Q12 (a) Derive the expression of pressure variation with altitude in a gas under adiabatic condition. (b) A single acting reciprocating pump has a piston diameter 15 cm and stroke length 30 cm. The centre of the pump is 5 m above the level of water in sump and 33 m below delivery water level. The lengths of suction and delivery pipes are 6.5 m and 39 m respectively and both the pipes have the same diameter of 75 mm. If the pump is working at 30 r.p.m., find the pressure head on the piston at the beginning, middle and end of both suction and delivery strokes, and find the power required to drive the pump, take Darcy's friction factor for both the pipes as 0.04. Draw the indicator diagram. Please solve both of the problem in detail,i badly need its solution .I need the solutions and proofs in detail, sometimes some chegg experts deliver only the processes in a very short way which is very difficult to understand,so i kindly request you to write all the steps and calculations and to draw all the necessary figures. I request you again not to skip any step and the diagrams.