CENTRIFUGAL PUMPING CIRCUIT

AIM: To familiarize the students with the working of a centrifugal pump.

To determine the system curve and efficiency curve of a centrifugal pump.

To do an energy balance across the system using Bernoulli’s equation.

To familiarize the students with net positive suction head and cavitation

NOMENCLATURE

Roman Symbols D Hydraulic diameter m ƒ Fanning friction factor Dimensionless g Gravitational constant m.s

-2 h Head m HD Head produced by the pump m Hf Total head on the suction side m HL Total head loss across system m hL(bends/fittings) Head loss attributed to a bend or fitting m hL(roughness) Head loss attributed to the roughness of the pipe m HSys System Head m K Minor loss coefficients for bends and fittings Dimensionless L Pipe length m NPSHA Net positive suction head available m NPSHR Net positive suction head required m P Absolute pressure Pa Powerf Power imparted to the fluid by the pump W Powerp Shaft power W Pvap Vapour pressure of the fluid Pa Q Volumetric low rate m

3.s

-1 V Fluid velocity m.s

-1 Z Fluid level above pump m Greek Symbols ρ Fluid density kg.m

-3 η Pump efficiency % Subscripts D Darcy

d discharge

F Fanning

s suction

1 Condition at point 1 in the piping system 2 Condition at point 2 in the piping system

INTRODUCTION

Centrifugal pumps are used to transport a fluid and are commonly used equipment in the

chemical engineering industry. The pump consists of a rotating shaft and impeller as well the

stationary volute casing and bearings. The impeller consists of radial vanes that curve opposite to

the direction of rotation. The fluid usually enters the pump at the eye of the impeller along the

axis of rotation. The impeller’s rotating vanes force the fluid to the periphery due to centrifugal

forces. The curvature of the vanes and the shape of the volute increase the velocity of the fluid.

The displaced fluid creates suction at the eye of the impeller, thereby causing more fluid to enter

the eye. The fluid is confined by the pump casing and forced towards the pump exit where it

leaves tangentially.

Figure 1 Cross sectional view of centrifugal pump

Centrifugal pumps work by imparting kinetic energy from rotating impeller vanes to a fluid. The

energy absorbed by the fluid can either be in the form of potential energy or kinetic energy or a

combination of the two and is expressed as static head or velocity head respectively.

The size of the pump to be installed depends on the requirements of the piping system.

Constraints such as capacity, friction losses in the system and the height the fluid should be

pumped all impact on the sizing of pump.

THEORY

SYSTEM HEAD AND ENERGY BALANCES USING BERNOULLI’S EQUATION:

Consider a piping system with bends and fittings such as in Fig 2.

Direction of fluid flow

Fluid enters the

impeller eye

Impeller vanes

Volute

Volute casing

V1

P1

Z1

V2 P2

Z2

Datum line

Point 1

Point 2

Figure 2 Schematic of a piping system with a centrifugal pump

The following general equation can be applied to a pumping system:

LD HZg

V

g

PZ

g

V

g

PH 2

2

221

2

11

22 ..1

The term HD is the head available for pumping the fluid. Similarly the system head, Hsys,

required to overcome all the resistances for a required flow rate can be given by

Lsys HZZg

VV

g

PPH 12

2

1

2

212

2 ..2

The head loss, HL, is the sum of the minor head losses and head loss due to the roughness of the

pipe. The minor losses due to bends and fittings can be given by

g

VKh fittingsbendsL

2

2

)/( ..3

The head loss due to roughness of the pipe can be given by the following equation:

g

V

d

Lfh

i

FroughnessL2

.42

)( ..4

The Fanning friction factor, f, for Laminar flow is:

Re

16Ff ..5

The Fanning friction factor for turbulent flow can be read from the Moody Chart or the Darcy

friction factor can be calculated by the Colesbrook equation:

DD f

D

f Re

51.2

7.3log0.2

1 ..6

It is important to note that the Darcy friction factor is four times larger than the Fanning friction

factor.

The theoretical system head can thus be calculated for any flow rate.

CONVERTING BETWEEN HEAD AND PRESSURE:

The following equation can be used to convert between pressure and head.

g

Ph ..7

PUMP TOTAL HEAD:

sdD hhH ..8

PUMP CURVE

There is a relationship between the head produced by a pump and volumetric flow rate through

the pump for a pump operating at a fixed speed. This relationship can be expressed as the pump

curve determined by the pump manufacturers. At zero flow the pump will produce the maximum

head while at maximum flow the pump will produce zero head. In practical terms the maximum

head at zero flow will be the height to which the pump can raise a fluid is the water level on the

suction side is at the level of the impeller eye. At this height the pressure at the impeller

discharge as a result of the column of water is equal to the pressure produced by the pump. The

flow will be zero because there is no head available for flow.

