Consider fully developed laminar flow in the annulus between two concentric pipes. The outer pipe is stationary, and the inner pipe moves in the \(x\) direction with speed \(V\). Assume the axial pressure gradient is zero \((\partial p / \partial x=0)\). Obtain a general expression for the shear stress, \(\tau\), as a function of the radius, \(r\), in terms of a constant, \(C_{1}\). Obtain a general expression for the velocity profile, \(u(r)\), in terms of two constants, \(C_{1}\) and \(C_{2}\). Obtain expressions for \(C_{1}\) and \(C_{2}\).

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P8.36 V x