Show how the Hagen-Poiseuille equation for the steady laminar flow of a Newtonian fluid in a uniform cylindrical tube can be derived starting from the general microscopic equations of motion (e.g., the continuity and momentum equations given in Appendix E).

Appendix E).

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E.1 CONTINUITY EQUATION Rectangular coordinates (x, y, z): P+ (pv.) + (pv,)+(pv.)-0 at Cylindrical coordinates (r, 0, z): , 1 at + -(prv,) +- 1 r or r 80 (pve)+- +(pv) = 0 Spherical coordinates (r, 0, 0): 1 a Ot + -(prv,)+ 2 r dr r sin 1 (pvo sin 0)+- 1 d -(pv)=0 r sin