Flow of a fluid with a suddenly applied constant wall stress, in the system studied in Example
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Flow of a fluid with a suddenly applied constant wall stress, in the system studied in Example 4.1-1, let the fluid be at rest before t = 0. At time t = 0 a constant force is applied to the fluid at the wall in the positive x direction, so that the shear stress τyx takes on a new constant value τ0 at y = 0 for t > 0.
(a) Differentiate Eq. 4.1-1 with respect to y and multiply by - μ to obtain a partial differential equation for τyx(y, t).
(b) Write the boundary and initial conditions for this equation.
(c) Solve using the method in Example 4.1-1 to obtain
(d) Use the result in (c) to obtain the velocity profile. The following relation1 will be helpful
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