Heads of Pump: Some example
Figure 1(a) Total head = Static head (suction and
delivery)+ friction head + velocity head for delivery.
Static head
Figure 1(b) Pump energy equals elevation
energy plus friction energy.
Figure 2 Measuring elevation
head and friction head.
Figure 3 Pressure depends on the height of the liquid surface. The pressure level
at the bottom of a tank depends on the liquid surface height.
Heads of Pump: Some example
Figure 4 The static head on the pump when the suction
tank is full and suction head is positive.
Figure 5 The static head on the pump with the discharge pipe
end open to atmosphere.
Heads of Pump: Some example
Figure 6 The height of the discharge pipe end is in this
case the correct height for static head.
Figure 8 Flow rate is limited by friction only in the system when
the static head is zero.
Figure 7 The effect of pipe end elevation on flow.
Figure 9 Negative static head increases flow rate.
Heads of Pump: Some example
Figure 10 The pump produces zero flow at its maximum
outlet pressure.
Figure 11 Highest possible
total head of a pump.
Heads of Pump: Some example
Zero flow, Max
Pressure
Figure 12 Variation of total head vs. pipe end elevation or static head.
Type of Impeller:
Three main categories of impeller due to type of impeller’s vane:
Vw2
U2
U2=Vw2
 Radial vanes, Fig. (a).
α2
 Backward vanes, Fig. (b).
β α2
β Vf2
Vf2= Vr2
Vr2
 Forward vanes, Fig. (c).
V2
V2
where :
V = absolute velocity of
the water.
U = Tangential velocity
of impeller (peripheral
velocity).
Vr = relative velocity of
water to the wheel.
Vf = velocity of flow.
vw = velocity of whirl
N = Speed of impeller
in (rpm).
β2=β= angle between
v2 with the direction of
motion of vane at outlet
α2= angle made by vr2
with direction of motion
of vane at outlet, vane
angle at outlet
β
Vw2
Vf2
β
V2
β
β
when β = 90o ,
radial curved vanes.
Vr2
U2
(b) when β < 90o, the
Backwards curved vanes .
(c) when β > 90o, the
Forwards curved vanes.
Due to inertial effect, the liquid which is trapped between the impeller vanes is reluctant to
move round with the impeller.This results difference of pressure force across the vane.
Therefore, high pressure developed in the leading side and low pressure on the trailing side.
This difference is called vane loading which increases with the number of vane.
where :
Fig (a) Γb = direction of blade
circulation
Fig (b) Vr = Distribution of relative
velocity in blade spaces.
Fig (c) Distribution of pressure in
a certain radial section.
The Γ decreases Vr in working side of blade and
vice versa. This forms pressure differential which is
overcome by torque developed by the drive.
Vr
Figs For
Backward vane
(a)
(b)
(c)
α2
Slip factor:
On high pressure side: liquid follows the blade contour, it leaves blade tangentially .
On low pressure side: liquid leaves the vane with a certain circumferential component.
As a result liquid leaves at an average angle β’ which is less than actual geometric blade
angle β.
• Due to deviation in flow path, tangential component get reduced by (Vw2-V’w2) which is
called slip of the impeller.
• The ideal slip coefficient is then defined as the ratio of whirl component with the fluid
deviation to the whirl component without fluid deviation
• Due to real fluid effect (friction and fluid separation on the wall of disc shroud and vanes)
the radial velocity may not be uniform around the periphery of the impeller.
• The net effect of the non-uniform velocity and slip is to reduce Euler Head (He)
• Also further reduction of the losses occurs due to intake loss, friction and separation loss
etc
Empirical Relations for Slip factor
U2=Vw2
V’w2 Slip
β’
V’r2
V’2 α’
β
Vf2= Vr2
V2
-ve
+ve
Velocity diagram
For Radial vane
α
Loss and actual Head-Q curve
The major loss considered is
shock losses at the impeller
inlet caused by the mismatch of
fluid and metal angles
The Affinity Law
The affinity laws for pumps/fans are used in hydraulics to express the relationship between variables involved in pump or fan
performance (such as head, volumetric flow rate, shaft speed) and power. They apply to pumps, fans, and hydraulic turbines.
In these rotary implements, the affinity laws apply both to centrifugal and axial flows.
The affinity laws are useful as they allow prediction of the head discharge characteristic of a pump or fan from a known
characteristic measured at a different speed or impeller diameter. The only requirement is that the two pumps or fans are
dynamically similar, that is the ratios of the fluid forced are the same.
Similarity relationship
Formulas for Refiguring Pump Performance with Impeller Diameter or Speed Change
Diameter constant
H
= constant
D2 N 2
H 2  N2 
=

H1  N1 
P
= constant
D5 N 3
P2  N 2 
=

P1  N1 
Specific Speed
N Q
H 3/ 4
3.65N Q
Ns =
H 3/ 4
Ns =
Specific Speed (IS code)
Q2  D2 
=

Q1  D1 
Q2  N 2 
=

Q1  N1 
Q
= constant
D3 N
Specific Speed for Pump
Speed constant
2
2
H 2  D2 
=

H1  D1 
2
P2  D2 
=

P1  D1 
2
Type of
impeller
Slow speed
radial flow
Normal speed
radial flow
High speed
radial flow
Mixed flow
Axial or
Propeller
Specific Speed
10-30
30-50
50-80
80-160
160-500
As per BIS Code: Speed of a Geometrically similar pump capable of lifting 75 kg of
water per second to a height of one meter.
Specific Speed has dimension L3/4T-3/2,
Dimensionless specific speed is Ns =
N Q
( gH )3/ 4
T −1 ( L3T −1 )1/ 2
Dimension of dimensionless specific speed Ns =
≡1
( LT −2 × L)3/ 4
17
Characteristic Curves of Centrifugal Pump
These curves are necessary to predict the behaviour
and performance of the pump when pump is
working under different flow rate , head and speed.
Main Characteristics Curve:
It consists of variation of head (Hm), power, discharge
with respect to speed. To plot this curve affinity law
has been used assuming D=constant.
Operating Characteristics Curve:
If speed is kept constant, the variation of manometric
head, power and efficiency with respect to discharge
gives the operating characteristics of the pump.
The input power curve for pumps shall not pass
through the origin. It will be slightly away from the
origin on the y-axis, as even at zero discharge some
power is needed to overcome mechanical losses.
Head curve is maximum wneh discharge is zero. The
output power curve will start from origin as at Q=0,
output power will be zero.
(Main Characteristics Curve)
(Operating Characteristics Curve)
Variable frequency drive = VFD
VFD can be used to operate pump for
different speed