Fluid Mechanics (2nd Edition)
2nd Edition
ISBN: 9780134649290
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 2, Problem 8P
To determine
The maximum pressure in the tank.
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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 2 Solutions
Fluid Mechanics (2nd Edition)
Ch. 2 - Prob. 1FPCh. 2 - The container is partially filled with oil, water,...Ch. 2 - The U-tube manometer is filled with mercury,...Ch. 2 - The tube is filled with mercury from A to B, and...Ch. 2 - The air pressure in the pipe at A is 300 kPa....Ch. 2 - Determine the absolute pressure of the water in...Ch. 2 - The bin is 1.5 m wide and is filled with water to...Ch. 2 - The bin is 2 m wide and is filled with oil to the...Ch. 2 - The 2-m-wide container is filled with water to the...Ch. 2 - Determine the resultant force of the water acting...
Ch. 2 - Determine the resultant force of the water acting...Ch. 2 - The tank is filled with water and kerosene to the...Ch. 2 - The 0.5-m-wide inclined plate holds water in a...Ch. 2 - Determine the resultant force the oil exerts on...Ch. 2 - Determine the resultant force the water exerts on...Ch. 2 - The tank has a width of 2 m and is filled with...Ch. 2 - Determine the horizontal and vertical components...Ch. 2 - The plate ABC is 2 m wide. Determine the angle θ...Ch. 2 - The cylindrical cup A of negligible weight...Ch. 2 - The 3-m-wide cart is filled with water to the...Ch. 2 - Prob. 21FPCh. 2 - Prob. 22FPCh. 2 - If the open cylindrical container rotates at ω = 8...Ch. 2 - Prob. 24FPCh. 2 - Prob. 1PCh. 2 - The oil derrick has drilled 5 km into the ground...Ch. 2 - Prob. 3PCh. 2 - Oxygen in a tank has an absolute pressure of 130...Ch. 2 - If the piezometer measures a gage pressure of 10...Ch. 2 - If the absolute pressure in a tank is 140 kPa,...Ch. 2 - The field storage tank is filled with oil. The...Ch. 2 - Prob. 8PCh. 2 - The closed tank was completely filled with carbon...Ch. 2 - The soaking bin contains ethyl alcohol used for...Ch. 2 - The soaking bin contains ethyl alcohol used for...Ch. 2 - Prob. 12PCh. 2 - Prob. 13PCh. 2 - The tank is filled with water and gasoline at a...Ch. 2 - Prob. 15PCh. 2 - Prob. 16PCh. 2 - Prob. 17PCh. 2 - Prob. 18PCh. 2 - Prob. 19PCh. 2 - Prob. 20PCh. 2 - A liquid has a density that varies with depth h,...Ch. 2 - Prob. 22PCh. 2 - In the troposphere, which extends from sea level...Ch. 2 - Prob. 24PCh. 2 - A heavy cylindrical glass is inverted and then...Ch. 2 - Prob. 26PCh. 2 - Prob. 27PCh. 2 - Butyl carbitol, used in the production of...Ch. 2 - Determine the level h′ of water in the tube if the...Ch. 2 - Determine the pressures at points A and B. The...Ch. 2 - Determine the pressure at point C. The containers...Ch. 2 - Determine the difference in pressure pB − pA...Ch. 2 - Prob. 33PCh. 2 - Prob. 34PCh. 2 - A solvent used for plastics manufacturing consists...Ch. 2 - A solvent used for plastics manufacturing consists...Ch. 2 - The inverted U-tube manometer is used to measure...Ch. 2 - Solve Prob. 2-37 if the top segment is filled with...Ch. 2 - The two tanks A and B are connected using a...Ch. 2 - Prob. 40PCh. 2 - Determine the height h of the mercury in the tube...Ch. 2 -
The micro-manometer is used to measure small...Ch. 2 - The Morgan Company manufactures a micro-manometer...Ch. 2 - Determine the difference in pressure pA − pB...Ch. 2 - The pipes at A and B contain oil and the...Ch. 2 - The vertical pipe segment has an inner diameter of...Ch. 2 - Prob. 47PCh. 2 - Prob. 48PCh. 2 - The storage tank contains oil and water acting at...Ch. 2 - The uniform rectangular relief gate AB has a...Ch. 2 -
