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Converging duct flow is modeled by the steady, two
Chapter 4, Problem 52P(choose chapter or problem)
Problem 52P
Converging duct flow is modeled by the steady, two dimensional velocity field of Prob. 4‒17. A fluid particle (A) is located on the x-axis at x = xA at time t = 0 (Fig. P4-54). At some later time t, the fluid particle has moved downstream
FIGURE P4‒54
with the flow to some new location. x = xA, as shown in the figure. Since the flow is symmetric about the x-axis, the fluid particle remains on the.x-axis at all times. Generate an analytical expression for the.x-location of the fluid particle at some arbitrary time t in terms of its initial location xA and constants U0 and b. In other words, develop an expression for xA (Hint: We know that u = dxparticle/dt following a fluid particle. Plug in u. separate variables, and integrate.)
Questions & Answers
QUESTION:
Problem 52P
Converging duct flow is modeled by the steady, two dimensional velocity field of Prob. 4‒17. A fluid particle (A) is located on the x-axis at x = xA at time t = 0 (Fig. P4-54). At some later time t, the fluid particle has moved downstream
FIGURE P4‒54
with the flow to some new location. x = xA, as shown in the figure. Since the flow is symmetric about the x-axis, the fluid particle remains on the.x-axis at all times. Generate an analytical expression for the.x-location of the fluid particle at some arbitrary time t in terms of its initial location xA and constants U0 and b. In other words, develop an expression for xA (Hint: We know that u = dxparticle/dt following a fluid particle. Plug in u. separate variables, and integrate.)
ANSWER:
ANSWER:
Step 1:-
The velocity field is given as,
Where,
And .
