Water flows through a thick-walled tube with an inner diameter of 12 mm and a length of 8 m. the tube is immersed in a well-stirred, hot reaction tank maintained at 85 degree c, and the conduction resistance of the tube wall (based on the inner surface area) is r_cond = 0.002 (m^2 k)/w. the inlet temperature of the process fluid is t_m, i = 20 degree c. and the flow rate is 33 kg/h. estimate a) what is the outlet temperature of the water for this condition? b) what would be the error you would have made if you assumed fully developed conditions to determine that outlet temperature?

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.