Concept explainers
The Lagrengian description of the velocity of a fluid particle flowing along the surface.
Answer to Problem 2P
The Lagrengian description of the velocity of a fluid particle flowing along the surface is
Explanation of Solution
Write the expression of surface velocity of the river.
Here, the constant initial velocity is
Write the expression of velocity.
Here, the time is
Substitute
Integrate Equation (II) on both sides with respect to time
Consider
Differentiate Equation (IV) with respect to displacement.
Substitute
Consider,
Differentiate Equation (VI) with respect to
Substitute
Substitute
Consider.
Differentiate Equation (IX) on both sides with respect to
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Thus, The Lagrengian description of the velocity of a fluid particle flowing along the surface is
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Chapter 4 Solutions
Munson, Young and Okiishi's Fundamentals of Fluid Mechanics, Binder Ready Version
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