FREE NO(free for only the 2nd person) :)

Derive the correction factor formula for conical nozzle i=-(1+ cosa) and calculate the nozzle angle correction factor for a nozzle whose divergence hal-fangle is 13 (hint: assume that all the mass flow originates at the apex of the cone.

Avertical steel rod of length 2.0 m and diameter 25 mm is rigidly fixed at its upper end and has a flange at its lower, free, end. what will be the maximum stress produced in the rod when a load of 20 kn is applied, (a) gradually to the lower end, (b) suddenly to the lower end, (c) by a collar falling from a height of 50 mm on to the flange?

An inventor claims to have developed a reversed heat engine (ie. a heat pump) which is able to deliver 10 kj heat into the room at 20°c from outside ambient temperature of -10°c by consuming only 2 kj electricity in winter. this claim is a)-impossible b)-possible only if the heat pump is ideal c)-practically possible d)-unable to be assessed as it depends on the working fluid used in the heat pump.