mtushinpar
۲۱ اردیبهشت ۱۳۸۸, ۰۰:۳۲
the hydraulic efficiency of the rotating-vane system and, for the range of
specific speeds indicated above, will generally fall between 0.85 and
0.95. This hydraulic efficiency is considerably higher than pump efficiency h since it does not include mechanical losses due to bearing or
packing friction, volumetric losses due to internal wearing-ring clearances, impeller-disk friction, or fluid-friction losses due to velocity
conversion or boundary-layer considerations ahead of or following the
impeller. For pumps in this specific-speed range, the hydraulic losses
1 2hH will generally be between one-quarter and three-quarters of total
pump losses 1 2h.
Fig. 14.2.20 Velocity diagram of a radial-flow impeller.
For pumps arranged with an axial inlet to the impeller (such as that
shown in Fig. 14.2.5), it is generally assumed that the entering flow will
have no rotational component, and Vu1 is therefore zero. Equation
14.2.1 can thus be reduced to
H 5hHU2Vu2/g (14.2.2)
In practice, Eq. (14.2.2) will provide a close approximation to total head
for any pump up to a specific speed of 2,000 (Nsm ' 40) since the term
U1Vu1 in Eq. (14.2.1) is very small compared with U2Vu2.
It should also be noted in Fig. 14.2.20 that the relative velocity y2
does not coincide in direction with the vane angle at the impeller discharge. The angular difference between y2 and the direction of the vane
is due to the irrotational nature of the flow between the vanes. The effect of this difference can be taken into account as the vector difference
Vu2* 2 Vu2 5 Na/229, where a is the shortest distance in inches taken in
the radial plane between the discharge tip of any vane and the upper
surface of the following vane. (Vu2* 2 Vu2 5 Na/19,100, where a is in
mm and velocities are in m/s.)
The foregoing relationships provide the basis for determining impeller diameters and vane angles required to produce a given total head
requirement at a specified rotative speed. It is equally necessary, of
course, to provide in the design for handling a specified flow volume,
and this is readily accomplished by providing the necessary cross-sectional area A between vanes to pass the required flow at velocities
previously determined. A useful relationship for this purpose, in light of
the units commonly employed in pump design, is Q 5 AV/0.321, where
Q is in gal/min, V in ft/s, and A in in2 (Q 5 AV/278, where Q is in m3/h,
V in m/s, and A in mm2).
Upon leaving the impeller, the liquid pumped enters either (1) a
system of diffusing vanes surrounded by an outer casing or (2) directly
into a casing designed to contain the fluid and control its velocities.
Where diffusing vanes are used, they are designed on the basis of velocity relationships very similar to those employed in impeller design but
with the objective being to slow the fluid down to convert velocity
energy to pressure energy and, further, to reduce frictional losses in the
discharge system following the diffuser. Where the impeller discharges
directly into the casing, this component of the machine is most frequently designed in the form of a volute to provide constant velocity all
around the impeller periphery up to the point of entry into the discharge
nozzle. From this point, commonly called the casing throat, to the discharge flange or to the inlet of a succeeding stage, the velocity is gradually reduced. Special circumstances related to pump design or application often result in modifications to the constant-velocity design of such
a casing, and variations may be found covering the entire range from
constant velocity to constant area. In addition, many casings are now
designed with one or more spiral vanes placed in such a way as to
approximate a condition of geometric similarity in relation to the impeller, which is advantageous when a pump is operated at capacities
other than those for which it is designed. A casing of this nature represents an effort by the designer to obtain an optimum balance between
the desirable geometric similarity of the diffuser discharge and the
manufacturing simplicity and generally high efficiency of the volute-
type casing. The most common form of such a casing is the twin-volute
type discussed under Nomenclature and Mechanical Design (see Fig.
14.2.1 and Table 14.2.1).
Fig. 14.2.21 Velocity diagram of an axial-flow vane system.
