A long, cylindrical, electrical heating element of diameter D = 12 mm, thermal conductivity k = 240 W/m ⋅ K, density rho = 2700 kg/m3 , and specific heat cp = 900 J/kg ⋅ K is installed in a duct for which air moves in cross flow over the heater at a temperature and velocity of 30°C and 8 m/s, respectively. (a) Neglecting radiation, estimate the steady‐state surface temperature when, per unit length of the heater, electrical energy is being dissipated at a rate of 1000 W/m. (b) If the heater is activated from an initial temperature of 30°C, e

Aloaded platform of total mass 500 kg is supported by a dashpot and by a set of springs of effective stiffness 72 kn/m. it is observed that when the platform is depressed through a distance x = 12.5 cm below its equilibrium position and then released without any initial velocity; it reaches its equilibrium position in the shortest possible time without overshoot. find the position and velocity of the loaded platform 0.10 sec. after its release. if a further load of 400 kg is added to the platform, find, i) the frequency of damped vibrations, and i) the amplitude of vibration after 2 complete oscillations, given that the initial amplitude is 15 cm.

Apump is used to circulate hot water in a home heating system. water enters the well-insulated pump operating at steady state at a rate of 0.42 gal/min. the inlet pressure and temperature are 14.7 lbf/in.2, and 180°f, respectively; at the exit the pressure is 60 lbf/in.2 the pump requires 1/15 hp of power input. water can be modeled as an incompressible substance with constant density of 60.58 lb/ft3 and constant specific heat of 1 btu/lb or. neglecting kinetic and potential energy effects, determine the temperature change, in °r, as the water flows through the pump.

Which of the following controllers anticipates the future from the slope of errors over time? a)-proportional b)-on/off c)-integral d)-derivative.