ME9

FLUID MACHINERY

“The school system has it‟s own definition of what

a genius is. It may not be the same definition of your genius.

Different genius comes out in different environments.

Thomas Edison‟s genius came out in a laboratory and Steve

Jobs genius came out in his family‟s garage where he started

Apple computers. Mark Zuckerberg created Facebook in his

college dorm room as he created a way for his fellow students

to connect and communicate.”

- Robert T. Kiyosaki

CHAPTER 1

Basic Energy Equations

1. Pressure head, hP

Figure 1.1

P = ρf hP, hP =

Where, P = gage pressure

hP = pressure head

ɣ = weight density

ɣf = weight density of fluid = (S.G.)(ɣwater)

Where, ɣw = 9.81

= 62.4

Exercise #1: What is the pressure of a 100 cm

column of water?

2. Velocity head, hV - Torricelli’s Theorem:

“The velocity of a liquid which discharges under a

head is equal to the velocity of a body which falls

in the same head.”

hv =

, v = √

Where, hv = velocity head

v = velocity of fluid

g = 9.81

= 32.2

Exercise #2: Determine the velocity of the liquid in a tank at the bottom, given that surface h = 7m.

3. Volume flow, Q

Figure 1.2

Q = (A v) =

Where, A = cross-sectional area

v = velocity

Q = volume flow rate

Flow through nozzle:

Q = Cd A v

Where, v = √

Cd = coefficient of discharge

Exercise #3: Water is flowing through a cast iron

pipe at the rate of 3500 GPM. The inside diameter of

pipe is 6 in. Find the flow velocity.

4. Power of a jet, P

Figure 1.3

P = ɣ Q h

Where, P = Power

ɣ = Weight density = ρg

5. For bubbles

Figure 1.4

A. T = c (Isothermal) if T is not given:

P1V1 = P2V2

B. Use any process if T is given:

=

Where, P1 = ɣh + Patm *absolute P

P2 = 101.325 KPa or 14.7 psi (if not given)

6. Bernoulli’s Energy Theorem - neglecting

friction, the total head or total amount of energy

per unit weight, is the same at every point in the

path of flow.

Figure 1.5

hT = hP + hv + z

Where, z = elevation head

Using continuity flow equation:

Q1 = Q2 or A1v1 = A2v2

+

+ z1 =

+

+ z2

7. Viscosity, – resistance to flow or the

property to resist shear deformation.

A. Absolute or dynamic viscosity, – viscosity

which is determined by direct measurement of shear

resistance in

or

.

B. Kinematic Viscosity, – absolute viscosity

divided the density in

.

8. Reynold’s Number, NR

NR =

(dimensionless)

Where, NR < 2000 - Laminar Flow

NR > 4000 - Turbulent Flow

v = velocity of fluid

D = internal diameter of pipe

Exercise #4: Water is flowing in a pipe with radius

of 30 cm at a velocity of 5 m/s. The viscosity of

water is 1.17 Pa-s. What is the Reynolds Number?

9. Friction head loss, hL

A. Using Morse Equation:

hL =

B. Using Darcy’s Equation:

hL =

Where, hL = friction head loss

f = coefficient of friction or friction factor

L = pipe length

g = 9.81

= 32.2

C. Pressure drop in the pipe, Pd

Pd = ɣhL

Exercise #5: Water is flowing at a rate of 3,500 GPM. The inside radius is 8 cm and coefficient of friction

is 0.0181. What is the pressure drop over a length of

50 m?

Venturi-meter - is used to measure the volume of

flow.

Pitot tube - is used to measure the velocity of

flow.

Q = A1v1 = A2v2

For circular cross-section: A =

For rectangular cross-section: A = bh

Where, ρ =

in

A. If venturi-meter is horizontal:

Figure 1.6

=

B. If venturi-meter is vertical

Figure 1.7

=

- (z1 - z2)

Where, P1 = inlet pressure

P2 = throat pressure

Exercise #6: A perfect venturi with throat

diameter of 2 in. is placed horizontally in a pipe

with 2 inches is placed horizontally in a pipe

with 6 inches inside diameter. What is the

difference between the pipe and venturi throat

static pressure if the mass flow rate of water is

100 lb/sec?

Bouyancy - Archimedes Principle: A body partly or

wholly submerged in a liquid is buoyed up by a force

equal to the weight of the liquid displaced.

