How can we describe the fluid element motions by using mathematical method?

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.

Refrigerant 134a enters an insulated compressor operating at steady state as saturated vapor at -26°c with a volumetric flow rate of 0.18 m3/s. refrigerant exits at 9 bar, 70°c. changes in kinetic and potential energy from inlet to exit can be ignored. determine the volumetric flow rate at the exit, in m3/s, and the compressor power, in kw.

Ahot wire operates at a temperature of 200°c while the air temperature is 20°c. the hot wire element is a tungsten wire of 5 um diameter and 2 mm in length. plot using excel current, heat transfer and heat generated by the wire for air velocity varying from 1-10 m/s in steps of lm/s? matlab the sensor voltage output, resistance, or assume nu 0.989 re033pr13 take air properties at tr (200°c20°c)/2 = 110°c properties of tungsten: c 0.13 kj/kg.k 3 p 19250 kg/m k (thermal conductivity) = 174 w/m.k