The pressure gradient, dxdP, in a a laminar flow of a Newtonian fluid inside a horizontal pipe is given by the Hagen-Poiseuille equation: dXdP=R28vavg Where R is the radius of the pipe, is the fluid viscosity, and vavg is the average velocity of the fluid in the pipe. a) Express this equation in terms of the fluid volumetric flow rate, Q, and the tube radius R. b) Express the equation in terms of the fluid mass flow rate, m, and the fluid kinematic viscosity . c) The shear stress distribution in the pipe is given by equation (82) rx=(dXdP)2r. Express this shear stress in terms of the fluid average velocity using the Hagen-Poiseuille equation. d) Evaluate the shear stress at the tube wall in terms of the fluid average velocity