A. Weight of object in air

Figure 1.8

Wo = oVo

Where, o = weight density of object = SGo w

Vo = total volume of object

B. If the object is floating

Figure 1.9

BF = bouyant force = Wo = ɣfVd = ɣoVo

Where, ρf = density of fluid = SGf ρw

Vd = volume displaced

Ve = volume exposed to air

Exercise #7: A 2 meter rod floats vertically in water. It has a 7 cm2 cross sectional and a specific gravity

of 0.6. What length, L, is submerged?

C. If the object is submerged

Figure 1.9.1

BF = ɣfVo

Wo = ɣoVo

R + BF = Wo

Where, R = weight of object in water

Vo = Vd

Exercise #8: What is the buoyant force of a body that weighs 100 kg in air and 70 kg in water?

Lao Tzu, the Chinese founder of Taoism

in the 5th Century BC, stated:

“If you give a man a fish, you feed him for a day.

If you teach a man to fish you feed him for a lifetime.”

“Are our schools failing to teach people to fish?

Or are our schools teaching students that they are

entitled to their daily fish?

Is this why there are more and more people are

dependent upon the government for life support?”

- RTK

“Ask not what your country can do for you -

Ask what you can do for your country.”

- President John Kennedy

CHAPTER 2

Hydro-electric Power

Hydraulics - branch of mechanics which deals with the

laws governing the behavior of water and other

liquids in the states of rest and motion.

Hydrostatics - is a branch of hydraulics which deals

on the study of fluids at rest.

Hydrokinetics - branch of hydraulics which deals with

the study of pure motion in liquids.

Hydrodynamics - branch of hydraulics which deals with

the study of forces exerted by or upon liquids in

motion.

Cohesion - is a fluid property which refers to the

intermolecular attraction by which the separate

particles of the fluid are held together.

Adhesion - is a fluid property which refers to the

attractive force between the molecules and any solid

substance with which they are in contact.

Surface tension - is the force per unit length that

an “imaginary film” formed on the surface of a liquid

due to intermolecular attraction is capable of

exerting.

Fluid Mechanics - is a branch of science which deals

with the study of water and other fluids that are at

rest or in motion.

Reservoir - stores the water coming from the opper

river or waterfalls.

Spillway - a weir in the reservoir which discharges

excess water so that the head of the plant will be

maintained.

Dam - a concrete structure that encloses the

reservoir.

Silt sluice - a chamber which collects the mud and

through which the mud is discharged.

Trash rack - a screen which prevents the leaves,

branches and other water contaminants to enter into

the penstock.

Surge chamber - a standpipe connected to the

atmosphere and attached to the penstock so that the

water will be at atmospheric pressure.

Penstock - the channel that leads the water from the

reservoir to the turbine.

Turbine - converts the energy of the water into

mechanical energy.

Generator - converts the mechanical energy of the

turbine into electrical energy output.

Draft tube - connects the turbine outlet to the

tailwater so that the turbine can be set above the

tailwater level. Used to keep the turbine up to 15

ft. above the tail water surface.

Tailrace - a channel which leads the water from the

turbine to the tailwater.

Tailwater - the water is discharged from the turbine.

Peripheral coefficient - ratio of the peripheral

velocity of the runner over the velocity of the jet.

Water hammer - caused because of sudden stoppage of

water flow in a pipe.

Surge tank - artificial reservoir used to relieve the

pipe line of excessive pressure.

Wicket gates - control the power and speed of turbine

Cavitation - occurs then the pressure at any point

in the flowing water drops below the vapor

pressure of the water which varies with

temperature.

Weir - any obstruction of a stream flow over which

water flows.

Types of turbine:

1. Propeller turbine (for small capacity) - axial

flow turbines have low heads up to 110 ft., high

rotational speeds and large flow rates. This

turbine operates with specific speeds in the range

of 80 and 200 rpm range. But best efficiencies is

between 120 and 160 rpm.

2. Reaction turbines or francis turbine (for

medium capacity) - the specific speed varies from

10 to 100. Best efficiencies are found in the 40

to 60 range. Heads between 110 to 800 ft.

3. Impulse turbine (for large capacity) - radial

flow or Pelton Wheel turbines have the lowest

specific speeds but are used when heads are high

(800 ft to 1,600 ft.). These turbines have

specific speeds below 5. The kinetic energy of the

jet is converted into rotating kinetic energy.

