FLUID MECHANICS-EBOOK>I<
2nd Edition
ISBN: 2819480256061
Author: HIBBELER
Publisher: INTER PEAR
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Chapter 6, Problem 71P
To determine
The power required for motor to lift the assembly, and the downward velocity of air for lift off to happen.
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Problem 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
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R
Scenario 1
R
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R
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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)…
Chapter 6 Solutions
FLUID MECHANICS-EBOOK>I<
Ch. 6 - Prob. 1FPCh. 6 - The shield of negligible weight is held at an...Ch. 6 - Prob. 3FPCh. 6 - Crude oil flows into the open air at the same rate...Ch. 6 - The table fan develops a slipstream that has a...Ch. 6 - Prob. 6FPCh. 6 - Determine the linear momentum of a mass of fluid...Ch. 6 - Prob. 2PCh. 6 - A volumetric discharge of 1.25 m3/s passes out the...Ch. 6 - Water flows with a velocity of 6 m/s through the...
Ch. 6 - Water is ejected from the hose at A with a...Ch. 6 - Water flows out of the reducing elbow at 0.6...Ch. 6 - Oil flows through the 100-mm-diameter pipe with a...Ch. 6 - Prob. 8PCh. 6 - Prob. 9PCh. 6 - Water flows through the elbow with a velocity of...Ch. 6 - Prob. 11PCh. 6 - The water jet is ejected from the 4-in.-diameter...Ch. 6 - The water jet is ejected from the 4-in.-diameter...Ch. 6 - Water flows through the elbow at 8 ft/s. Assuming...Ch. 6 - The steady jet of water flows from the...Ch. 6 - The steady jet of water flows from the...Ch. 6 - Crude oil flows through the horizontal tapered 45°...Ch. 6 - A speedboat is powered by the jet drive shown....Ch. 6 - The 160-lb man stands on the scale. If the bucket...Ch. 6 - Prob. 20PCh. 6 - Prob. 21PCh. 6 - Water flows out of the reducing elbow at 0.4...Ch. 6 - Water flows through the 2-in.-diameter pipe...Ch. 6 - The pipe AB has a diameter of 40 mm. If water...Ch. 6 - Prob. 25PCh. 6 - Prob. 26PCh. 6 - Pipe AB has a diameter of 40 mm. If water flows...Ch. 6 - Pipe AB has a diameter of 40 mm. If the tensile...Ch. 6 - The disk valve is used to control the flow of...Ch. 6 - Prob. 30PCh. 6 - Prob. 31PCh. 6 - Prob. 32PCh. 6 - Water flows through the pipe C at 4 m/s. Determine...Ch. 6 - Prob. 34PCh. 6 - The 1-in.-diameter pipe ejects water towards the...Ch. 6 - Prob. 36PCh. 6 - Water flows through the hose with a velocity of 3...Ch. 6 - Water flows through the hose with a velocity of 3...Ch. 6 - A 20-mm-diameter stream flows at 8 m/s against the...Ch. 6 - Determine the power required to keep the vane...Ch. 6 - Prob. 41PCh. 6 - The boat is powered by the fan, which develops a...Ch. 6 - The vane is moving at 80 ft/s when a jet of water...Ch. 6 - The car is used to scoop up water that is in a...Ch. 6 - The water stream strikes the inclined surface of...Ch. 6 - Prob. 46PCh. 6 - Prob. 47PCh. 6 - A 25-mm-diameter stream flows at 10 m/s against...Ch. 6 - Prob. 49PCh. 6 - Water flows into the bend fitting with a velocity...Ch. 6 - Prob. 51PCh. 6 - Water flows into the Tee fitting at 3.6 m/s. If a...Ch. 6 - Prob. 53PCh. 6 - Prob. 54PCh. 6 - If the velocity through the pipe is 4 m/s,...Ch. 6 - Water flows through the 200-mm-diameter pipe bend...Ch. 6 - Water flows through the pipe with a velocity of 5...Ch. 6 - The bend is connected to the pipe at flanges A and...Ch. 6 - The fan blows air at 6000 ft3/min. If the fan has...Ch. 6 - Prob. 60PCh. 6 - Prob. 61PCh. 6 - Prob. 62PCh. 6 - The lawn sprinkler consists of four arms that...Ch. 6 - Prob. 64PCh. 6 - Prob. 65PCh. 6 - Prob. 66PCh. 6 - Prob. 67PCh. 6 - Prob. 68PCh. 6 - The propeller of a boat discharges 67.5 ft3/s of...Ch. 6 - Determine the largest speed of the breeze that can...Ch. 6 - Prob. 71PCh. 6 - Prob. 72PCh. 6 - Prob. 73PCh. 6 - Prob. 74PCh. 6 - Prob. 75PCh. 6 - Prob. 76PCh. 6 - Prob. 77PCh. 6 - Prob. 78PCh. 6 - Prob. 79PCh. 6 - The jet is traveling at a velocity of 400 m/s in...Ch. 6 - Prob. 81PCh. 6 - Prob. 82PCh. 6 - Prob. 83PCh. 6 - The jet is traveling at 500 mi/h, 30° above the...Ch. 6 - Prob. 85PCh. 6 - Prob. 86PCh. 6 - The rocket is traveling upwards at 300 m/s and...Ch. 6 - The balloon has a mass of 20 g (empty) and it is...Ch. 6 - Prob. 89PCh. 6 - Prob. 90PCh. 6 - Prob. 91PCh. 6 - Prob. 92P
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