divergent nozzle. This is the case, for instance, in the Parsons turbine, where the whole expansion is divided into many stages each of which involves only a small drop in pressure.
111. Influence of Friction.βWe have dealt so far with the ideal
case of no friction, and have taken the whole work of expansion as
going to produce kinetic energy in the jet. But under real conditions
there is a progressive dissipation of energy through friction;
as expansion proceeds the steam loses part of its kinetic energy
which is restored to it as heat. Thus, at every stage in the process
the velocity acquired is less than it would be in frictionless adiabatic expansion,
but the steam is drier and its volume is greater in consequence
of the restored heat. Referring to the entropy-temperature diagram
Fig. 54.
(fig. 54) the process of expansion under
conditions involving friction is represented
not by the adiabatic line ππ but by some
such line as ππ lying between the adiabatic
line and the saturation line ππ. The final
condition of dryness is ππ/ππ instead of
ππ/ππ. During this expansion the effect
of friction, as regards the entropy, is
equivalent to the communication to the
substance of a quantity of heat represented
by the area ππππ. Hence that
area represents the work converted by
friction into heat. The whole work done
during expansion is the area ππππ, which
is more than before by the area πππ. The difference, namely ππππ
minus ππππ, represents what may be called the net heat drop when
friction is allowed for: it represents what is effectively available for
giving kinetic energy to the jet. This net area may also be
expressed as equal to ππππ minus ππππ. Compared with frictionless
adiabatic expansion the net loss resulting from friction is the area
ππππ. The volume is increased in the ratio of ππ to ππ, and this
has to be taken account of in determining the proper dimensions of
the divergent nozzle.
112. Turning now to the question of utilizing the kinetic energy of steam in a steam turbine, it will be clear from the figures that have been given that if the whole heat drop is allowed to give kinetic energy to the steam in one operation, as in the De Laval nozzle, a velocity of about 4000 ft. per second has to be dealt with. To take advantage of a jet in the most efficient manner in a turbine consisting of a single wheel the velocity of the buckets against which the steam impinges should be nearly one half the velocity of the stream. But a peripheral velocity approaching 2000 ft. per second is impracticable. Apart from the difficulties which it would involve as regards gearing down to such a speed as would serve for the driving of other machines, which are to employ the power, there are no materials of construction fitted to withstand the forces caused by rotation at such a speed.
Hence it is advantageous to divide the process into stages. This may be done by using more than one wheel to absorb the kinetic energy of the jet, as is done in the Curtis turbine, or by dividing the heat drop into many steps, making each of these so small that the steam never acquires an inconveniently great velocity, as is done in the Parsons turbine. Turbines which employ one or other of these two methods, or a combination of both, achieve a greater economy of steam than is practicable with a single wheel.
113. De Laval Turbine.βThanks, however, to the inventions
of De Laval, the single expansion single wheel type of turbine,
with buckets in the rim, has been brought to a degree of efficiency
which, while considerably less than is reached in compound
turbines, is still remarkably good. This has been done
by the use of the divergent nozzle and with the help of mechanical
devices which enable the peripheral speed to be very high,
though even with the help of these devices the speed of the
buckets falls considerably short of that which would be suitable
to the velocity of the jet. In De Lavalβs turbine the steam
expands at one step from the full pressure of the supply to the
pressure of the exhaust by discharge in the form of a jet from a
divergent nozzle. It then acts on a ring of buckets or blades
in much the same way as the jet of water acts on the buckets of a
Pelton wheel or other form of pure impulse turbine. To utilize
a fair fraction of the kinetic energy of the jet the blades have to
run at an enormous velocity, and the speed of the shaft which
carries them is so great that gearing down is resorted to before
the motion is applied to useful purposes. The general arrangement
of the steam nozzle and turbine blades is illustrated
in fig. 55. The blades project from the circumference of
a disk-shaped wheel and 
Fig. 55.
form a complete ring round
it, only a few of the blades
being shown in the sketch.
The increasing section of
the nozzle is calculated
with reference to the final
pressure, according to the
principles already explained. The jet impinges at one side
of the wheel and escapes at the other after having had its
direction of motion nearly reversed. The expansion in the nozzle
is carried to atmospheric pressure, or near it, if the turbine
is to be used without a condenser; but in many cases an ejector
condenser is employed, and when that is done the nozzle is
of a form which adapts it to expand the steam to a correspondingly
lower pressure. It is only in the smaller sizes of these
turbines that a single nozzle is used; in the larger steam turbines,
as in large Pelton wheels, several nozzles are applied at intervals
along the circumference of the disk. The peripheral velocity
of the blades ranges from about 500 ft. per second in the smallest
sizes (5 h.p.) up to nearly 1400 ft. per second in turbines of
300 h.p. In a 50 h.p. De Laval turbine the shaft which carries
the turbine disk makes 16,000 revolutions per minute; in the
5 h.p. size it makes as many as 30,000 revolutions per minute.
A turbine developing 300 h.p. uses a wheel 30 in. in diameter,
running at over 10,000 revolutions per minute, with a peripheral
speed of nearly 1400 ft. per second. These enormous
speeds are made possible by the ingenious device of using a
flexible shaft, which protects the bearings and foundations
from the vibration which any want of balance would otherwise
produce. The elasticity of the shaft is such that its period of
transverse vibration is much longer than the time taken to
complete a revolution. The high-speed shaft which carries
the turbine disk is geared, by means of double helical wheels
with teeth of specially fine pitch, to a second-motion shaft,
which runs at one-tenth of the speed of the first; and from this
the motion is taken, by direct coupling or otherwise, to the
machine which the turbine is to drive. The wheel carrying
the buckets is much thickened towards the axis to adapt it to
withstand the high stresses arising from its rotation. Turbines
of this class in sizes up to 300 or 400 h.p. are now in extensive
use for driving dynamos, fans and centrifugal pumps. Compared
with the Parsons turbine, De Lavalβs lends itself well
to work where small amounts of power are wanted, and there 
Fig. 56.
it achieves a higher efficiency, but in large sizes the Parsons
turbine is much the more efficient of the two. Trials of a De
Laval turbine used with a condenser, and developing about
63 h.p., have shown an average steam consumption at the rate
of about 20 β per brake-horse-power-hour,
and even better results are
reported in turbines of a larger size.
114. Action of the Jet in De Lavalβs Turbine.βIn entering the turbine the jet is inclined at an angle a to the plane of the wheel. Calling its initial velocity V1 and the velocity of the buckets π’ we have, as in fig. 56, V2 for the velocity of the steam relatively to the wheel on admission. A line AB parallel to V2 therefore determines the proper angle of the blade or bucket on the entrance side if the steam is to enter without shock. As the steam passes through the blade channel the magnitude of this relative velocity does not change, except that it is a little reduced on account of friction. The action is one of pure impulse; there is no change of pressure during the passage, and consequently no acceleration of the steam through drop in pressure after once it has left the nozzle. Hence V3, the relative velocity at exit may (neglecting friction) be taken as equal to V2
The direction of V3 or BC is tangent to the exit side of the bucket.