FLUID MECHANICS-EBOOK>I<
2nd Edition
ISBN: 2819480256061
Author: HIBBELER
Publisher: INTER PEAR
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Chapter 13, Problem 54P
To determine
The temperature at
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Problem 2 (40 Points)
A particle of mass m is embedded at a distance a from the center of a massless circular disk of
radius r. The disk rolls without slipping down a plane inclined at an angle a with the horizontal.
A horizontal force of Ễ = −Fxî + Fyĵ resists motion of the disk down the plane by pushing on
the disk at the axle that runs through the center of the disk.
a) Find the kinetic energy T. (10 points)
b) Find the potential energy V. (10 points)
c) Write a position vector to the axle at the center of the wheel in terms of x and y. (10
points)
d) Using virtual work, find the applied force Q₁ that would go in Lagrange's Equations. DO
NOT WRITE OUT OR SOLVE LAGRANGES'S EQUATIONS. (10 points)
x
r
m
e
10
g
F
α
HINTS
1) Consider using the STATIONARY red xy frame a reference frame from which to draw
vectors
2) The red xy system DOES NOT move. It is stationary.
3) Consider that the disk rolls a distance of re down the ramp
Draw a counter balance circuit of a vertical cylinder.
using counter balance valve and external load.
Chapter 13 Solutions
FLUID MECHANICS-EBOOK>I<
Ch. 13 - Prob. 1PCh. 13 - Prob. 2PCh. 13 - Prob. 3PCh. 13 - Prob. 4PCh. 13 - Prob. 5PCh. 13 - Prob. 6PCh. 13 - Prob. 7PCh. 13 - Prob. 8PCh. 13 - Prob. 9PCh. 13 - Prob. 10P
Ch. 13 - Prob. 11PCh. 13 - Prob. 12PCh. 13 - Prob. 13PCh. 13 - Prob. 14PCh. 13 - Prob. 15PCh. 13 - Prob. 16PCh. 13 - Prob. 17PCh. 13 - Prob. 18PCh. 13 - Prob. 19PCh. 13 - Prob. 20PCh. 13 - Prob. 21PCh. 13 - Prob. 22PCh. 13 - Prob. 23PCh. 13 - Prob. 24PCh. 13 - Prob. 25PCh. 13 - Prob. 26PCh. 13 - Determine the greatest possible mass flow through...Ch. 13 - Prob. 28PCh. 13 - Prob. 29PCh. 13 - Prob. 30PCh. 13 - Prob. 31PCh. 13 - Prob. 32PCh. 13 - The large tank contains air at an absolute...Ch. 13 - Prob. 34PCh. 13 - Prob. 35PCh. 13 - Prob. 36PCh. 13 - Prob. 37PCh. 13 - Prob. 38PCh. 13 - Prob. 39PCh. 13 - Prob. 40PCh. 13 - Prob. 41PCh. 13 - Prob. 42PCh. 13 - Prob. 43PCh. 13 - Prob. 44PCh. 13 - Prob. 45PCh. 13 - Prob. 46PCh. 13 - Prob. 47PCh. 13 - The converging-diverging nozzle at the end of a...Ch. 13 - Prob. 49PCh. 13 - Prob. 50PCh. 13 - Prob. 51PCh. 13 - Prob. 52PCh. 13 - Prob. 53PCh. 13 - Prob. 54PCh. 13 - Air flows into the nozzle at MA = 0.2 and...Ch. 13 - Prob. 56PCh. 13 - Prob. 57PCh. 13 - Prob. 58PCh. 13 - Prob. 59PCh. 13 - Prob. 60PCh. 13 - Prob. 61PCh. 13 - Prob. 62PCh. 13 - Prob. 63PCh. 13 - Prob. 64PCh. 13 - Prob. 65PCh. 13 - Prob. 66PCh. 13 - Prob. 67PCh. 13 - Prob. 68PCh. 13 - Prob. 69PCh. 13 - Prob. 70PCh. 13 - Prob. 71PCh. 13 - Outside air at a temperature of 25°C is drawn into...Ch. 13 - Outside air at a temperature of 25°C is drawn into...Ch. 13 - Air is drawn into the pipe at M1 = 1.85, T1 =...Ch. 13 - Air is drawn into the 6-in.-diameter pipe at...Ch. 13 - Nitrogen having a temperature of T1 = 270 K and...Ch. 13 - Prob. 77PCh. 13 - Prob. 78PCh. 13 - Prob. 79PCh. 13 - Prob. 80PCh. 13 - Prob. 81PCh. 13 - Prob. 82PCh. 13 - Prob. 83PCh. 13 - The converging nozzle has an exit diameter of 0.25...Ch. 13 - The jet engine has a converging-diverging exhaust...Ch. 13 - Prob. 86PCh. 13 - Prob. 87PCh. 13 - Prob. 88PCh. 13 - Prob. 89PCh. 13 - Prob. 90PCh. 13 - Prob. 91PCh. 13 - Prob. 92PCh. 13 - Prob. 93PCh. 13 - Prob. 94PCh. 13 - Prob. 95PCh. 13 - Prob. 96PCh. 13 - Prob. 97PCh. 13 - Prob. 98PCh. 13 - Prob. 99PCh. 13 - Prob. 100PCh. 13 - Prob. 101PCh. 13 - Prob. 102PCh. 13 - Prob. 103PCh. 13 - Prob. 104PCh. 13 - Prob. 105PCh. 13 - Prob. 106PCh. 13 - Prob. 107PCh. 13 - Prob. 108PCh. 13 - Prob. 109PCh. 13 - Prob. 110PCh. 13 - Prob. 111PCh. 13 - Prob. 112PCh. 13 - Air flows at 700 m/s through a long duct in a wind...Ch. 13 - Prob. 114PCh. 13 - Prob. 115PCh. 13 - Prob. 116PCh. 13 - Prob. 117PCh. 13 - Prob. 118PCh. 13 - Prob. 119PCh. 13 - The wing of a jet plane is assumed to have the...Ch. 13 - Prob. 121PCh. 13 - Prob. 122P
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- please sketch a stress-strain diagram for a typical structural steel in tension and display all of the important features.arrow_forwardProblem 1 (30 Points) Consider the following 2 scenarios. In scenario 1, a mass m slides on a cylindrical surface of radius R. In scenario 2, a mass m hangs at the end of a thin massless rod of length R. In both scenarios, there is no friction either on the surface (scenario 1), or at the pivot point of the pendulum (scenario 2). Also in both scenarios, there is one generalized coordinate, . R Scenario 1 R m R g Scenario 2 m HINT: In both scenarios, it is much easier to choose your datum for potential energy as the center of the bowl (scenario 1), or the pivot point of the pendulum (scenario 2). Part I a) Determine the Lagrangian for each system. DO NOT FIND THE EQUATIONS OF MOTION (5 points) b) What can you say about the systems based on the Lagrangian? (2 points) c) Solve for the equations of motion for both systems. (8 points) Part II Now, for scenario 1, introduce an additional coordinate and treat it as a nonholonomic system to determine the normal force acting on the mass. a)…arrow_forwardConsider 0.65 kg of N2 at 300 K, 1 bar contained in a rigid tank connected by a valve to another rigid tank holding 0.3 kg of CO2 at 300 K, 1 bar. The valve is opened and gases are allowed to mix, achieving an equilibrium state at 290 K. Determine: (a) the volume of each tank, in m³. (b) the final pressure, in bar. (c) the magnitude of the heat transfer to or from the gases during the process, in kJ. (d) the entropy change of each gas and of the overall system, in kJ/K.arrow_forward
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