Figure 2.1: Hydro-electric Power Plant

Formulas:

A. Gross head, hg

hg = head water elevation - tail water elevation

B. Friction head loss, hf

Using Morse Equation:

hf =

Using Darcy’s Equation:

hf =

Where, hf = friction head loss

f = coefficient of friction or friction

factor

L = length of penstock

g = 9.81

= 32.2

D = inside diameter

C. Net head, h

h = hg - hf

D. Penstock efficiency, e

e =

E. Volume flow of water, Q

Q = Av

F. Water Power, PW

PW = ɣwQh

Where, ɣw = specific weight of water

= 9.81

= 62.4

G. Turbine efficiency, eT

eT =

Where, PB = Brake power or turbine output

H. Generator efficiency, eG

eG =

I. Turbine output, PB

PB = PW eT

J. Generator output, Pgen

Pgen = PB eG = (PW eT) eG

K. Generator speed, N

N =

Where, N = speed

f = frequency

p = no. of poles (must be even no.)

L. Utilized head, hw

hw = h eh

Where, eh = hydraulic efficiency

Exercise #1: In a hydroelectric power plant the tail

water elevation is at 500 m. What is the head water

elevation if the net head is 30 m and the head loss

is 5% of gross head?

Exercise #2: The tailwater and the headwater of a

hydro-electric plant are 150 m and 200 m

respectively. What is the water power if the flow is

15 m³/s and a head loss of 10% of the gross head?

M. Head of Pelton (Impulse) turbine:

h =

+

Where, ρ = density of water = 1,000

Figure 2.2: Pelton Type Turbine

Exercise #3: An impulse wheel at best produces 125

hp under a head of 210 ft. By what percent should

the speed be increased for 290 ft. head?

Exercise #4: In a double-overhung impulse-turbine

installation is to develop 20,000 hp at 275 rpm

under a net head of 1,100 ft. Determine the

specific speed.

N. Head of Reaction (Francis and Kaplan) turbines:

h =

+

+ z

Figure 2.3: Francis Turbine

O. Peripheral coefficient, Φ

Φ =

=

√

Where, D = diameter of runner, m

N = speed of runner, rps

P. Specific speed of hydraulic turbine

NS = √

, rpm NS = √

, rpm

*h in feet *h in meters

*N in rpm

Q. Total efficiency, et

et = ehemev

Where, ev = volumetric efficiency

em = mechanical efficiency

R. Turbine type selection based on head, ft.

NET HEAD TYPE OF TURBINE

Up to 70 feet Propeller Type

70 - 110 ft. Propeller or Francis

110 – 800 ft. Francis Turbine

800 – 1,300 ft. Francis or Impulse

1,300 ft. and above Impulse Turbine

For small capacity, use Propeller Turbine.

For medium capacity, use Francis Turbine.

For high capacity, use Impulse Turbine.

Exercise #5: A pelton type of turbine has a gross

head of 40 m and a friction head loss of 6 m. What is

the penstock diameter if the penstock length is 90 m

and the coefficient of friction head loss is 0.001

Morse?

Exercise #6: A Pelton type turbine has 25 m head

friction loss of 4.5 m. The coefficient of

friction head loss (from Morse) is 0.00093 and

penstock length of 80 m. What is the penstock

diameter?

“You cannot bring about prosperity by discouraging thrift.

You cannot strengthen the weak by weakening the strong.

You cannot help the wage earner by

pulling down the wage payer.

You cannot further the brotherhood of man by

encouraging class hatred.

You cannot help the poor by destroying the rich.

You cannot keep out of trouble by

spending more than you earn.

You cannot build character and courage by taking

away man's initiative and independence.

You cannot help men permanently by doing for them what

they could and should do for themselves.” - Rev. William J. H. Boetcker

CHAPTER 3

Air Compressor

Air Compressor - a machine which is used to increase

the pressure of a gas by decreasing its volume.

The work input to a compressor is minimized when the

compression process is executed in an internally

reversible manner.

Isentropic process in compression process involves no

cooling. (n = k). For most steady-flow devices, this

is the ideal process that can be served as a suitable

model.

Polytropic process in compression process involves

some cooling. (1 n k)

Isothermal process in compression process involves

maximum cooling. (n = 1)

Adiabatic compression requires maximum work of

compression.

Isothermal process requires minimum work of

compression.

Practically, all compressors are powered by electric

motors.

The ratio of mechanical power required to the

electrical power consumed during operation is called

the motor efficiency.

We =

Where, We = electric power/work, Wc = compressor

power/work, em = motor efficiency

Adiabatic efficiency is a measure of the deviation of

actual process from corresponding idealized zone.

