WORK DONE BY IMPELLER

The velocity vector diagram at inlet and outlet of the impeller of a centrifugal pump.

V1, V2 = absolute velocity of fluid at inlet and outlet.

u1, u2 = blade velocity at inlet and outlet.

Vr1, Vr2 = relative velocity of fluid at inlet and outlet.

Vu1, Vu2 = whirl component or tangential component of absolute velocity at inlet and outlet.

Vf1, Vf2 = axial component of absolute velocity at inlet and outlet.

ω = angular velocity.

r1, r2 = impeller radius at inlet and outlet.

N = rotational speed.

α1, α2 = flow angle at inlet and outlet.

β1, β2 = blade angle at inlet and outlet.

Assumptions:

Flow is steady and one-dimension.

No energy loss in the impeller due to friction and eddy formation.

Infinite no. of blades; liquid flowing in the blades.

No loss due to shock at entry.

Power supplied by the motor

From the momentum theorem,

Torque = rate by change of angular momentum equals the torque exerted by the impeller on the liquid.

since and

TP

)122 1()( rVrVmTTorque uu

)122 1()( rVrVQTTorque uu

)()( 12 12rVuVQPPower uu

22 ru 11 ru

)()( 12 12rVrVQPPower uu

Pump output in the terms of head

Equation (1) and (2) are referred as Euler equations.

For an axial or radial fluid entry (fluid entering the impeller has no whirl component.)

gHQP

)( 12 12uVuVQgHQ uu

g

uVuVH

uu )( 12 12

01uV

g

uVH

u 22

But the velocity triangle at outlet (Fig. 3.12)

Subtracting above equations

11 1

2

1

2

1

22 ur VuVuV

22 2

2

2

2

2

22 ur VuVuV

12

2

1

2

2

2

1

2

2

22

12122 uVuVVVuuVV uurr

Head developed by pump impeller

222

222

1

2

2

2

1

2

212

11

12

rr

uu

vVVVuuuVuV

g

uVuVH

uu )( 12 12

g

vV

g

VV

g

uu rr

222

222

1

2

2

2

1

2

2 11

g

vV

g

VV

g

uuH

rr

222

222

1

2

2

2

1

2

2 11

HEAD OF A PUMP

Suction head: Distance between center line of pump and water level of sump is called suction head

Delivery head: Distance between center line of pump and level of discharge is called delivery head

Static head: It is the sum of suction and delivery head. If Hs and Hd be the suction and delivery heads resp. the static head

Manometric head: It is the head measured across the pump inlet and outlet flanges, it is expressed as the increase in pressure energy per unit weight of liquid handled by the impeller

dsstaticH HHH

g

d

mano Hg

PPH s

Hmano=Hth (theoretical head developed by pump) +loss of head in pump

Manometric head is the different between the delivery head (+) and suction (-) pressure head (difference between reading shown by gauge plus vertical distance between the pressure tapping for suction and delivery gauge )

Total Gross or effective head: This is the actual head against which the pump has to work. It is equal to the static head plus all the head losses occurring to flow before through, and after the impeller.

Where

H =total or effective head in meters of liquid column

Vd = velocity of water in delivery pipe

Vs=velocity of water in suction pipe

g

VVH

g

PPH

sd

g

sd

2

22

If total loss of head, then the manometric head,

The above heads are independent of the density of the liquid being raised. A centrifugal pump rotating at a particular speed will raise water, oil or mercury to the same height. But pressure generated in pump will be different in each case also power required to be different.

Lstaticmano HHH

LOSSES AND EFFICIENCY

1. Manometric efficiency

It is defined as ratio of manometric head developed by pump to the head imparted by the impeller of the liquid.

2. Mechanical efficiency

It is defined as the ratio of power actually delivered by the Impeller to the power supplied to the shaft by the prime mover or motor.

Power delivered by the impeller

Power given to shaft

)(22lossesH

H

g

uV

H

m

m

U

m

mano

mech

3. Volumetric efficiency

It is defined as the ratio of the quantity of liquid discharge from the pump to the quantity passing by the impeller.

If Q is the volume actually delivered per second by the pump, and Q volume liquid from the impeller leaks through the clearance between the impeller and the casing.

4. Overall efficiency

It is defined as the power output from the pump to the power input from the motor driving the pump.

The overall efficiency is the product of all the three efficiencies.

QQ

Qv

i

o

oP

P

input

m

P

gqH

mechvmanoo

MINIMUM STARTING SPEED

When the pump is started, there will no flow of water until the pressure difference in the impeller is large enough to overcome the gross or manometeric head. Therefore a centrifugal head or pressure head caused by the centrifugal force on the rotating water will be (u2

2-u12)/2g.

SPECIFIC SPEED

mHg

uu

2

2

1

2

2

mHNDND

2

1

2

2

6060

4

3

H

QNN s

Main characteristic curves of centrifugal pump

Operating characteristic curves of centrifugal pump

During operation the pump must run at a constant speed. Normally, this is the designed speed. The particular set of main characteristics which correspond to the designed speed is mostly used in operation and is therefore known as operating characteristics.

2. Muschal Curve or Constant Efficiency Curve

With the help of data obtained from the above curve, a series of constant. Efficiency curve can be obtained. They facilitate the job of the salesman and enable the prospective customer to see directly the range of operation with a particular efficiency.

CAVITATION

The pressure at any point drops below the vapor pressure corresponding to temperature of the

liquid, liquid will vaporize and form cavities of vapor. Vapour bubbles are carried along with the stream

until a region of higher pressure is reached where they collapse or implode with a tremendous shock on

the adjacent wall. This phenomenon is called cavitations. Cavitation affects the pump performance and

may damage pump parts in severe cases.

