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For the velocity field of Prob. 4?63, what relationship
Chapter 4, Problem 60P(choose chapter or problem)
Problem 60P
For the velocity field of Prob. 4‒63, what relationship must exist between the coefficients to ensure that the flow field is incompressible?
PROBLEM: A general equation for a steady, two-dimensional velocity field that is linear in both spatial directions (x and y) is
Where U and V and the coefficients are constants. Their dimensions are assumed to be appropriately defined. Calculate the x- and y-components of the acceleration field.
Questions & Answers
QUESTION:
Problem 60P
For the velocity field of Prob. 4‒63, what relationship must exist between the coefficients to ensure that the flow field is incompressible?
PROBLEM: A general equation for a steady, two-dimensional velocity field that is linear in both spatial directions (x and y) is
Where U and V and the coefficients are constants. Their dimensions are assumed to be appropriately defined. Calculate the x- and y-components of the acceleration field.
ANSWER:
Step 1:
Consider a steady flow in the two dimensional field. If the flow is incompressible the volumetric strain rate of the flow must be zero.
The given velocity field is
= = +----(1)
The components of velocity field are
= -----(2)
= -----(3)
Where and are constants.
The coefficients are and