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

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

Where b=mean blade speed

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

Mean blade radius=600mm

Nozzle angle=200

Exit angle from first row moving blade=220

Exit angle from second row moving blade=340

Blade velocity coefficient for all blades=0.9

Mass flow rate of steam=6kg/s

Absolute of steam at discharge from the nozzle=700m/s

Exit angle from fixed blade=270

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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