1. A thin tape (surface area A) will be pulled at constant velocity between two fixed plates separated by a distance h by means of a force F (see figure). The regions between the tape and the fixed plates are filled with liquids of different viscosities. The purpose of the setup is to coat both sides of the tape with different materials. We would like to develop a quantitative criterion to decide where to locate the tape between the plates (i.e. we would like to find the optimum value of 8). Fixed plates 8 ui F Tape h U2 (a) Consider the following data set: Mi = 1.5 Pas U2 = 0.5 Pas h= 2 cm A = 100 cm? To get an idea of the effect of d on the tape velocity (vo), plot vo vs. S for F= 0.5 N. Note that there is an optimum location that gives a maximum tape velocity. (b) If the objective is to locate the tape at a position that maximizes its velocity (and thus the productivity of the coating process), find an expression to calculate the optimum value of 8 as a function of h and the viscosities of the two fluids. What is this optimum value and the corresponding value of the tape velocity for the data set in part (a) and F = 0.5 N? = (c) If the tape moves at a velocity vo = 0.7 m/s and the objective is to minimize the force F needed to pull it, find an expression to calculate the optimum value of 8. What is this optimum value and the corresponding value of the minimum force for the data set in part (a)