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TITLE: CENTRIFUGAL PUMP PERFOMANCE CHARACTERISTICS INTRODUCTION Pump A pump is a device used to move gases, liquids or slurries. A pump moves liquids or gases from lower pressure to higher pressure, and overcomes this difference in pressure by adding energy to the system (such as a water system). A gas pump is generally called a compressor, except in very low pressure-rise applications, such as in heating, ventilating, and air- conditioning, where the operative equipment consists of fans or blowers. Centrifugal pump A centrifugal pump is a rotodynamic pump that uses a rotating impeller to increase the velocity of a fluid. Centrifugal pumps are commonly used to move liquids through a piping system. The fluid enters the pump impeller along or near to the rotating axis and is accelerated by the impeller, flowing radially outward into a diffuser or volute chamber, from where it exits into the downstream piping system. Centrifugal pumps are used for large discharge through smaller heads.

Centrifugal Pump Complete Lab Report

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Page 1: Centrifugal Pump Complete Lab Report

TITLE: CENTRIFUGAL PUMP PERFOMANCE CHARACTERISTICS

INTRODUCTION

Pump

A pump is a device used to move gases, liquids or slurries. A pump moves liquids or gases from

lower pressure to higher pressure, and overcomes this difference in pressure by adding energy to

the system (such as a water system). A gas pump is generally called a compressor, except in very

low pressure-rise applications, such as in heating, ventilating, and air-conditioning, where the

operative equipment consists of fans or blowers.

Centrifugal pump

A centrifugal pump is a rotodynamic pump that uses a rotating impeller to increase the velocity

of a fluid. Centrifugal pumps are commonly used to move liquids through a piping system. The

fluid enters the pump impeller along or near to the rotating axis and is accelerated by the

impeller, flowing radially outward into a diffuser or volute chamber, from where it exits into the

downstream piping system. Centrifugal pumps are used for large discharge through smaller

heads.

Figure 1.Basic element of a centrifugal pump

Page 2: Centrifugal Pump Complete Lab Report

Centrifugal pump works

A centrifugal pump works by the conversion of the rotational kinetic energy, typically

from an electric motor or turbine, to an increased static fluid pressure. This action is described by

Bernoulli's principle. The rotation of the pump impeller imparts kinetic energy to the fluid as it is

drawn in from the impeller eye (centre) and is forced outward through the impeller vanes to the

periphery. As the fluid exits the impeller, the fluid kinetic energy (velocity) is then converted to

(static) pressure due to the change in area the fluid experiences in the volute section. Typically

the volute shape of the pump casing (increasing in volume), or the diffuser vanes (which serve to

slow the fluid, converting to kinetic energy in to flow work) are responsible for the energy

conversion. The energy conversion results in an increased pressure on the downstream side of

the pump, causing flow.

Cavitations is the problems in the pump.It is defined as the phenomenon of formation of

vapour bubbles of a flowing liquid in a region where the pressure of the liquid falls below its

vapour pressure. Cavitation is usually divided into two classes of behavior: inertial (or transient)

cavitation and non-inertial cavitation. Inertial cavitation is the process where a void or bubble in

a liquid rapidly collapses, producing a shock wave. Such cavitation often occurs in pumps,

propellers, impellers, and in the vascular tissues of plants. Non-inertial cavitation is the process

in which a bubble in a fluid is forced to oscillate in size or shape due to some form of energy

input, such as an acoustic field. Such cavitation is often employed in ultrasonic cleaning baths

and can also be observed in pumps, propellers etc.

Due to the general complexity of flow through a centrifugal pump ,the actual

performance of the pump cannot be predicted on a completely theoretical basis .Actual pump

performance is determine experimentally through test on the pump and the result are presented as

pump performance curve .Performance characteristics for a given pump geometry and operating

speed are usually given in the form of plots of head rise ,efficiency and power versus flow rate

( commonly referred as capacity).This information is most helpful to the engineer responsible for

incorporating pump into a given pipe flow system.

Page 3: Centrifugal Pump Complete Lab Report

THEORY-Performance characteristics

Consider the experimental arrangement for determining the head rise (or pressure rise) gained by

fluid flowing through a pump, as show schematically below.

Figure 2. Experimental Arrangement for Pump Performance Characteristics.

