Acylindrical part of diameter d is loaded by an axial force p. this causes a stress of p/a, where a = πd2/4.

if the load is known with an uncertainty of ±12 percent, the diameter is known within ±3 percent (tolerances), and the stress that causes failure (strength) is known within ±17 percent, determine the minimum design factor that will guarantee that the part will not fail.

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)?