Noise and vibrations

Drop in head capacity and efficiency curve

Impeller vane pitting and corrosion fatigue failure of metal.

NET POSITIVE SUCTION HEAD AND CAVITATION

• Net Positive Suction Head: that pressure required at the suction of a pump to prevent cavitation.

– cavitation: the formation of bubbles due to area where P < PSAT, and the subsequent collapse upon migration to a high-press. area.

• causes noise and damage due to erosion and fatigue failure.

NPSH AVAILABLE:

Net positive suction available head is defined as the net head

required to force the liquid into the pump through the suction pipe.

NPSHA = Pb - (Hs + Pvap / ρg + frictional head + kinetic head)

NPSHA depends upon barometric pressure, location, up to sea level,

suction height of machine , loss in suction head , all the factors depends

on the layout independent of the pump performance.

Hs (Suction head)

NPSH

Pav/Pg

Barometric

pressure

NPSHr is a pump characteristic (increases as Q increases) If NPSHa > NPSHr: Design is OK If NPSHa < NPSHr: Cavitation will be a problem (good idea to have a factor of safety)

Pump pressure effects in an open system

= h x density x 9.81

= atmospheric

= 101,325 Pa

Thus, h = 10.33 m

Neutral point

CONVENTIONAL DESIGN OF PUMP:

Conventional design method of centrifugal pump are largely based on the

application of empirical and semi-empirical rules along with the use of available

information in the form of different types of charts and graphs in the existing

literature. The program developed is best suitable for low specific speed centrifugal

pump. Same program is also suitable for the design of high specific speed and

multistage centrifugal pump with few modifications.

CALCULATION OF NPSH:-

P = Ks x R

Where P = Pfle i derer’s coefficient 0.2447( for low specific speed)

R = Blade loading ratio

Ks = constant for free vortex volute casing range 1.6 to 1.8

R = P/K = 0.2447/1.6 = 0.1529

Impeller mean Blade loading can be found as dp/r = R x Ht Ht = theoretical head =

40 m

So dp/? = 0.1529 x 40 = 6.116 m

. Depression head Hd = K x (dp/r )

K= 0.620

Hd = 0.62 x 6.116 = 3.796 m

MINIMUM STARTING SPEED

When the pump is started, there will no flow of water until the

pressure difference in the impeller is large enough to overcome the gross or manometeric head. Therefore a centrifugal head or pressure head caused by the centrifugal force on the rotating water will be (u2

2-u12)/2g.

mHg

uu

2

2

1

2

2

mHNDND

2

1

2

2

6060

PRIMING When a centrifugal pump is not running for sometime,

the water present in the pump casing and suction pipe flows back to the sump and these spaces get filled with air. Now when the pump motor is switched on and pump starts running, the head developed equals H =(Vu2.u2)/g of air.

Since ρair<<<ρwater the head generated cannot produce spontaneously the vacuum required to start the pumping action then the water cannot be sucked in along the suction pipe to reach the impeller , for making the pump deliver water, there is need to make the pump section free from air and fill these space with water .

PRIMING DEVICES a) Pouring water: Water is poured in the pump through

priming funnel. Air vent is opened to provide exit to the air. It is closed after the priming is over.

b) Connection with main waterline: - The pump may be connected with the city water main which can be opened to fill the impeller and suction pipe in order to prime the pump.

c) Priming chamber:-in small pumps a priming chamber may be used on the delivery side of the impeller. When the pump is stopped, some water is store in the tank and this can be used to impeller and the suction line before restarting.

d) Vacuum producing devices: - An injector using high pressure water, stream or compressed air is employed to create vacuum at the top of the casing. So that water is sucked into the suction pipe and the impeller.

BLADE SHAPE

The shape of impeller blades is changed depending on the

blade angle β2 which has a significant influence on the conversion of energy. The different blade and velocity vectors are represented in fig

AXIAL THRUST IN CETRIFUGAL PUMPS

Axial thrust is a force casting parallel to the axis of the pump shaft, caused due to the following reason:-

(a). The water while passing through the impeller is rotating with a forced vortex , but that the outside the surrounding other component are in the rest condition , this cause a differential static thrust acting parallel to the axis of pump shaft and towards the impeller inlet.

(b). Liquid enters the pump axially and is then deflected from its

original path to a radial direction. The dynamic action of liquid causes a force to act on the pump in the direction of flow of inlet. To enable the pump to withstand the thrust, the following methods may be employed.

1.For small pumps (1) Providing a thrust ball bearing in the direction of axial thrust. (2) Inserting a cast iron ring in the casing which should fit in with a

similar ring cast integral with impeller.

2.For large pumps

Where the axial thrust is heavy.

(1) Use of double suction impeller Suction on two sides of the impeller neutralizes the thrust. But this method can be only for single stage pump.

(2) Provision of reliving holes are provided in the impeller to allow suction pressure to act on both sides. (3) A balance plate fitted at the end of the pump shaft.

Pumps in Parallel

PUMPS

– Centrifugal:

• Parallel pumps:

1 pump

2 pumps HP

V GPM

V2 = 2V1

HP2 = HP1

PUMPS

• Series (called staging):

HP

V GPM

HP2 = 2HP1

V2 = V1 1 pump

2 pumps

PUMP LAWS

Apply to centrifugal (non-positive displacement)

pumps only

V N

Hp N2

W N3

V = volumetric flow rate

N = speed of rotation

Hp = pump head

W = power required (prime mover)

.

.

.