The pump head rise can be expressed using the energy equation as

h2=p2−p1

ρg+( z2−z1 )+

V 22−V 1

2

2 g

Typically the differences in elevation and velocities (between inlet and outlet) are also small so

that

hp=p2−p1

ρg

The power P, gained by the fluid is given by the equation

Pf =ρgQ hp

The pump overall efficiency η, is the ratio of power actually gained by the fluid to the shaft

power supplied W shaft as given by the equation

Page 4: Centrifugal Pump Complete Lab Report

η=Pf

W shaft

Typical performance characteristic for a centrifugal pump of given size operating at a constant

speed is shown below.

Figure 3. Typical Performance Characteristics of a centrifugal pump.

OBJECTIVES

The objective of the experiment is to obtain performance characteristics (as described

above) for variable speed centrifugal pump operating at different impeller speeds.

Page 5: Centrifugal Pump Complete Lab Report

APPARATUS

The experimental set-up consists of

I. Water-flow bench and centrifugal pump

II. Instrumentation for data acquisition

Instrument Panel- Refer to the schematic diagram below

I. Speed Control to change pump speed. Pump speed can be varied over range

Of 0-3000 rpm.

II. Pump suction and delivery pressures

III. Torque measurement.

Flow Measurement- Using “V” notch weir

I. Flow rate in the system can be measured relating the height of the water seen in the sight

glass to graph and reading of the flow rate in liters per minute.

Page 6: Centrifugal Pump Complete Lab Report

Preliminaries

1) We were supervised adequately.

2) The pump discharge and suction valves were turned to fully open and the motor speed

turned to zero.

3) The electrical supply and motor drive switch are switched on. The motor control knob

is adjusted slowly to around half way position. The system is ensured to have no

leaking. All the gauges etc. are checked to reduce the motor speed back to zero and it is

ready for testing.

Actual Experiment

i) Suction valve is opened and the discharge valve is closed. The maximum speed N1 is

selected by adjusting speed control to 50%.

ii) Discharge valve is fully opened and water is allowed to circulate. The volume of flow

indicator is noted and decides suitable increments in flow to give adequate sample

points about 15 points between zero and maximum flow).

iii) The discharge valve is closed (corresponding to no flow). When the measured readings

are steady read all the measurements.

iv) The discharge valve is opened slightly, to give the first increment in volume flow. When

readings are steady, take the measurements.

v) Step 4 is repeated. The final measurements corresponding to the valve being fully open.

vi) The entire experiment is repeated at pump speed corresponding to speed control position

of 75% and 100%.

Page 7: Centrifugal Pump Complete Lab Report

RESULT AND DATA ANALYSIS

Pump Performance Curves (N=1439 rpm@ ω =150.69 rad/s@50%)

0 0.5 1 1.5 2 2.50.00

5.00

10.00

15.00

20.00

25.00

30.00

35.00

40.00

45.00

0.00

50.00

100.00

150.00

200.00

250.00

Head Polynomial (Head) EfficiencyPolynomial (Efficiency) BHP Polynomial (BHP)

Pump Performance Curves (N=2178 rpm@ ω =228.08 rad/s@75%)

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.500.00

5.00

10.00

15.00

20.00

25.00

30.00

35.00

40.00

45.00

50.00

0.00

100.00

200.00

300.00

400.00

500.00

600.00

700.00

Head Polynomial (Head) EfficiencyPolynomial (Efficiency) BHP Polynomial (BHP)

Page 8: Centrifugal Pump Complete Lab Report

Pump Performance Curves (N=2945 rpm@ ω =308.40 rad/s@100%)

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.000.00

10.00

20.00

30.00

40.00

50.00

60.00

0.00

200.00

400.00

600.00

800.00

1000.00

1200.00

1400.00

1600.00

Head Polynomial (Head) EfficiencyPolynomial (Efficiency) BHP Polynomial (BHP)

From the pump performance curve, we can see that the maximum volume flow rate

through a pump occurs when its net head is zero, H=0; this flow rate is called the pump’s free

delivery. The free delivery condition is achieved when there is no flow restriction at the pump

inlet or outlet or when there is no load on the pump. At this operating point, Q is large, but H is

zero and the pump’s efficiency is zero because the pump is doing no useful work. At the other

extreme, the shutoff head is the net head that occurs when the volume flow rate is zero, Q=0,

and is achieved when the outlet port of the pump is blocked off. Under this condition, H is large

but Q is zero; the pump’s efficiency is again zero because the pump is doing no useful work.

