Pump Lecture Notes02 2 Up New

8/12/2019 Pump Lecture Notes02 2 Up New

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7

in order to minimise energy loss the fluid should impinge on the bladetangentially, in terms of the vector triangle this means that the angle

between u1andR1should equal the blade angle, (defined as the angle

between the tangent to the pitch circle and the leading edge of the

impeller blade).

Figure 4(a) shows the fluid entering the runner tangentially, this is called shockless

entry, and Figure 4(b) shows the fluid entering the impeller non-tangentially i.e.under

non design conditions. When this happens the follow occur

impact losses occur boundary layer separation takes place eddies arise which give rise to some back flow into the inlet pipe, this

causes the incoming flow to have some whirl velocity

The result of this non tangential entry is a dramatic drop in the efficiency of the pump.

4.2 Analysis of centrifugal pump behaviour

Consider the inlet triangle in Figure 3, under design conditions we can immediately

write down

11

11

1

1

1

1Vand

60,tan

BD

QV

NDu

u

Vf

where

D1 diameter of the impeller at inletN speed of rotation in RPM

Q flow through the pump

B1 width of the impeller at inlet

Therefore we can write

NBD

Q

ND

BDQ

121

2

1

1

11

60

tan

60tan

This defines the entry angle of the vane if 01wV .

For the exit triangle three cases have to be considered as follows

(i) Forward facing blades < /2

Forward facing blades are ones which face in the same direction as the

rotation as shown in Figure 5(a), the symbols have the same meaning as

for the inlet triangle with the subscripts changed to 2

8

V2

Vt2

Vw2

U2

R2

Figure 5(a)

(ii) Radial blades = /2

This case is shown in Figure 5(b), the vector triangle is right angled

hence22 22

and fw VRuV

V2 Vt2

Vw2U2

R2

=

=

= 90

Figure 5(b)

(iii) Backward facing blades > /2

This is shown in Figure 5(c), for the time being all that needs be noted

from this triangle is that V2is smaller than in the other two cases.


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V2

Vt2

Vw2

U2

R2

For analytical purposes it is easiest to consider the triangle resulting from the forward

facing blades however the results obtained will apply to all the cases with no changes

in the signs.

Using equation 2.1 with1w

V set to zero and recalling that since we are now

considering pumps the sign will change then we can say that for an inviscid fluid the

head difference across the pump would be

g

uVw 22

from the triangle in Figure 5(a) we can write

cot22 2 fw

VuV

cot22 2 fw

VuV (4.1)

The head imposed on the fluid

5

is the energy given to it g

uVw 22less any losses, hi, in

travelling through the impeller. As the fluid leaves the impeller and enters the volute

a relatively small amount of the total energy is potential (i.e.pressure) energy much of

it is kinetic; this has to be converted to potential energy by the volute and diverging

delivery pipe. However efficiently the volute converts the kinetic energy to potential

there is still a head loss, hv.

We can now write the energy conservation equation in the form

5Remember that head is energy per unit weight of fluid.

10

g

vhhH

g

uV pvi

w

2

222

where vpis the velocity of flow in the outlet pipe. In order to advance this analysis wemust be able to evaluate the losses hiand hv, it is not possible to do this analytically

therefore the same method will be used as for minor losses in pipes. We assume that

the loss in the impeller is proportional to 22R since this is the velocity of flow relative

to the impeller, similarly the loss in the volute is assumed to be proportional to 22V

hence we can now write the energy equation as

g

v

g

Vk

g

Rk

g

uVH

pvi

w

222

222

2222

vpis very small compared to the other terms and can safely be ignored.We can write

2222 22 fw

VVV

Using equation 4.1 we can now write

g

VVuukVkVuuH

VV

R

VVuu

VVuuV

VVuV

ffvfif

ff

ff

ff

ff

2

coseccot2coseccot22

cosecsin

also

coseccot2

cot1cot2

cot

222

22

222

22

22

2

222

22222

222

22

22

222

22

2222

2

2

22

22

22

Tidying this expression up yields

22

22

222

22

2

22

and60

but

2

cosec1cot22

BD

QV

DNu

g

kkvkVuku

H

f

ivfvfv

aswritten-rebelyconvenientcanequationthehence

22 QCQNBNAH

whereA,Band Care constants defined by the properties of the pump.


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Matching Pump to Pipeline

0.00

10.00

20.00

30.00

40.00

50.00

60.00

0 0.02 0.04 0.06 0.08 0.1 0.12

Flow

Head

0

10

20

30

40

50

60

70

80

90

Pump

Pipeline

Operating point

Figure 7 An inefficient system

Matching a pump to a pipeline

0.00

10.00

20.00

30.00

40.00

50.00

60.00

0 0.02 0.04 0.06 0.08 0.1 0.12

Flow

Head

0

10

20

30

40

50

60

70

Pump

Pipeline

Operating point

hstatic

Figure 8 An efficient system

From these diagrams it is clear that the part of theH Qthat lies under the point of

maximum efficiency is quite short thus the remainder of the curve is of little interest.

Pump manufacturers use this property to put the efficient part of theH- Qfor all the

pumps in an homologous series onto one graph. An example7of this is shown in

Figure 9. The short length of curve is that part of the curve under the highest point of

the efficiency curve, this enables the user, once theH Qfor the pipeline is known to

read off the model number of the pump most suitable for the job.

7 This diagram is reproduced by kind permission of Weir Pumps Ltd., Glasgow.

16

Figure 9

If one pump cannot produce sufficient head then two or more pumps may be used in

series; for the great majority of pipelines this would not be considered a good


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Pump Lecture Notes02 2 Up New