Some non-Newtonian fluids behave as a Bingham plastic for which shear stress can be expressed as \(\tau=\tau_{y}+\) \(\mu(d u / d r)\). For laminar flow of a Bingham plastic in a horizontal pipe of radius \(R\), the velocity profile is given as \(u(r)=\) \((\Delta P / 4 \mu L)\left(r^{2}-R^{2}\right)+\left(\tau_{y} / \mu\right)(r-R)\), where \(\Delta P / L\) is the constant pressure drop along the pipe per unit length, \(\mu\) is the dynamic viscosity, \(r\) is the radial distance from the centerline, and \(\tau_{y}\) is the yield stress of Bingham plastic. Determine

(a) the shear stress at the pipe wall and

(b) the drag force acting on a pipe section of length \(L\).