Between these two extremes, from shutoff to free delivery, the pump’s net head may increase

from its shutoff value somewhat as the flow rate increases, but H must eventually decrease to

zero as the volume flow rate increases to its free delivery value. The pump’s efficiency will

reaches its maximum value somewhere between the shutoff condition and the free delivery

condition; this operating point of maximum efficiency is appropriately called the best efficiency

point (BEP).

The pump performance curves change with rotational speed as shown above from the

three different rotational speeds (N = 50%, 75%, 100%) that we do in the experiment. It is

Page 9: Centrifugal Pump Complete Lab Report

important to realize that for steady conditions, a pump can operate only along its performance

curve.

Sample Calculation

For N = 1439 rpm,

ω=2 πN60

ω=2 π (1439)

60

ω = 150.69 rad/s-1

Torque = 1.1 Nm

BHP=ωT

= (150.69 rad/s-1) ( 1.1 Nm)

= 165.76 Watt

Capacity, Q

Q = 90 L/min

= 90 L/min / (1000L) (60s)

= 1.5 x 10-3 m3/s

Page 10: Centrifugal Pump Complete Lab Report

water head , h=(P2−P1)1

ρg

= (41.36 +0.98) kPa/ (1000 kgm-3) (9.81 ms-2)

= 4.32 m

WHP= ρgQh

= (1000 kgm-3) (9.81 ms-2) (1.5 x 10-3 m3/s)( 4.32 m)

= 63.52 Watt

Efficiency ,η=WHPBHP

= ρgQhωT

= (63.52 Watt) / (165.76 Watt)

= 0.383 x 100%

= 38.3%

Page 11: Centrifugal Pump Complete Lab Report

TEST 1

PUMP SPEED.N : 1439 rpm @ 50%

ω : 150.69 rad/s

No BHP,

(Watt)

Volume flow rate Water head,

h

(m)

Efficiency,η

(%)l/min m3/s (10-3)

1 75.35 0 0 5.87 0

2 120.55 45 0.75 5.57 34.0

3 150.69 70 1.17 4.92 37.5

4 165.76 90 1.50 4.32 38.3

5 180.83 105 1.75 3.81 36.2

6 180.83 120 2.00 3.21 34.8

7 195.90 130 2.17 2.61 28.3

8 195.90 135 2.25 2.11 23.7

Page 12: Centrifugal Pump Complete Lab Report

TEST 2

PUMP SPEED.N : 2178 rpm @ 75%

ω : 228.08 rad/s

No BHP,

(Nm)

Volume flow rate Water head,

h

(m)

Efficiency,η

(%)l/min m3/s (10-3)

1 228.08 0 0 13.85 0

2 433.35 95 1.58 12.54 45.0

3 501.78 123 2.05 11.54 46.2

4 547.39 135 2.25 10.53 42.5

5 570.20 163 2.72 9.33 43.6

6 593.01 173 2.88 8.32 39.7

7 615.82 183 3.05 7.12 34.6

8 638.62 200 3.33 6.01 30.8

9 638.62 210 3.50 4.71 25.3

Page 13: Centrifugal Pump Complete Lab Report

TEST 3

PUMP SPEED.N : 2945 rpm @ 100%

ω : 308.40 rad/s

No BHP,

(Nm)

Volume flow rate Water head,

h

(m)

Efficiency,η

(%)l/min m3/s (10-3)

1 493.44 0 0 0 0

2 1017.72 118 1.97 24.19 45.9

3 1171.92 158 2.63 22.68 50.0

4 1233.60 178 2.97 20.88 49.3

5 1326.12 205 3.42 19.17 48.4

6 1356.96 218 3.63 17.46 45.9

7 1418.64 243 4.05 15.75 44.1

8 1449.48 248 4.13 14.04 39.3

9 1480.32 260 4.33 12.13 34.8

10 1511.16 273 4.55 10.33 30.5

Page 14: Centrifugal Pump Complete Lab Report

DISCUSSION:

From the experiment, the best operating range for the pump is from 1439 rpm . This is

base on the characteristics of the pump at that instant speed. From our analysis, the average

efficiency is equal to 0.383%. While for brake horsepower the average value is 165.76 Watt and

the head is 4.32 m. From the three average of that value, it is found that the flow rate, Q is

between the ranges of 0 to 273 (liter/minutes). Therefore due to this factor, we have chosen that

the pump will operate efficiently between this range compare to the other two speeds.