Copyright (C) 1999 by The McGraw-Hill Companies, Inc. All rights reserved. Use of
this product is subject to the terms of its License Agreement. Click here to view.
For axial-flow impellers (7,500 # Ns # 15,000 or 150 # Nsm # 300)
velocity relationships can be approximated in a manner similar to that
used for lower-specific-speed pumps, but refinement of these approximations is approached in a somewhat different manner, largely because
of the considerable body of knowledge available in the form of airfoil
data which can be applied. Velocity diagrams for pumps of this type are
shown in Fig. 14.2.21.
Considering a cylindrical stream tube intersecting the vanes of an
axial-flow impeller, we can rewrite Eq. (14.2.1) in the form
H 5hHU DVu /g (14.2.3)
where DVu represents the increase in the tangential component of the
absolute velocity as the fluid passes through the impeller. For pumps in
this specific-speed range, hH will generally fall between 0.80 and 0.90
and 1 2hH will generally be between one-half and three-quarters of
1 2h.
As in the case of radial-flow impellers, the relative velocity y2 at the
impeller exit does not coincide with the vane angle. In this case, the
necessary correction can be applied by means of the expression
DVu 5 2D Vu*/[(t/l)(2/pK )(1/sin b) 1 1] (14.2.4)
where t is vane spacing, l is vane length, b is the discharge vane angle,
and K is the coefficient determined from Fig. 14.2.22, which provides
for the fact that the impeller blades are, in effect, arranged in a continuous lattice.
Fig. 14.2.22 Lattice-effect coefficient. (Weinig.)
In the design of axial-flow pumps, it is generally assumed that the
head developed by the blade elements within all the cylindrical stream
tubes between the impeller hub and its outer diameter will be the same.
For this condition to be achieved, it will be evident from Eq. (14.2.3)
that since U will vary directly with the radius, DVu must vary inversely
with the radius. Thus vane camber (or curvature) will be greater near the
hub than at the periphery. It is further generally assumed that the axial
velocity is constant throughout the impeller, and to satisfy this condition, the blade angles will be greater at the hub than at the periphery,
giving rise to the twist of the vane.
specific speeds indicated above, will generally fall between 0.85 and
0.95. This hydraulic efficiency is considerably higher than pump efficiency h since it does not include mechanical losses due to bearing or
packing friction, volumetric losses due to internal wearing-ring clearances, impeller-disk friction, or fluid-friction losses due to velocity
conversion or boundary-layer considerations ahead of or following the
impeller. For pumps in this specific-speed range, the hydraulic losses
1 2hH will generally be between one-quarter and three-quarters of total
pump losses 1 2h.
Fig. 14.2.20 Velocity diagram of a radial-flow impeller.
For pumps arranged with an axial inlet to the impeller (such as that
shown in Fig. 14.2.5), it is generally assumed that the entering flow will
have no rotational component, and Vu1 is therefore zero. Equation
14.2.1 can thus be reduced to
H 5hHU2Vu2/g (14.2.2)
In practice, Eq. (14.2.2) will provide a close approximation to total head
for any pump up to a specific speed of 2,000 (Nsm ' 40) since the term
U1Vu1 in Eq. (14.2.1) is very small compared with U2Vu2.
It should also be noted in Fig. 14.2.20 that the relative velocity y2
does not coincide in direction with the vane angle at the impeller discharge. The angular difference between y2 and the direction of the vane
is due to the irrotational nature of the flow between the vanes. The effect of this difference can be taken into account as the vector difference
Vu2* 2 Vu2 5 Na/229, where a is the shortest distance in inches taken in
the radial plane between the discharge tip of any vane and the upper
surface of the following vane. (Vu2* 2 Vu2 5 Na/19,100, where a is in
mm and velocities are in m/s.)
