duct
(c) Air temperature, in K, at outlet (station 2)
(d) Air velocity, in m/s, and Mach number at outlet (station 2)
(e) Air density, in kg/m3, at outlet (station 2)
AE301
Your solution must be less than total 2-pages for each problem. (Page 10 of 14) Write your name and student ID on all pages.
ID (-1 point, if missing): NAME (-1 point, if missing):
AE301
Your solution must be less than total 2-pages for each problem. (Page 11 of 14) Write your name and student ID on all pages.
ID (-1 point, if missing): NAME (-1 point, if missing):
NO PARTIAL CREDITS FOR YOUR WORK, IF THESE GENERAL REQUIREMENTS ARE NOT SATISFIED
Show all steps of your work and list all assumptions. Explain, in your own words, full details of your work. Clearly show your
conclusion (box your answer) associated with proper units specified for each problem. Show all engineering units for all your values.
THIS IS QUIZ: Absolutely no external help of any kind. You MUST solve problems using your own fluid mechanics notes ONLY.
PROBLEM 5 (2 point each = 4 points total)
This is the review of fluid mechanics (Dr. Hayashibara's Fluid Mechanics Unit C: Fluid Dynamics)
Airspeed Measurements
Here is the actual photo taken at the ERAU wind tunnel laboratory. Apparently, this wind tunnel is equipped with a “custom
designed” inclined U-tube manometer for the test section airspeed measurement. It looks like the manometer is in terms of “inches of
water,” and the maximum measurable value is about 5 “inches” (of water).
(a) Explain the meaning of “inches of water.” What does “inches of water” represent for wind tunnel testing? Why do we need to
employ such a thing for wind tunnel testing?
(b) Suppose, if the air density in this wind tunnel test section is “known” (say, 0.002 slug/ft3), what would be the corresponding wind
tunnel test section airspeed, in miles per hour (mph), for the 5.7 “inches of water” reading of this manometer?
Note: gravity is g = 32.2 ft/s2, and density of water is 1.94 slug/ft3. Unit conversion: 60 mph = 88 ft/s.
AE301
Your solution must be less than total 2-pages for each problem. (Page 12 of 14) Write your name and student ID on all pages.
ID (-1 point, if missing): NAME (-1 point, if missing):
AE301
Your solution must be less than total 2-pages for each problem. (Page 13 of 14) Write your name and student ID on all pages.
ID (-1 point, if missing): NAME (-1 point, if missing):
NO PARTIAL CREDITS FOR YOUR WORK, IF THESE GENERAL REQUIREMENTS ARE NOT SATISFIED
Show all steps of your work and list all assumptions. Explain, in your own words, full details of your work. Clearly show your
conclusion (box your answer) associated with proper units specified for each problem. Show all engineering units for all your values.
THIS IS QUIZ: Absolutely no external help of any kind. You MUST solve problems using your own fluid mechanics notes ONLY.
PROBLEM 6 (2 point each = 4 points total)
This is the review of fluid mechanics (Dr. Hayashibara's Fluid Mechanics Unit E: Model and Prototype)
Dimensional analysis
The aerodynamic drag force of a new car is to be predicted at a designed (standard) operating
condition of speed of 57 mph at a standard air temperature of 25 C (corresponding air density
1.184 kg/m3 and air viscosity 1.84910−5 kg/ms). Due to some circumstances, however, a wind
tunnel testing must be conducted using a 1/5 scale model during a winter (temperature 5 C, with
corresponding air density 1.269 kg/m3 and air viscosity 1.75410−5 kg/ms).
(a) Calculate the required test section airspeed, in “mph,” for this wind tunnel test, in order to
properly predict the aerodynamic drag force of a new car. (NOTE: you must maintain exact
same Reynolds number, in order to satisfy dynamic similitude of this wind tunnel testing).
(b) If the measured drag force in this wind tunnel (scale model) is 25.5 lb, what will be the drag
force, in “lb,” predicted for the prototype (actual size) car in designed (standard) operating condition?
Note: Drag coefficient of a car is defined as: 2 2D
DragC
V= ( is called the length scale)