The efficiency of the pump tends to fall because of the increasing frictional losses in the

long blade passages of these narrow impellers. Since impeller blade have finite thickness, an

impellers with too many blades leads to passage losses due to excessive flow and large skin

friction drag. Also, the efficiencies depend upon the design of the machine, shape of the blade

and, hence, the capacity handled.

CONCLUSION :

From the experiment, the characteristics of this pump which is the efficiency, brake

horsepower and the head can be defined by using a different speed of pump. Thus, the objective

of this experiment is achieved in order to define any centrifugal pump characteristics.

It also can be concluded that the main objectives of this experiment have been achieved

successfully. We can also determine all the parameters required. However, it is to be noted that,

some of the value of readings obtained may be inaccurate due to certain errors that occurred

during the experiment i.e. parallax error and human error. Yet it still leads and produced the

expected results accordingly and as required.

Page 15: Centrifugal Pump Complete Lab Report

DISCUSSION:

For this experiment, we have follow the procedure in order to obtain the performance

characteristic of the pump by using variable speed operating centrifugal pump at three impeller

speeds. The pump performance characteristic, which is pressure (head) jump, power

requirement, flow rate influence and pump speed influence. Below is the obtain data result for

the experiment.

Speed

(rpm)

Water Head

(m) Output Power

(W)

Volume Flow Rate

(m3/s)

Efficiency

(%)Start End

N1=1439 5.87 2.11 46.47 2.25 23.7

N2=2178 13.85 4.71 161.70 3.5 25.3

N3=2945 25.90 10.33 460.91 4.55 30.5

Based on the table above, we can see the overall data result obtained from the experiment

from three different speed. In these three speeds, all value for water head pump from the start to

the end of the experiment is decreased. This is because due to starting point of the discharge

pressure where we slowly decreased the amount of pressure in certain gap, and as expected it

effect the value of water head result.

For output power and volume flow rate obtain from the experiment, we can see the

increased number of value in volume flow rate due to water height is increasing in the matter of

time. For output power, it also can be put as increasing but if we see the data obtain from the

Page 16: Centrifugal Pump Complete Lab Report

experiment, we can see the inclined and declined number of data. The output power is affected

due to the water head value, where if the water head is decreased, the output will be decreased.

By comparing with these three speeds, we can say the more speed is occurred in the experiment,

the bigger number of output power will produced.

For the efficiency, the number of the effectiveness of the experiment data is increasing

due to the increasing value of the speed. In this part, we can see that we may have some error

occurred in this experiment where our overall efficiency is low which is in 20-30% range. We

can say the bigger number of efficiency, the bigger effectiveness of the operated machine. To get

the better efficiency, the rate of power output and input must be bigger.

Other error that may occur during the experiment is parallax error when taking the data

reading of water height. Also it happens in pressure gauge for inlet pressure. And when the

adjusting the discharge water pressure, the machine cause other apparatus, such as the discharge

pipe is vibrating extremely hard. This may be due to the material of pipe which it cannot absorb

the vibration, and a steel pipe is recommended in this situation.

CONCLUSION:

From the nut shell, we can say that we have achieve our objective, which is to obtain

performance characteristics for variable speed centrifugal pump operating in three different

impeller speeds. Based on the graph obtain from the data result, we can see the entire graph are

inclined at first then slowly it started to declined. Based on these three speed performance, we

can see the difference of parameter calculated to achieving our objective.

Page 17: Centrifugal Pump Complete Lab Report

DISCUSSION:

From the experiment, we conducted three tests which are at pump speed of 50%, 75%

and 100%. The test requires us to record the values for water height, torque, inlet pressure and

discharge pressure. For each test, we are required to plot graph head pump vs flow rate, graph

efficiency vs flow rate and graph shaft power vs flow rate. From the graph, we can see clearly

the relationship between flow rate and head pump, efficiency and shaft power.

Below are the important details for 3 different speeds of pump.

For the pump speed, N1 = 1439 rpm:

The efficiency is proportional to the flow rate and it is increase until the maximum value

of 38.30%.

