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Biharmonic stream function for planar Stokes flow

Biharmonic stream function for a fixed disk in planar shear

The surface shear stress is
$$
\sigma_{r\theta}(a,\theta)
=-\mu\gamma+2\mu\gamma\cos2\theta.
$$
The torque exerted by the fluid on the disk per unit axial length is therefore
$$
\mathcal T_z
=a^2\int_0^{2\pi}\sigma_{r\theta}(a,\theta)\,d\theta
=-2\pi\mu\gamma a^2.
$$


Hydrodynamic torque on a fixed disk in planar shear

Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 1 / 39C / b / iii / Solution

Hydrodynamic torque on a fixed disk in planar shear

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Hydrodynamic torque on a fixed disk in planar shear

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