# With the aid of a graph show how the indicated power and brake power vary with the engine speed for a variable speed engine and explain the general shape of the graph. ii) State any FOUR advantages of super charging of an internal combustion engine

a) Show that the diagram efficiency, ?_d, of an impulse turbine is given by:

?_d=4b/a_i (cos??a_i- b/a_i ? )

a_i=nozzle angle
ai=absolute velocity of steam from nozzle. (7 marks)

b) The following data applies to the first stage of an impulse turbine which is a two-row velocity compounded wheel:
Turbine speed=2000rev/min
Nozzle angle=200
Exit angle from first row moving blade=220
Exit angle from second row moving blade=340
Mass flow rate of steam=6kg/s
Absolute of steam at discharge from the nozzle=700m/s

Determine the:
Blade inlet angle for each row.
Diagram power. (13 marks)

a) Show that the logarithmic mean area Am of a cylinder of unit length, internal radius r1, external radius r2, thermal conductivity k, whose inside and outside surface temperature are t1 and t2 respectively are given by:

A_m=(2p(r_2-r_1))/(l_n r_2/r_1 ) (6 marks)

b) Wet steam at 20 bar is carried in a steel steam mains of outside diameter 140mm, thickness 6mm and length 8m. The mains is insulated with an inner layer of diatomaceous earth 38mm, and an outer layer of magnesia 30mm thick. The inside heat transfer coefficient is 8.5 W/m2K and that of the outside surface lagging is 18W/m2K. The thermal conductivities of the diatomaceous earth, magnesia and steel are 0.09, 0.06 and 48W/mK, respectively.

Determine:

The rate of heat loss.
The temperature of the outside surface of the lagging. (14 marks)

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