The water head of pump is decrease slowly from 5.87 m to 2.11 m.

For the pump speed, N2 = 2178 rpm:

The efficiency is proportional to the flow rate and it is increase until the maximum value

of 46.2o%.

The water head of pump is decrease slowly from 13.85m to 4.71m

For the pump speed N3 = 2945 rpm:

The efficiency is proportional to the flow rate and it is increase until the maximum value

of 49.30%.

The water head of pump is decrease slowly from 25.90 m to 10.33 m.

Page 18: Centrifugal Pump Complete Lab Report

From our inspection, it is found that the overall efficiencies of centrifugal pumps are high, of the

order of 90% in the range. They tend to fall of rapidly at lower type numbers, mainly because of

the increased frictional losses in the long inter blade passages of these narrow impellers.

Also, the efficiencies depend upon the size of the machine and, hence, the capacity handled. The

larger the machine, the higher is the efficiency.

CONCLUSION:

From the experiment, we can conclude that the best performance of this centrifugal pump

to operate is at speed N1 = 1439 rpm and flow rate, Q between the range of 0 to 130

(liter/minutes). By doing this experiment also, all the characteristics of this pump which is

efficiency, break horsepower and the head can be defined by using a different speed of pump,

and thus the objective of this experiment is achieved already. Finally, we can conclude that this

experiment is success by achieve the objective.

DISCUSSION:

Page 19: Centrifugal Pump Complete Lab Report

According to my observation, it is known that the centrifugal pump is a type of turbo

machines which has two main components;

an impeller attached to a rotating shaft

stationary casing which cover the impeller

The impeller consists of a few blades arranged in a pattern around the shaft. Theoretically, both

pressure and absolute velocity are increased as the fluid flows from the eye to the periphery of

the blades. But the results obtained shows quite a great result and meet the objectives besides all

the difficulties I had experienced during the experiment as to be compared with typical

performance characteristics for a centrifugal pump, it is not that far. Maybe there are several

mistakes have been made s during the experiment such example by taking inaccurate data and

etc. This happen because it takes some times for the water in the basin to achieve its steady state

as the measurement meter can’t be read as long as the water still churning. Otherwise maybe the

machine itself is quite old and the efficiency of the equipment has dropped a little bit. While

doing the experiment, I have taken the data for several times in order to ensure that the data is

accurate by taking average data for all readings. The best operating range for the 3 different

speed controls are determined from the graph at the highest pump efficiency that is the best

condition for the pump to operate

CONCLUSION:

As a conclusion, what I get here is that I know what a centrifugal pump is and how it functioned.

I also learned new knowledge on the performance characteristics which is very useful for me as a

future mechanical engineer in order for me to select an appropriate pump for several operations,

which depends largely on the brake horsepower, the efficiency, and also the pump head varies

with the capacity or the flow rate. All these need to be considered in selecting an ideal pump.

DISCUSSION:

Page 20: Centrifugal Pump Complete Lab Report

There are major and minor losses in the piping system for example friction in the pipe

surfaces, elevation of the piping system, vibration of the centrifugal pump, valves, cavitations

occur at the impeller blade, etc. For a fluid entering a circular pipe at a uniform velocity. Because

of the no-slip condition, the fluid particle in the layer in contact with the surface of the pipe

comes to complete. This layer also causes the fluid particle in adjacent layers to slow down

gradually as a result of friction.

For friction, elevation and vibration losses, we cannot avoid these losses but we can

minimize it, but we can prevent the cavitations by minimize the performance parameter which is

called as the required net positive suction head (NPSHrequired) to give us a better result and

increase the efficiency.

For a minor losses, the fluid in typical piping system passes through various fitting

valves, bends, elbows, tees, inlet, exit, enlargement, and contractions in addition to the pipes.

These components interrupt the smooth flow of the fluid and cause additional losses because of

the flow separation and mixing they induce. In a typical system with long pipes, these losses are

minor compared to the total head loss in the pipes (the major losses) and are called minor losses.

Although this is generally true, in some cases the minor losses may be greater than the major

losses. This is the case, for example in system with several turns and valves in a short distance.

The head loss introduced by a completely open valve, for example, may be negligible. But a

partially closed valve may cause the largest head loss in the system, as evidenced by the drop in

the flow rate. Flow through valves and a fitting is very complex, and a theoretical analysis is

generally not plausible. Therefore, minor losses are determined experimentally, usually by the

manufactures of the components.

