An infinite cylindrical rod falls down in the middle of an infinite tube filled with fluidat a constant speed V (terminal velocity). The density of the rod and the fluid are different. Assume that the pressure field is hydrostatic.(a)[5pts] Solve for the velocity profileas a function of rin terms of V and the other variables.(b)[2pts] Calculate upward force per unit length of the rod from the fluid wall shear stress on the rod.(c)[2 pts] Calculate upward force per unit length of the rod from bouyancy.(d)[1pts] Calculate V. VR1

An external consultant recommends that a plant installs a bank of capacitors for power factor correction. this will reduce the peak electrical demand charges by an average of 93 kw every month. the plant current pays $13 per kw in peak demand charges. the capacitor bank will include 223 kw of fixed capacitors, and 183 of variable capacitors. the fixed capacitors cost $59 per kw, and the variable capacitors will cost $65 per kw. the consultant charges 21% of the equipment costs to install the capacitors. because this project will reduce the demand for the electric utility, they are prepared to provide a one-time rebate of $42 per kw of reduced demand. what is the simple payback period for this project (in years)?