Mechanics of Fluids

∴ Hydraulic efficiency =
Overall efficiency =
39.67 − 4.12
39.67
= 0.896
P
QϱgH =
200 × 103 0.601 × 1000 × 9.81 × 39.67
= 0.855
Euler head = (39.67 − 4.12) m = 35.55 m
= u1vw1/g since vw2 = 0
u1 = 69.1 × 0.25 m · s −1 = 17.28 m · s −1
∴ vw1 = gH/u1 = (9.81 × 35.55/17.28) m · s −1 = 20.18 m · s −1
vr = Q/A ={0.601/(π × 0.5 × 0.06 × 0.95)} m · s −1
= 6.71 m · s −1
∴ α1 = arctan(vr/vw1) = arctan(6.71/20.18) = 18.4 ◦
and β1 = arctan vr/(vw1 − u1) = arctan(6.71/2.90) = 66.6 ◦
13.3.6 Cavitation
u2 = 69.1 × 0.325/2 m· s −1 = 11.23 m · s −1
∴ β2 = arctan(vr/u2) = arctan(6.71/11.23) = 30.9 ◦
Non-uniformity of flow in machines may cause the pressure, even in a given
cross-section, to vary widely. There may thus be, on the low-pressure side
of the rotor, regions in which the pressure falls to values considerably below
atmospheric. In a liquid, if the pressure at any point falls to the vapour
pressure (at the temperature concerned), the liquid boils and small bubbles
of vapour form in large numbers. These bubbles are carried along by the
flow, and on reaching a point where the pressure is higher they suddenly
collapse as the vapour condenses to liquid again. A cavity results and the
surrounding liquid rushes in to fill it. The liquid moving from all directions
collides at the centre of the cavity, thus giving rise to very high local pressures
(up to 1 GPa). Any solid surface in the vicinity is also subjected to these
intense pressures, because, even if the cavities are not actually at the solid
surface, the pressures are propagated from the cavities by pressure waves
similar to those encountered in water hammer. This alternate formation
and collapse of vapour bubbles may be repeated with a frequency of many
✷
Turbines 619