4. Problem 4-42: The velocity field for solid-body rotation in the re-plane (Fig. P4-42) is given by u, = 0 Ue = wr Where w is the magnitude of the angular velocity (@ points in the z-direction). For the case with w = 1.5 s, 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 P4-42
4. Problem 4-42: The velocity field for solid-body rotation in the re-plane (Fig. P4-42) is given by u, = 0 Ue = wr Where w is the magnitude of the angular velocity (@ points in the z-direction). For the case with w = 1.5 s, 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 P4-42
Elements Of Electromagnetics
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![**Problem 4-42**: The velocity field for solid-body rotation in the rΘ-plane (Fig. P4-42) is given by
\[ u_r = 0 \quad \quad u_θ = ωr \]
Where \( ω \) is the magnitude of the angular velocity \( (\vec{ω} \) points in the z-direction). For the case with \( ω = 1.5 \, \text{s}^{-1} \), plot a contour plot of velocity magnitude (speed). Specifically, draw curves of constant speed \( V = 0.5, 1.0, 1.5, 2.0, \) and \( 2.5 \, \text{m/s} \). Be sure to label these speeds on your plot.
**Figure Description**:
The figure shows a diagram with concentric circles centered around a point, representing the velocity field for solid-body rotation. The circles correspond to different values of radius \( r \), and the velocity vector \( u_θ = ωr \) is shown as arrows tangential to the circles, indicating the direction of rotation. The size of the arrows increases with \( r \), illustrating the increase in speed with distance from the center. Velocity vectors are labeled \( u_θ = ωr \) along these circles.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F08a0d1a7-4387-4b00-bd8e-a511cc6565f1%2F2fe0e31c-eb50-48e4-b5bb-8fe046d06f31%2Fhpukbwf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 4-42**: The velocity field for solid-body rotation in the rΘ-plane (Fig. P4-42) is given by
\[ u_r = 0 \quad \quad u_θ = ωr \]
Where \( ω \) is the magnitude of the angular velocity \( (\vec{ω} \) points in the z-direction). For the case with \( ω = 1.5 \, \text{s}^{-1} \), plot a contour plot of velocity magnitude (speed). Specifically, draw curves of constant speed \( V = 0.5, 1.0, 1.5, 2.0, \) and \( 2.5 \, \text{m/s} \). Be sure to label these speeds on your plot.
**Figure Description**:
The figure shows a diagram with concentric circles centered around a point, representing the velocity field for solid-body rotation. The circles correspond to different values of radius \( r \), and the velocity vector \( u_θ = ωr \) is shown as arrows tangential to the circles, indicating the direction of rotation. The size of the arrows increases with \( r \), illustrating the increase in speed with distance from the center. Velocity vectors are labeled \( u_θ = ωr \) along these circles.
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