A plot of the system curve and the pump curve on the same axis indicates the operating point for

the specific pump in the given system. Figure 3 shows a typical pump curve and theoretical

system curves.

Figure 3 Pump and various theoretical system curves

The system curves were generated by considering a piping set up similar to Fig 1. The set up

assumes a valve to be in place to adjust the flow rate. Partly closing the valve increases the

resistance and results in a higher system head for a specific flow rate, as can be seen from the

graph. Different system curves will be generated depending on the degree to which the valve is

open or closed. For all the system curves at zero flow the static head is the same.

0

2

4

6

8

10

12

0 2 4 6 8

Flow rate (m3.h-1)

Head

(m

) Pump Curve

S (1)

S (2)

S (3)

S (3)

FLUID POWER AND PUMPING EFFICIENCY

The power the fluid receives from the pump is given by:

gHQPower Df ..9

The efficiency of the pump can be given by:

p

f

Power

Power ..10

It is important to note that the power consumption of the motor is higher than the the pump.

Energy is lost due to the motor efficiency as well as the pump efficiency. The pump efficiency is

a function of system flow rate and is usually plotted on the pump curve by the manufacturers.

NET POSITIVE SUCTION HEAD (NPSH)

The point preceding a pump experiences suction during pumping. The pressure at the suction

point depends on various factors such as the liquid level on the suction side, the absolute

pressure on the surface of the liquid and the head loss due to friction on the suction side. If the

pressure at the inlet of the pump is below the vapour pressure of the fluid at the pumping

temperature then the liquid will boil and create cavities. This phenomenon is called cavitation

and is undesirable. The pockets of vapour tend to form on the impeller vanes and travel along the

vane to an area of higher pressure. Once subjected to a higher pressure, the bubble rapidly

collapses and causes a shock wave that sounds like a rumble and can damage the impeller vanes

and result in pitting.

The Net Positive Suction Head Required, (NPSHR), is the measure of the head present at the

suction to prevent the pressure from dropping below the vapour pressure and causing cavitation.

The Net Positive Suction Head Available, (NPSHA), is the amount of head above the vapour

pressure at the suction of the pump and is a function of the system. It shows how much head

there is to act as a buffer before cavitation occurs.

The NPSHA, can be given by this equation:

)(11

suctionf

vap

A Hg

PZ

g

PNPSH ..11

The height Z1 will be negative if the surface of the liquid on the suction side is below the pump

centre line.

PROCEDURE

1. Follow the pipe work and examine the valves to gain a clear understanding of the system.

2. Check the level in the tank. If the level is too low, fill with water to an appropriate level.

3. Measure the height of the water entry and exit levels, Z1 and Z2.

4. Read of the power consumption on the pump.

5. Adjust the valves to isolate the single speed pump and ensure that all the valves in the

correct path are totally open.

6. Switch on the pump and allow the system to reach steady state.

7. Read the volumetric flow rate from the rotameter and the discharge and suction pressure

from the pressure gauges.

8. Reduce the flow rate with the discharge valve to a predetermined flow rate and repeat the

measurement.

9. Repeat the measurements at various flow rates.

10. Open the discharge valve fully.

11. Throttle the suction valve and record the flow rate and suction pressure.

12. Repeat step 11 for four flow rates until cavitation occurs.

13. Record and observations during cavitation.

14. Continue throttling the suction side and record the flow rate and suction pressure.

15. Open the suction valve fully

16. If time permits repeat the procedure after adjusting the level of water in the reservoir.

17. Turn the apparatus off.

RESULTS AND DISCUSSION

1. Calculate the head produced by the pump for each flow rate,

2. Determine the head loss due to friction for each flow rate using Bernoulli’s equation,

3. Calculate the power of the fluid for each flow rate,

4. Calculate the pump efficiency for each flow rate and plot on a curve against flow rate.

5. Determine the friction loss on the suction side, Hf(suction) for the flow rates when throttling

the suction side.

6. Calculate the NPSHA for each flow rate.

7. Discuss cavitation, NPSHR and NPSHA in relation to the results.