Fluid Mechanics: Fundamentals and Applications
4th Edition
ISBN: 9781259696534
Author: Yunus A. Cengel Dr., John M. Cimbala
Publisher: McGraw-Hill Education
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Chapter 11, Problem 95EP
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The required towing power.
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I tried solving this one but have no idea where I went wrong can you please help me out with this?
Question 1.
A tube rotates in the horizontal xy plane with a constant angular velocity w about the z-axis. A
particle of mass m is released from a radial distance R when the tube is in the position shown.
This problem is based on problem 3.2 in the text.
y
ω
R
m
2R
Figure 1
X
a) Draw a free body diagram of the particle if the tube is frictionless.
b) Draw a free body diagram of the particle if the coefficient of friction between the sides of the
tube and the particle is μs = flk = fl.
c) For the case where the tube is frictionless, what is the radial speed at which the particle
leaves the tube?
d) For the case where there is friction, derive a differential equation that would allow you to
solve for the radius of the particle as a function of time. I'm only looking for the differential
equation. DO NOT solve it.
e) If there is no friction, what is the angle of the tube when the particle exits?
• Hint: You may need to solve a differential equation for the last part. The "potentially…
I tried this problem but I can't seem to figure out what I am missing here can you please help me?
Chapter 11 Solutions
Fluid Mechanics: Fundamentals and Applications
Ch. 11 - What is drag? What causes it? Why do we usually...Ch. 11 - Prob. 2CPCh. 11 - Which bicyclist is more likely to go faster: one...Ch. 11 - Prob. 4CPCh. 11 - Define the frontal area of a body subjected to...Ch. 11 - Define the planform area of a body subjected to...Ch. 11 - Prob. 7CPCh. 11 - What is the difference between streamlined and...Ch. 11 - Prob. 9CPCh. 11 - During flow over a given body, the drag force, the...
Ch. 11 - During flow over a given slender body such as a...Ch. 11 - What is terminal velocity? How is it determined?Ch. 11 - What is the difference between skin friction drag...Ch. 11 - What is the effect of surface roughness on the...Ch. 11 - Prob. 15CPCh. 11 - What is flow separation? What causes it? What is...Ch. 11 - Prob. 17CPCh. 11 - Consider laminar flow over a flat plate. How does...Ch. 11 - In general, how does the drag coefficient vary...Ch. 11 - Fairings are attached to the front and back of a...Ch. 11 - Prob. 21PCh. 11 - The resultant of the pressure and wall shear...Ch. 11 - Prob. 23PCh. 11 - Prob. 24PCh. 11 - To reduce the drag coefficient and thus to improve...Ch. 11 - A circular sign has a diameter of 50 cm and is...Ch. 11 - Prob. 28PCh. 11 - Prob. 29PCh. 11 - At highway speeds, about half of the power...Ch. 11 - A submarine can be treated as an ellipsoid with a...Ch. 11 - A 70-kg bicyclist is riding her 1 5-kg bicycle...Ch. 11 - A wind turbine with two or four hollow...Ch. 11 - During steady motion of a vehicle on a level road,...Ch. 11 - Prob. 37EPCh. 11 - A 0.80-m-diameter, 1 .2-rn-high garbage can is...Ch. 11 - An 8-mm-diameter plastic sphere whose density is...Ch. 11 - Prob. 40PCh. 11 - The drag coefficient of a vehicle increases when...Ch. 11 - To reduce the drag coefficient and thus to improve...Ch. 11 - During major windstorms, high vehicles such as RVs...Ch. 11 - What does the friction coefficient represent in...Ch. 11 - What fluid property is responsible for the...Ch. 11 - How is the average friction coefficient determined...Ch. 11 - Prob. 47EPCh. 11 - The local atmospheric pressure in Denver, Colorado...Ch. 11 - Prob. 50PCh. 11 - Prob. 51EPCh. 11 - Air at 25C and 1 atm is flowing over a long flat...Ch. 11 - Prob. 54PCh. 11 - During a winter day, wind at 70 km/h, 5C , and I...Ch. 11 - Prob. 56PCh. 11 - The forming section of a plastics plant puts out a...Ch. 11 - Prob. 58CPCh. 11 - Why is flow separation in flow over cylinders...Ch. 11 - Prob. 60CPCh. 11 - A 5-mm-diameter electrical transmission line is...Ch. 11 - A 1ong 5-cm-diameter steam pipe passes through...Ch. 11 - Consider 0.8-cm-diameter hail that is falling...Ch. 11 - Prob. 64EPCh. 11 - Prob. 65PCh. 11 - Prob. 66PCh. 11 - Prob. 67EPCh. 11 - One of the popular demonstrations in science...Ch. 11 - Prob. 69PCh. 11 - What is stall? What causes an airfoil to stall?...Ch. 11 - Prob. 71CPCh. 11 - Air is flowing past a symmetrical airfoil at zero...Ch. 11 - Both the lift and the drag of an airfoil increase...Ch. 11 - Prob. 74CPCh. 11 - Prob. 75CPCh. 11 - Air is flowing past a symmetrical airfoil at an...Ch. 11 - Prob. 77CPCh. 11 - Prob. 78CPCh. 11 - Prob. 79CPCh. 11 - Prob. 80CPCh. 11 - How do flaps affect the lift and the drag of...Ch. 11 - Prob. 82EPCh. 11 - Consider an aircraft that takes off at 260 km/h...Ch. 11 - Prob. 84PCh. 11 - Prob. 85PCh. 11 - A tennis ball with a mass of 57 and a diameter of...Ch. 11 - A small aircraft has a wing area of 40 m2, a lift...Ch. 11 - Prob. 89PCh. 11 - Consider a light plane that has a total weight of...Ch. 11 - A small airplane has a total mass of 1800 kg and a...Ch. 11 - An airplane has a mass of 48.000 k. a wins area of...Ch. 11 - Prob. 93EPCh. 11 - Prob. 94PCh. 11 - Prob. 95EPCh. 11 - A 2-zn-high, 4-zn-wide rectangular advertisement...Ch. 11 - 11-97 A plastic boat whose bottom surface can be...Ch. 11 - Prob. 99PCh. 11 - Prob. 100EPCh. 11 - A commercial airplane has a total mass of 150.000...Ch. 11 - Prob. 102PCh. 11 - Prob. 103PCh. 11 - Prob. 104PCh. 11 - Prob. 105PCh. 11 - Prob. 107PCh. 11 - Prob. 108PCh. 11 - Prob. 109PCh. 11 - Prob. 110PCh. 11 - Prob. 111PCh. 11 - Prob. 113PCh. 11 - Prob. 115PCh. 11 - Prob. 116PCh. 11 - Prob. 117PCh. 11 - Prob. 118PCh. 11 - Prob. 119PCh. 11 - The region of flow trailing the body where the...Ch. 11 - Prob. 121PCh. 11 - Prob. 122PCh. 11 - Prob. 123PCh. 11 - Prob. 124PCh. 11 - Prob. 125PCh. 11 - Prob. 126PCh. 11 - An airplane has a total mass of 3.000kg and a wing...Ch. 11 - Prob. 128PCh. 11 - Write a report on the history of the reduction of...Ch. 11 - Write a report oil the flips used at the leading...Ch. 11 - Discuss how to calculate drag force a unsteady...Ch. 11 - Large commercial airplanes cruise at high...Ch. 11 - Many drivers turn off their air conditioners and...Ch. 11 - Consider the boundary layer growing on a flat...
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