Question

8.3 A flow field is represented by the following equations: \frac{1 + 2/3(\mu/\mu')}{1 + \mu/\mu'} \mathbf{u} = r\mathbf{e}_\theta \times \mathbf{e}_r p = 0. Show that this representation satisfies the Stokes equations. Using this solution, find the velocity and pressure fields for a fluid that is contained between two concentric spheres of radii $r$ and $r_o > r$ in which the outer sphere is rotating with angular velocity $\Omega$, about the x axis and the inner sphere is rotating with angular velocity $\Omega_i$, in the same direction. Calculate the torque that acts on each of the spheres. From the results obtained above, deduce the velocity and pressure fields in a fluid that is contained inside a rotating sphere and find the torque that acts on the sphere.

          8.3 A flow field is represented by the following equations:
\frac{1 + 2/3(\mu/\mu')}{1 + \mu/\mu'}
\mathbf{u} = r\mathbf{e}_\theta \times \mathbf{e}_r
p = 0.
Show that this representation satisfies the Stokes equations. Using this solution, find the velocity and pressure fields for a fluid that is contained between two concentric spheres of radii $r$ and $r_o > r$ in which the outer sphere is rotating with
angular velocity $\Omega$, about the x axis and the inner sphere is rotating with angular velocity $\Omega_i$, in the same direction. Calculate the torque that acts on each of the spheres.
From the results obtained above, deduce the velocity and pressure fields in a fluid that is contained inside a rotating sphere and find the torque that acts on the sphere.

8.3 A flow field is represented by the following equations:
(1 + 2/3(μ/μ'))/(1 + μ/μ')
𝐮 = r𝐞θ×𝐞r
p = 0.
Show that this representation satisfies the Stokes equations. Using this solution, find the velocity and pressure fields for a fluid that is contained between two concentric spheres of radii r and ro > r in which the outer sphere is rotating with
angular velocity Ω, about the x axis and the inner sphere is rotating with angular velocity , in the same direction. Calculate the torque that acts on each of the spheres.
From the results obtained above, deduce the velocity and pressure fields in a fluid that is contained inside a rotating sphere and find the torque that acts on the sphere.

Added by Carolyn F.

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