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The velocity field for solid-body rotation in the r? plane
Chapter 4, Problem 39P(choose chapter or problem)
Problem 39P
The velocity field for solid-body rotation in the rθ plane (Fig. P4-41) is given by
u r=0 uθ=ωr
where ω is the magnitude of the angular velocity ( points in the z-direction). For the case with ω = 1.5 s -1, plot a contour plot of velocity magnitude (speed). Specifically, draw curves of constant speed V = 0.5, 1.0, 1.5, 2.0, and 2.5 m/s. Be sure to label these speeds on your plot.
FIGURE P4‒41
Questions & Answers
QUESTION:
Problem 39P
The velocity field for solid-body rotation in the rθ plane (Fig. P4-41) is given by
u r=0 uθ=ωr
where ω is the magnitude of the angular velocity ( points in the z-direction). For the case with ω = 1.5 s -1, plot a contour plot of velocity magnitude (speed). Specifically, draw curves of constant speed V = 0.5, 1.0, 1.5, 2.0, and 2.5 m/s. Be sure to label these speeds on your plot.
FIGURE P4‒41
ANSWER:
Solution 39P
We need to draw curves of constant speed V = 0.5, 1.0, 1.5, 2.0, and 2.5 m/s.
Step 1
We are given, angular speed
Different values of constant speed are given as V = 0.5, 1.0, 1.5, 2.0, and 2.5 m/s.
Since,
So,