Water is pumped from a lower reservoir to a higher reservoir by a pump that provides 23 kw of useful mechani- cal power to the water. the free surface of the upper reservoir is 57 m higher than the surface of the lower reservoir. if the flow rate of water is measured to be 0.03 m3/s, determine the irreversible head loss of the system and the lost mechanical power during this process.

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.

Prove the equivalence between the two statements of the 2nd law of thermodynamics (i.e., a violation of one statement leads to the violatio the other statement)

For a process taking place in a closed system containing gas, the volume and pressure relationship is pvi-constant. -1.5 bar, the process starts with initial conditions, pi = =0.03 m3 and ends with final volume, v2-0.05 m3 determine the work done by the gas.