Explanation Write the expression for the stream line. d y d x = v u (I) Here, the velocity of the component in x direction is v and the velocity of the component in the y direction is u . Write the expression for the velocity field equation. V = x i ^ + x ( x − 1 ) ( y + 1 ) j ^ (II) Write the expression for the velocity component in u using Equation (II). u = x Write the expression for the velocity component in v using Equation (II). v = x ( x − 1 ) ( y + 1 ) Substitute x for u and x ( x − 1 ) ( y + 1 ) for v in Equation (I). d y d x = x ( x − 1 ) ( y + 1 ) x d y d x = ( x − 1 ) ( y + 1 ) d y ( y + 1 ) = ( x − 1 ) d x (III) Integrate Equation (III). ∫ d y ( y + 1 ) = ∫ ( x − 1 ) d x ln ( y + 1 ) = x 2 2 − x + C (IV) Here, the integration constant is C . Apply boundary condition. Substitute 0 for x and 0 for y in Equation (IV). ln ( 0 + 1 ) = ( 0 ) 2 2 − 0 + C C = ln ( 1 ) C = 0 Substitute 0 for C in Equation (III). ln ( y + 1 ) = x 2 2 − x + 0 y + 1 = e x 2 2 − x y = e x 2 2 − x − 1 (IV) Conclusion: Substitute − 1 for x in Equation (IV)

Munson, Young and Okiishi's Fundamentals of Fluid Mechanics, Binder Ready Version

8th Edition

ISBN: 9781119080701

Author: Philip M. Gerhart, Andrew L. Gerhart, John I. Hochstein

Publisher: WILEY

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The branch of science that deals with objects which are either in motion or stationary are studied under the branch of classical mechanics. Fluid mechanics is a subcategory of classical mechanics that deals with the behavior of fluids at rest (fluid stat…

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Chapter 4.1, Problem 11P

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The comparison of the stream line with the streak line through the origin.

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Chapter 4.1, Problem 10P

Chapter 4.1, Problem 12P

Chapter 4 Solutions

Munson, Young and Okiishi's Fundamentals of Fluid Mechanics, Binder Ready Version

Ch. 4.1 - Prob. 2P Ch. 4.1 - The velocity field of a flow is given by m/s,...Ch. 4.1 - A two-dimensional velocity field is given by u = 1...Ch. 4.1 - Streamlines are given in Cartesian coordinates by...Ch. 4.1 - Prob. 6P Ch. 4.1 - Prob. 8P Ch. 4.1 - Prob. 9P Ch. 4.1 - Prob. 10P Ch. 4.1 - Prob. 11P Ch. 4.1 - Prob. 12P

Ch. 4.1 - The x and y components of a velocity field are...Ch. 4.1 - Prob. 14P Ch. 4.1 - Prob. 15P Ch. 4.1 - For any steady flow the streamlines and...Ch. 4.1 - Prob. 17P Ch. 4.1 - Prob. 18P Ch. 4.1 - Prob. 19P Ch. 4.1 - Prob. 21P Ch. 4.1 - Classify the following flows as one-, two-, or...Ch. 4.2 - Prob. 23P Ch. 4.2 - Air is delivered through a constant-diameter duct...Ch. 4.2 - Water flows through a constant diameter pipe with...Ch. 4.2 - The velocity of air in the diverging pipe shown in...Ch. 4.2 - A certain flow field has the velocity...Ch. 4.2 - Prob. 28P Ch. 4.2 - Prob. 29P Ch. 4.2 - A shock wave is a very thin layer (thickness = ℓ)...Ch. 4.2 - Estimate the average acceleration of water as it...Ch. 4.2 - Prob. 32P Ch. 4.2 - As a valve is opened, water flows through the...Ch. 4.2 - The fluid velocity along the x axis shown in Fig....Ch. 4.2 - A fluid flows along the x axis with a velocity...Ch. 4.2 - A constant-density fluid flows through a...Ch. 4.2 - Prob. 37P Ch. 4.2 - Prob. 38P Ch. 4.2 - Prob. 39P Ch. 4.2 - An incompressible fluid flows through the...Ch. 4.2 - Prob. 41P Ch. 4.2 - Prob. 42P Ch. 4.2 - Prob. 43P Ch. 4.2 - Prob. 44P Ch. 4.2 - Prob. 45P Ch. 4.2 - Prob. 46P Ch. 4.2 - Assume that the streamlines for the wingtip...Ch. 4.2 - The velocity components for steady flow through...Ch. 4.2 - Water flows through the curved hose shown in Fig....Ch. 4.2 - Water flows though the slit at the bottom of a two...Ch. 4.2 - Prob. 51P Ch. 4.2 - Prob. 52P Ch. 4.2 - Fluid flows through a pipe with a velocity of 2.0...Ch. 4.2 - A gas flows along the x axis with a speed of V =...Ch. 4.2 - Assume the temperature of the exhaust in an...Ch. 4.2 - A bicyclist leases from her home at 9 a.m. and...Ch. 4.2 - The following pressures for the air flow in...Ch. 4.4 - In the region just downstream of a sluice gate,...Ch. 4.4 - At time t = 0 the valve on an initially empty...Ch. 4.4 - From calculus, one obtains the following formula...Ch. 4.4 - Air enters an elbow with a uniform speed of 10 m/s...Ch. 4.4 - A layer of oil flows down a vertical plate as...Ch. 4.4 - Figure P4.64 shows a fixed control volume. It has...Ch. 4.4 - Water enters a 5-ft-wide, 1-ft-deep channel as...Ch. 4.4 - The wind blows across a field with an approximate...Ch. 4.4 - Water flows from a nozzle with a speed of V = 10...

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