name (-1 point, if missing): id (-1 point, if missing): no

AE301

Your solution must be less than total 2-pages for each problem. ( 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.

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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.

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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.

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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)

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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)

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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.

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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)

AE301



name (-1 point, if missing): id (-1 point, if missing): no

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