The foregoing relationships provide the basis for determining impeller diameters and vane angles required to produce a given total head
requirement at a specified rotative speed. It is equally necessary, of
course, to provide in the design for handling a specified flow volume,
and this is readily accomplished by providing the necessary cross-sectional area A between vanes to pass the required flow at velocities
previously determined. A useful relationship for this purpose, in light of
the units commonly employed in pump design, is Q 5 AV/0.321, where
Q is in gal/min, V in ft/s, and A in in2 (Q 5 AV/278, where Q is in m3/h,
V in m/s, and A in mm2).
Upon leaving the impeller, the liquid pumped enters either (1) a
system of diffusing vanes surrounded by an outer casing or (2) directly
into a casing designed to contain the fluid and control its velocities.
Where diffusing vanes are used, they are designed on the basis of velocity relationships very similar to those employed in impeller design but
with the objective being to slow the fluid down to convert velocity
energy to pressure energy and, further, to reduce frictional losses in the
discharge system following the diffuser. Where the impeller discharges
directly into the casing, this component of the machine is most frequently designed in the form of a volute to provide constant velocity all
around the impeller periphery up to the point of entry into the discharge
nozzle. From this point, commonly called the casing throat, to the discharge flange or to the inlet of a succeeding stage, the velocity is gradually reduced. Special circumstances related to pump design or application often result in modifications to the constant-velocity design of such
a casing, and variations may be found covering the entire range from
constant velocity to constant area. In addition, many casings are now
designed with one or more spiral vanes placed in such a way as to
approximate a condition of geometric similarity in relation to the impeller, which is advantageous when a pump is operated at capacities
other than those for which it is designed. A casing of this nature represents an effort by the designer to obtain an optimum balance between
the desirable geometric similarity of the diffuser discharge and the
manufacturing simplicity and generally high efficiency of the volute-
type casing. The most common form of such a casing is the twin-volute
type discussed under Nomenclature and Mechanical Design (see Fig.
14.2.1 and Table 14.2.1).
Fig. 14.2.21 Velocity diagram of an axial-flow vane system.
Copyright (C) 1999 by The McGraw-Hill Companies, Inc. All rights reserved. Use of
this product is subject to the terms of its License Agreement. Click here to view.
For axial-flow impellers (7,500 # Ns # 15,000 or 150 # Nsm # 300)
velocity relationships can be approximated in a manner similar to that
used for lower-specific-speed pumps, but refinement of these approximations is approached in a somewhat different manner, largely because
of the considerable body of knowledge available in the form of airfoil
data which can be applied. Velocity diagrams for pumps of this type are
shown in Fig. 14.2.21.
Considering a cylindrical stream tube intersecting the vanes of an
axial-flow impeller, we can rewrite Eq. (14.2.1) in the form
H 5hHU DVu /g (14.2.3)
where DVu represents the increase in the tangential component of the
absolute velocity as the fluid passes through the impeller. For pumps in
this specific-speed range, hH will generally fall between 0.80 and 0.90
and 1 2hH will generally be between one-half and three-quarters of
1 2h.
As in the case of radial-flow impellers, the relative velocity y2 at the
impeller exit does not coincide with the vane angle. In this case, the
necessary correction can be applied by means of the expression
DVu 5 2D Vu*/[(t/l)(2/pK )(1/sin b) 1 1] (14.2.4)
where t is vane spacing, l is vane length, b is the discharge vane angle,
and K is the coefficient determined from Fig. 14.2.22, which provides
for the fact that the impeller blades are, in effect, arranged in a continuous lattice.
Fig. 14.2.22 Lattice-effect coefficient. (Weinig.)
In the design of axial-flow pumps, it is generally assumed that the
head developed by the blade elements within all the cylindrical stream
tubes between the impeller hub and its outer diameter will be the same.
For this condition to be achieved, it will be evident from Eq. (14.2.3)
that since U will vary directly with the radius, DVu must vary inversely
with the radius. Thus vane camber (or curvature) will be greater near the
hub than at the periphery. It is further generally assumed that the axial
velocity is constant throughout the impeller, and to satisfy this condition, the blade angles will be greater at the hub than at the periphery,
giving rise to the twist of the vane.