Fox and McDonald's Introduction to Fluid Mechanics
9th Edition
ISBN: 9781118912652
Author: Philip J. Pritchard, John W. Mitchell
Publisher: WILEY
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Chapter 3, Problem 38P
If the temperature in the atmosphere is assumed to vary linearly with altitude so T = To − αz where To is the sea level temperature and α = −dT/dz is the temperature lapse rate, find p(z) when air is taken to be a perfect gas. Give the answer in terms of po, α, g, R and z only.
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(b): Let us first consider controlling the orbit of deputy spacecraft to rendezvous with chief spacecraft.
Define x = [r] and x = x = R to represent the deputy orbital state and its target (= chief
orbit) in Cartesian coordinates, respectively. The control input is thruster acceleration, u € R³, in the
ECI frame. Denote the relative state by dx = x-x. Table 2 summarize the initial orbital elements.
Table 2: Keplerian orbital elements at epoch (t = 0) for deputy and chief about Earth (ECI frame)
Orbital element
Deputy
Unit
Chief
semi-major axis
ad =
11500
ac 10000 km
eccentricity
inclination
ed = 0.15
id=35
ee = 0.3
i = 50
degree
right ascension of ascending node d = 50
Ως = 50
degree
argument of periapsis
true anomaly at epoch
Wd
Vd= 0
=
40
We =
40
degree
Ve=0
degree
(b.1): Derive the error dynamics of our system in ECI frame under the influence of u.
(b.2): Consider a candidate Lyapunov function V = ½dr¹ K₁dr+dv₁dv, where K₁ = K, and K, > 0.
Discuss the positive definiteness of V, and…
One image show problem c.1 and c.2 that I need help with. The second image shows the lyapunov function and its derivative but it is NOT the same function that is given in problem. I have attached that image as an example.
This is a tilt and rotation question. Here are notes attached for reference.
Chapter 3 Solutions
Fox and McDonald's Introduction to Fluid Mechanics
Ch. 3 - Because the pressure falls, water boils at a lower...Ch. 3 - Ear popping is an unpleasant phenomenon sometimes...Ch. 3 - When you are on a mountain face and boil water,...Ch. 3 - Your pressure gauge indicates that the pressure in...Ch. 3 - A 125-mL cube of solid oak is held submerged by a...Ch. 3 - The tube shown is filled with mercury at 20C....Ch. 3 - Calculate the absolute and gage pressure in an...Ch. 3 - An open vessel contains carbon tetrachloride to a...Ch. 3 - A hollow metal cube with sides 100 mm floats at...Ch. 3 - Compressed nitrogen (140 lbm) is stored in a...
Ch. 3 - If at the surface of a liquid the specific weight...Ch. 3 - In the deep ocean the compressibility of seawater...Ch. 3 - Assuming the bulk modulus is constant for sea...Ch. 3 - An inverted cylindrical container is lowered...Ch. 3 - A water tank filled with water to a depth of 16 ft...Ch. 3 - A partitioned tank as shown contains water and...Ch. 3 - Consider the two-fluid manometer shown. Calculate...Ch. 3 - The manometer shown contains water and kerosene....Ch. 3 - Determine the gage pressure in kPa at point a, if...Ch. 3 - With the manometer reading as shown, calculate px....Ch. 3 - Calculate px py for this inverted U-tube...Ch. 3 - An inclined gauge having a tube of 3-mm bore, laid...Ch. 3 - Water flows downward along a pipe that is inclined...Ch. 3 - A reservoir manometer has vertical tubes of...Ch. 3 - A rectangular tank, open to the atmosphere, is...Ch. 3 - The sketch shows a sectional view through a...Ch. 3 - The manometer reading is 6 in. when the funnel is...Ch. 3 - A reservoir manometer is calibrated for use with a...Ch. 3 - The inclined-tube manometer shown has D = 96 mm...Ch. 3 - The inclined-tube manometer shown has D = 76 mm...Ch. 3 - A barometer accidentally contains 6.5 inches of...Ch. 3 - A water column stands 50 mm high in a 2.5-mm...Ch. 3 - Consider a small-diameter open-ended tube inserted...Ch. 3 - Compare the height due to capillary action of...Ch. 3 - If atmospheric pressure at the ground is 101.3 kPa...Ch. 3 - If the temperature in the atmosphere is assumed to...Ch. 3 - A hydropneumatic elevator consists of a...Ch. 3 - Semicircular plane gate AB is hinged along B and...Ch. 3 - A circular gate 3 m in diameter has its center 2.5...Ch. 3 - For the situation shown, find the air pressure in...Ch. 3 - What is the pressure at A? Draw a free body...Ch. 3 - A plane gate of uniform thickness holds back a...Ch. 3 - A rectangular gate (width w = 2 m) is hinged as...Ch. 3 - Gates in the Poe Lock at Sault Ste. Marie,...Ch. 3 - Calculate the minimum force P necessary to hold a...Ch. 3 - Calculate magnitude and location of the resultant...Ch. 3 - Calculate magnitude and location of the resultant...Ch. 3 - A window in the shape of an isosceles triangle and...Ch. 3 - A large open tank contains water and is connected...Ch. 3 - The circular access port in the side of a water...Ch. 3 - The gate AOC shown is 6 ft wide and is hinged...Ch. 3 - The gate shown is hinged at H. The gate is 3 m...Ch. 3 - For the dam shown, what is the vertical force of...Ch. 3 - The parabolic gate shown is 2 m wide and pivoted...Ch. 3 - An open tank is filled with water to the depth...Ch. 3 - A dam is to be constructed using the cross-section...Ch. 3 - The quarter cylinder AB is 10 ft long. Calculate...Ch. 3 - Calculate the magnitude, direction (horizontal and...Ch. 3 - A hemispherical shell 1.2 m in diameter is...Ch. 3 - A cylindrical weir has a diameter of 3 m and a...Ch. 3 - If you throw an anchor out of your canoe but the...Ch. 3 - A hydrometer is a specific gravity indicator, the...Ch. 3 - A cylindrical can 76 mm in diameter and 152 mm...Ch. 3 - If the 10-ft-long box is floating on the oil-water...Ch. 3 - The timber weighs 40 lb/ft3 and is held in a...Ch. 3 - Find the specific weight of the sphere shown if...Ch. 3 - The fat-to-muscle ratio of a person may be...Ch. 3 - An open tank is filled to the top with water. A...Ch. 3 - If the timber weighs 670 N, calculate its angle of...Ch. 3 - The barge shown weighs 40 tons and carries a cargo...Ch. 3 - Quantify the experiment performed by Archimedes to...Ch. 3 - Hot-air ballooning is a popular sport. According...Ch. 3 - It is desired to use a hot air balloon with a...Ch. 3 - The opening in the bottom of the tank is square...Ch. 3 - A balloon has a weight (including crew but not...Ch. 3 - A helium balloon is to lift a payload to an...Ch. 3 - The stem of a glass hydrometer used to measure...Ch. 3 - A sphere of radius R is partially immersed to...Ch. 3 - A sphere of 1-in.-radius made from material of...Ch. 3 - You are in the Bermuda Triangle when you see a...Ch. 3 - Three steel balls (each about half an inch in...Ch. 3 - A proposed ocean salvage scheme involves pumping...
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