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Consider a two-dimensional, compressible flow field in
Chapter 4, Problem 78P(choose chapter or problem)
Problem 78P
Consider a two-dimensional, compressible flow field in which an initially square fluid particle moves and deforms. The fluid particle dimension is a at time t and is aligned with the x- and y-axes as sketched in Fig. P4‒81. At some later time, the particle is still aligned with the x- and y-axes but has deformed into a rectangle of horizontal length 1.06a and vertical length 0.931a. (The particle’s dimension in the z-direction does not change since the flow is two-dimensional.) By what percentage has the density of the fluid particle increased or decreased?
Questions & Answers
QUESTION:
Problem 78P
Consider a two-dimensional, compressible flow field in which an initially square fluid particle moves and deforms. The fluid particle dimension is a at time t and is aligned with the x- and y-axes as sketched in Fig. P4‒81. At some later time, the particle is still aligned with the x- and y-axes but has deformed into a rectangle of horizontal length 1.06a and vertical length 0.931a. (The particle’s dimension in the z-direction does not change since the flow is two-dimensional.) By what percentage has the density of the fluid particle increased or decreased?
ANSWER:
Solution 78P
Consider a two-dimensional, compressible flow field in which an initially square fluid particle moves and deforms. The fluid particle dimension is a at time t and is aligned with the x- and y-axes as sketched in fig. below. At some later time, the particle is still aligned with the x- and y-axes but has deformed into a rectangle of horizontal length 1.06a and vertical length 0.931a. (The particle’s dimension in the z-direction does not change since the flow is two-dimensional.)
By what percentage has the density of the fluid particle increased or decreased can be calculated by finding the density of the fluid particle after deformation and comparing it with initial density.