In a manufacturing plant that produces cosmetic products, glycerin is being heated by flowing through a 25-mm-diameter and 20-m-long tube. with a mass flow rate of 0.5 kg/s, the flow of glycerin enters the tube at 25°c. the tube surface is maintained at a constant surface temperature of 140°c. evaluate the properties for glycerin at 30°c.

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.

At 12 noon, the count in a bacteria culture was 400; at 4: 00 pm the count was 1200 let p(t) denote the bacteria cou population growth law. find: (a) an expression for the bacteria count at any time t (b) the bacteria count at 10 am. (c) the time required for the bacteria count to reach 1800.

Slip occurs via two partial dislocations because of (a) the shorter path of the partial dislocation lines; (b) the lower energy state through partial dislocations; (c) the charge balance.