A continuous belt moving vertically through a bath of viscous liquid drags a layer of liquid, of thickness h, along with it. The volume flow rate of liquid, Q, is assumed to depend on μ, rho, g, h, and V, where V is the belt speed. (a) Apply dimensional analysis to predict the form of dependence of Q on the other variables. (b) Calculate dimensionless parameter dependent on rho (proportional to rho) with h = 0.132 m, rho = 345 kg/m3, V = 0.131 m/s, μ = 0.5 × 10-4 N-s/m2.

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.