Athermocouple, with a spherical junction diameter of 0.5 mm, is used for measuring the temperature of hot air flow in a circular duct. the convection heat transfer coefficient of the air flow can be related with the diameter (d) of the sphere and the average air flow velocity (v) as h = 2.2(v /d)0.5, where d, h, and v are in m, w/m2•k, and m/s, respectively. the properties of the thermocouple junction are k = 35 w/m•k, rho = 8500 kg/m3, and cp = 320 j/kg•k. the maximum response time of the thermocouple to record 78 percent of the initially applied temperature difference is 5 s. determine the minimum air flow velocity that the thermocouple can be used.

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)?