There is also an error that cause from the reading that we taken while undergo the experiment

and to minimize this error, we can do some action to overcome this problems. The actions that

we must consider during the experiment are:

1. The apparatus must be check carefully to make sure it is in a good condition before

carrying the experiment because it may effects the results of the experiment.

Page 21: Centrifugal Pump Complete Lab Report

2. The reading at the pump suction and delivery pressure gauges must be read with more

carefully to avoid any error.

3. The reading should be taken several times and the average value should be taken to know

the average reading that more accurate.

4. The eyes must sharp and perpendicular to the scale of the water level.

CONCLUSION:

From the experiment, we can conclude that the performance characteristics of a

centrifugal pump from the theory are a little bit similar with the result from the experimental

value. The different value from the theory is because of some errors and losses in the system and

also a little bit error in reading process.

DISCUSSION:

This experiment has been carried out to differentiate and identify the properties of pump

by different speed. Three tests have been carried out to identify the properties of the pump at

Page 22: Centrifugal Pump Complete Lab Report

different speed. For the pump speed, Test 1, N1 = 1439rpm, the efficiency increase as the flow

rate increase until the maximum value of effeciency of 38.3% and at the flow rate of 1.5 m3/s.

The head of pump decrease slowly from 5.87m to 2.11m as the valve is opened. The brake

horsepower (bhp) is increase proportionally to the flow rate from 75.35W to 195.90W. For Test

2, the pump speed, N2 = 2178rpm, the efficiency is proportional to the flow rate and it increases

until the maximum value of 46.2% and at the flow rate of 2.05 m3/s. The reduction of head pump

slowly decrease from 13.85m to 4.71m as the water flow rate increases until maximum flow rate

of 3.5 m3/s. The slope for the brake horsepower graph increases as the flow rate increase to

maximum value. The maximum bhp is 638.62W, and the best bhp with the highest effeciency for

this operating speed of the pump is 501.78W. In Test 3, the pump speed used is N3 = 2945rpm.

The effeciency is proportional to the flow rate and it is increase until the maximum value of

50.0%. The head of pump decrease slowly from 25.90m to 10.33m. The brake horsepower is

proportional to the flow rate and it is increased from 493.44 W to 1511.16W.

The effeciencies of the pump depends on the size of the machine and, hence, the capacity

handled. The larger the machine, the higher is the efficiency. From our observation, overall, for

the case of motor speed with the percentage with 50% and 75% the condition of the result is

almost the same. The readings are different but the condition is almost the same. In the case of

the torque, the values keep increasing for conditions, 50% and 75%. As for the average pump

speed also, both conditions stated the same result, which keep on increasing. For Test 1, the

reading for Q is from 0 to 2.25 m3/s and for Test 2 the value of Q is from 0 to 3.50 m3/s. As for

the efficiency, we can see that in both conditions it increase first but later on it decreased because

of the flow rates. In the other hand, as for the bhp, the same thing happens also because of the

flow rates where the valve is fully opened causing less pressure. In all cases, 50%, 75%, and

100% motor speed, the values of the head keeps on decreasing.

CONCLUSION

As the conclusion from this experiment, the objective of the experiment has been achieved. From

the experiment, we know that the principal dependent variables in the pump are the head ( h ),

brake horsepower (bhp) and the efficiency (). The efficiency depends upon the size of machine

and hence, the capacity handled. The larger the machine, the higher is the efficiency. As the

speed of pump increases, the torque (T) increases, followed by the brake horse power (bhp) and

Page 23: Centrifugal Pump Complete Lab Report

also the volume flow rate (Q). Since the pump speed increase, the head value of the pump will

also increase.

REFERENCES

1. Bruce R. Munson, D. F. (2006.). Fundementals of Fluid Mechanics, 5th Edition . Asia:

John Wiley & Sons.

2. Frank M. White. (2003). Fluid Mechanics, 5th Edition. New York, USA: Mc Graw Hill.

3. John F. Douglas, J. M. (2001). Fluid Mechanics, 4th Edition. Scotland: Pearson Prentice

Hall.

4. Fluid Dinamics Handbook By; R. D. Blevins, Van Nostrand Reinhold Co., New

York,1984.