Determine the critical height h of the water...Ch. 2 - A swimming pool has a width of 12 ft and a side...Ch. 2 - Prob. 53PCh. 2 - The uniform control gate AB is pinned at A and...Ch. 2 - Prob. 55PCh. 2 - Determine the critical height h of the water level...Ch. 2 - The gate is 2 ft wide and is pinned at A and held...Ch. 2 - The uniform rectangular relief gate AB has a...Ch. 2 - The tide gate opens automatically when the tide...Ch. 2 - The tide gate opens automatically when the tide...Ch. 2 - The bin is used to store carbon tetrachloride, a...Ch. 2 - Prob. 62PCh. 2 - Prob. 63PCh. 2 - The pressure of the air at A within the closed...Ch. 2 - The uniform plate, which is hinged at C, is used...Ch. 2 - Determine the placement d of the pin on the...Ch. 2 - Determine the placement d of the pin on the...Ch. 2 - The tapered settling tank is filled with oil....Ch. 2 - The tapered settling tank is filled with oil....Ch. 2 - Ethyl alcohol is pumped into the tank, which has...Ch. 2 - The bent plate is 2 m wide and is pinned at A and...Ch. 2 -
The tank is filled to its top with an industrial...Ch. 2 - Solve Prob. 20–72 using the integration...Ch. 2 - If the tank is filled with vegetable oil,...Ch. 2 -
If the tank is filled with vegetable oil,...Ch. 2 - Prob. 76PCh. 2 - Determine the resultant force acting on the...Ch. 2 - Solve Prob. 2-77 using the integration...Ch. 2 - Prob. 79PCh. 2 - Prob. 80PCh. 2 - Prob. 81PCh. 2 - Prob. 82PCh. 2 - Prob. 83PCh. 2 - Prob. 84PCh. 2 - Prob. 85PCh. 2 - Prob. 86PCh. 2 - Prob. 87PCh. 2 - Prob. 88PCh. 2 - Prob. 89PCh. 2 -
The control gate ACB is pinned at A and rests on...Ch. 2 - Prob. 91PCh. 2 -
The uniform plate, which is hinged at C, is used...Ch. 2 -
The bent plate is 1.5 m wide and is pinned at A...Ch. 2 - Prob. 94PCh. 2 - Prob. 95PCh. 2 - Prob. 96PCh. 2 - Prob. 97PCh. 2 - The 5-m-wide overhang is in the form of a...Ch. 2 - Determine the resultant force that water exerts on...Ch. 2 - Prob. 100PCh. 2 - Prob. 101PCh. 2 - Prob. 102PCh. 2 - Prob. 103PCh. 2 - A quarter-circular plate is pinned at A and tied...Ch. 2 - Prob. 105PCh. 2 - The semicircular gate is used to control the flow...Ch. 2 - Prob. 107PCh. 2 - Plate AB has a width of 1.5 m and a radius of 3 m....Ch. 2 - Prob. 109PCh. 2 - Prob. 110PCh. 2 - Prob. 111PCh. 2 - Prob. 112PCh. 2 - Prob. 113PCh. 2 - Prob. 114PCh. 2 - Prob. 115PCh. 2 - Prob. 116PCh. 2 - Prob. 117PCh. 2 - Prob. 118PCh. 2 - Prob. 119PCh. 2 - Prob. 120PCh. 2 - Prob. 121PCh. 2 - A glass having a diameter of 50 mm is filled with...Ch. 2 - Water in the container is originally at a height...Ch. 2 - Prob. 124PCh. 2 - Prob. 125PCh. 2 - Prob. 126PCh. 2 -
The hot-air balloon contains air having a...Ch. 2 - Prob. 128PCh. 2 - Prob. 129PCh. 2 - Prob. 130PCh. 2 - Prob. 131PCh. 2 - The truck carries an open container of water. If...Ch. 2 - Prob. 133PCh. 2 - The open rail car is 6 ft wide and filled with...Ch. 2 - Prob. 135PCh. 2 -
A large container of benzene is being transported...Ch. 2 - If the truck has a constant acceleration of 2...Ch. 2 - Prob. 138PCh. 2 - Prob. 139PCh. 2 - Prob. 140PCh. 2 - Prob. 141PCh. 2 - Prob. 142PCh. 2 - Prob. 143PCh. 2 - Prob. 144PCh. 2 - Prob. 145PCh. 2 - Prob. 146PCh. 2 - Prob. 147PCh. 2 - Prob. 3CPCh. 2 - Prob. 4CP
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