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La ecuaci6n de energia formdada entre dos puntos
la proporciona
(9) ( PI
Y+ zl+
\
v,2 P;2 v22
!(
y + z2 + 29
q-
U’V’ cos ai- lJ& cos a2
= HL +
9
donde HL representa las p&didas por fricci6n y el
titimo tkrmino en el lado de la derecha de la
ecuaci6n representa la caida absorbida por la turbina.
De las ecuaciones (7) y (8) se desprende que
(10) w = v2 + u2 $ 2 vu cos p
(1’) uV COS a = u(u -t vcos p)
Combinando las ecuaciones (9) (10) y (11) se obtienc
la liamada ecuacibn de energia en un marco de
referencia rotativo.
(12)
i pi v,2- I$
Y+zl+ 29 i -
=
p2 v$- I$
y + z2 +
( al )
AdviMase que si no hay flujo. Vl=V2= 0 y la
ecuacidn se reduce a ello para un vortice. Si no hay
rotaci6n, la ecuacidn se reduce a la forma conocida
de la ecuacibn de energia,
Eficiencia de las Turbinas
La eficiencia hidrtiulica de una turbina se define
mediante
(13)
H’
‘1H= 7
donde H es la ctida total disponible (posteriormente
la definiremos mtis cietenidamente). La eficiencia
mec&nica es definida por
Ehp
(I41 ‘Im =
Bhp + FHp
donde FHp es el caballaje consumido por la fricci6n
tanto mecanica coma toda la fricci6n de 10s fltidos
que no sea la de las prop& paletas. La eficiencia
volum&rica representa el flujo de escape que no
trabaja,
(i5j T,, = “i*’
donde QL es el flujo de escape. La eficiencia general
es, pues, el producto de 10s tres tirminos
i4C\
\‘“I
q = ‘iH rim W
HL
123
(11)
uv cos a = u(u + vcos p)
Combining Eqs. (9), (10) and (11) results in the so-
called energy equaion in a rotating frame of
reference.
S2)
( Pl v+ u,2
Y+zl+ 29 > -
y + z2 + v$ - u$
( p2
\
HL
29 ) =
Note that if there is no flow, v1 = v2 = 0 and
the equation reduces to that for a vortex. If there
is no rotation, the equation reduces to the
familiar form of the new energy equation.
Turbine Efficiency
The hydraulic efficiency of a turbine is defined
by
k-l’
(13) ‘IH = ;i
wherein H is the total head available (this will be
defined in more detail later). Mechanical efficien-
cy is defined by
(14) ‘Im = EpB:pFHp
where FHp is the horsepower consumed by fric-
tion both mechanical and all fluid friction other
than the blades themselves. The volumetric effi-
ciency accounts for leakage flow which does no
work
(15) ‘Iv = yQL
where QL is the leakage flow. The overall effi-
ciency is then the product of the three terms
(l6) t7 = qH rim rlv
Equation (16) clearly delineates those factors
which detract from optimum efficiency of a tur-
bine. The hydraulic efficiency is an expression of
how effective the turbine blade is in producing an
optimum variation in velocity (both in magnitude
and direction through the machine). The
mechanical efficiency expresses the losses due
to seals, bearings, and fluid friction on the runner
shroud, whereas volumetric efficiency is an in-
dication of the effectiveness of the turbine seals.