Problem 2 The volume flowrate Q of a fluid in a tube is related to the pressure difference AP across the tube by Poiseuille law AP = R4Q where the term R, is known as hydraulic resistance, given by...

Extracted text: Problem 2 The volume flowrate Q of a fluid in a tube is related to the pressure difference AP across the tube by Poiseuille law AP = R4Q where the term R, is known as hydraulic resistance, given by 8µl with L = length of the tube, r = inner radius and u = dynamic viscosity coefficient. The value of the coefficient u depends on the specific fluid and, in general varies with temperature. For water, it can range between ca. 1.3 [mPa-s] at 10 °C and ca. 0.3 (mPa-s] at 90 °c. Suppose then the temperature of the water flow in a tube to be a r.v. uniformly distributed between 90 and 10 °C, so that also u is a r.v. uniformly distributed between 0.3 and 1.3 [mPa•s] a) Find the mean and variance of u. 8L b) Letting = 2.5 · 10*, so that Ry = 2.5 · 10*µ, find the pdf of Ry. c) The fluidity f is defined as the inverse of viscosity (F = 1/u). Find the pdf of F. d) Compute the mean and variance of f.