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Hydrodynamic torque on a fixed disk in planar shear

The surface shear stress is

σ_{r θ} (a, θ) = - μ γ + 2 μ γ cos 2 θ .

The torque exerted by the fluid on the disk per unit axial length is therefore

T_{z} = a^{2} \int_{0}^{2 π} σ_{r θ} (a, θ) d θ = - 2 π μ γ a^{2} .

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