In fully-developed laminar pipe flow, consider the rate of work done on an annulus of thickness dr (hint: consider, for each face of the annulus, rate of work = power = force × velocity).

(i) Find an expression for the power (per unit volume) dissipated by the flow in the fluid annulus, and show that it is equal to µ(du/dr)

(ii) By using u(r) from 3(ii) above, and integrating this expression, show that the power dissipated across a length of pipe is Q∆P

Amass of 1.5 kg of air at 120 kpa and 24°c is contained in a gas-tight, frictionless piston-cylinder device. the air is now compressed to a final pressure of 720 kpa. during the process, heat is transferred from the air such that the temperature inside the cylinder remains constant. calculate the boundary work input during this process.

If you were designing a bumper for a car, would you prefer it to exhibit elastic or plastic deformation? why? consider the functions of a bumper in both a minor "fender-bender" and a major collision.

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.