$1)$ A four$-$stroke diesel engine on test gave the following results:

Speed $=3000[$rev$/$min$]$

Torque $=116\mathrm{.}5[$Nm$]$

fuel flow $=175[$ml$/$min$]$

Calculate the following engine parameters:

i$)$ the shaft power output in kW

ii$)$ the brake mean effective pressure in bar

iii$)$ the specific fuel consumption in g$/$kWh

iv$)$ the thermal efficiency

Given data :$-$

no$.$ of cylinders $=4$

engine capacity per cylinder $=0\mathrm{.}44[$litre$]$

relative density of fuel oil $=0\mathrm{.}82$

calorific value of fuel $=43,250[$kJ$/$kg$]$

$2)$ The pressure in the evaporator of an ammonia refrigerator is $1\mathrm{.}196$ bar and the

pressure in the condenser is $15\mathrm{.}54$ bar. Calculate the refrigerating effect per unit

mass of refrigerant and the COP for the following refrigeration cycle:

$$ The vapor delivered to the compressor is superheated by $20$K;

$$ The isentropic efficiency of the compressor is $85\%,$ and

$$ The liquid after the condensation is undercooled by $10$ K

$3)$ Air is drawn in a gas turbine unit at SSL conditions. The gas turbine plant has a

pressure ratio of $6$:$1$ and a maximum cycle temperature of $610$oC$.$ The compressor is

driven by the HP turbine and the LP power turbine drives a separate shaft for power

output. The isentropic efficiencies of the compressor, the HP turbine and the LP

power turbine are $0\mathrm{.}78,0\mathrm{.}82$ and $0\mathrm{.}82$ respectively. Calculate:

$($a$)$ The pressure and temperature of the gases entering the power turbine

$($b$)$ The net power developed by the plant per unit kg of air flow rate

$($c$)$ The thermal efficiency of the plant.

$4)$ The radial clearance between a piston and the walls of a cylinder is $0\mathrm{.}075$ mm$,$

the length of the piston is $250$ mm and its diameter is $100$ mm$.$ There is a

difference in pressure of oil on the two ends of the piston of $2$ bar, and the

kinematic viscosity of the oil is $32$ cSt$.$ Treating the flow as if it occurred

between parallel flat plates, estimate the leakage rate.

Assume oil density is $900$ kg$/$m$3$

$,1$ cSt $=1$ mm$2/$s $=10-6$ m$2$

$/$s