Question 4: The flow field for pipe flow with a circular cross-section of radius R is given by \underline{\mathbf{u}}(r)=\frac{1}{4 \mu} \frac{\Delta P}{L}\left(R^{2}-r^{2}\right) \hat{\mathbf{e}}_{z} ^^20where^^20\quad \nablap_m=-\frac{\Delta P}{L}\hat{\mathbf{e}}z Find the pressure field,

p(x), given that p(x.) = pe is measured during flow, assume x, is at the center of the pipe (r = 0 and z = ze). Now write the traction due to the fluid on the pipe wall in cylindrical coordinates. Integrate the viscous part of the traction, tp, over the entire surface of the pipe (of length L) to find the total viscous force E. Describe why the result is physically sensible.

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