10. (a) Prove that the centrifugal stress at the root of an untapered blade attached to the drum of anaxial flow turbomachine is given byo. = 7p„N°A‚/1800,where pm = density of blade material, N=rotational speed of drum, in rpm and A, = area ofthe flow annulus.(b) The preliminary design of an axial-flow gas turbine stage with stagnation conditions at stageentry of Po1 = 400 kPa, To1 = 850 K, is to be based upon the following data applicable to themean radius:Flow angle at nozzle exit, a, = 63.8°;Reaction, R=0.5;Flow coefficient, cJUm=0.6;Static pressure at stage exit, p3 = 200 kPa;Estimated total-to-static efficiency, 1s=0.85.Assuming that the axial velocity is unchanged across the stage, determine(i) the specific work done by the gas;(ii) the blade speed;(ii) the static temperature at stage exit.(c) The blade material has a density of 7850 kg/m³ and the maximum allowable stress in therotor blade is 120 MPa. Taking into account only the centrifugal stress, assuming untaperedblades and constant axial velocity at all radii, determine for a mean flow rate of 15 kg/s(1) the rotor speed (rev/min);(ii) the mean diameter;(iii) the hub-tip radius ratio.For the gas assume that Cp=1050 J/(kg K) and R=287 J/(kg K).

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Prove that the centrifugal stress at the root of an untapered blade attached to the drum of an axial flow turbomachine is given by ac = xp„N²A‚/1800, where p„= density of blade material, N=rotational speed of drum, in rpm and A, = area of the flow annulus.

Prove that the centrifugal stress at the root of an untapered blade attached to the drum of an axial flow turbomachine is given by ac = xp„N²A‚/1800, where p„= density of blade material, N=rotational speed of drum, in rpm and A, = area of the flow annulus.

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Applied Fluid Mechanics

A fluid is a substance that is continuously deformed by the application of shear stress. The rate of deformation of a fluid depends on its viscosity. The fluid tries to flow when it interacts with some other system.

Question

10. (a) Prove that the centrifugal stress at the root of an untapered blade attached to the drum of an
axial flow turbomachine is given by
o. = 7p„N°A‚/1800,
where pm = density of blade material, N=rotational speed of drum, in rpm and A, = area of
the flow annulus.
(b) The preliminary design of an axial-flow gas turbine stage with stagnation conditions at stage
entry of Po1 = 400 kPa, To1 = 850 K, is to be based upon the following data applicable to the
mean radius:
Flow angle at nozzle exit, a, = 63.8°;
Reaction, R=0.5;
Flow coefficient, cJUm=0.6;
Static pressure at stage exit, p3 = 200 kPa;
Estimated total-to-static efficiency, 1s=0.85.
Assuming that the axial velocity is unchanged across the stage, determine
(i) the specific work done by the gas;
(ii) the blade speed;
(ii) the static temperature at stage exit.
(c) The blade material has a density of 7850 kg/m³ and the maximum allowable stress in the
rotor blade is 120 MPa. Taking into account only the centrifugal stress, assuming untapered
blades and constant axial velocity at all radii, determine for a mean flow rate of 15 kg/s
(1) the rotor speed (rev/min);
(ii) the mean diameter;
(iii) the hub-tip radius ratio.
For the gas assume that Cp=1050 J/(kg K) and R=287 J/(kg K).

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