Isentropic efficiency of turbine is the ratio of the

actual work output of the turbine to the work output

that would be achieved of the process between the

inlet state and the exit pressure were isentropic.

eT =

Where, eT - isentropic efficiency, Wa - actual turbine

work, Wi - ideal turbine work

Isentropic efficiency of compressor is the ratio of

the work input required to raise the pressure of a

gas to a specified value in an isentropic manner to

the actual work input.

eT =

Where, eT - isentropic efficiency, Wa - actual

compressor work, Wi - ideal compressor work

Uses of compressor:

- to drive pneumatic tools

- sand blasting

- industrial cleaning

- spray painting

- starting a diesel engine

- to supply air in mine tunnels

- manufacture of plastic and industrial products

Classification of air compressor:

1. Reciprocating compressor

2. Centrifugal compressor

3. Rotary compressor

Single-stage reciprocating compressor:

Figure 3.1

Formulas:

A. Compression process 1 to 2:

Figure 3.2

P1V1n = P2V2

n

= (

)

= (

)

B. Piston displacement, VD

For singe-acting compressor:

VD =

B2SN,

For double-acting compressor:

Figure 3.3

Figure 3.4

Piston rod neglected:

VD = 2(

),

Piston rod neglected:

VD = (

) + *

( ) +,

Where, B = D = piston rod diameter or bore

S = stroke or piston length

C. Capacity of compressor, V1

V1 = volume flow at suction =

D. Volumetric efficiency, ev

ev =

= 1 + c - c(

)

E. Compressor power, Wc

Wc =

[(

)

]

Where, P1 = suction pressure

P2 = discharge pressure

F. Compressor efficiency, ec

ec =

Where, PB = Brake power

G. Piston speed = 2SN

Exercise #1: The discharge pressure of an air

compressor is 5 times the suction pressure. If volume

flow at suction is 0.1 m³/sec, what is the suction

pressure if compressor work is 19.57 KW? (Use n =

1.35).

Exercise #2: The initial condition of air in an air

compressor is 98 KPa and 27°C and discharges air at

450 KPa. The bore and stroke are 355 mm and 381 mm,

respectively with percent clearance of 8% running at

300 rpm. Find the volume of air at suction.

Two-stage reciprocating compressor:

Figure 3.5

Formulas:

A. Compressor work, Wc

Wc =

[(

)

]

B. Intercooler pressure, Px

Px = √

Figure 3.6

C. Heat rejected in the intercooler, Q

Q = mcp(Tx - T1)

Where, cp = 1

m =

= (

)

Tx = intercooler temperature

D. Adiabatic compressor efficiency

ec =

E. Ideal indicated power, IP

IP = PmiVD

Exercise #3: A two stage air compressor has an

intercooler pressure of 4 kg/cm². What is the

discharge pressure if suction pressure is 1

kg/cm²?

3. Three-stage air compressor

Figure 3.7

Figure 3.8

Formulas:

A. Intercooler pressure, Px

Px =

B. Compressor power, Wc

Wc =

[(

)

]

C. Heat rejected in the intercooler, Q

Q = 2mcp(Tx - T1)

Where, cp = 1

m =

= (

)

“The test of a first-rate intelligence is the ability to

hold two opposed ideas in the mind at the same

time, and still retain the ability to function.”

– F. Scott Fitzgerald

“All coins have three sides: heads, tails, and the edge.

The most intelligent people live on the edge,

able to see both sides.

In school there is only one right answer.

In real life there is more than one right answer, a wave of

choices from different perspectives and points of view.

Here‟s an example. When I asked my poor dad what 1+1

equaled, his answer was “2.” Rich dad‟s answer to that same

question was different. His answer was “11.”

This is why one man was poor and the other rich.

In other words, the idea of right vs. wrong,

which is taught in school, is unintelligent.

In fact it is ignorant, since „right vs. wrong‟ ignores,

rather than explores, the other side.

In my opinion, the idea of right versus wrong is the basis of all

disagreements, arguments, divorce, unhappiness,

aggression, violence, and war.”

- RTK

CHAPTER 4

Fans and Blowers

Fan - a machine which is used to apply power to a

gas in order to cause movement of the gas.

Blower - a fan which is used to force air under

suction, that is, the resistance to gas flow is

imposed primarily upon the discharge.

Exhauster - a fan which is used to withdraw air

under suction, that is, the resistance to gas flow

is imposed primarily upon the inlet.

Capacity of fan - volume flow rate measured at the

outlet.

Types of fans:

1. Propeller fan

2. Tubeaxial fan

3. Vaneaxial fan

4. Centrifugal fan

Figure 4.1

Formulas:

A. Static head, hs

hs =

Where, hw = manometer reading, meters of water

ɣw = specific weight of water = 9.81

ɣa = specific weight of air = 1.2

If both static head at suction and discharge are

given,

hs =

B. Velocity head, hv

hv =

Where, vo = outlet velocity,

g = 9.81

= 32.2

If both velocity at suction and discharge are

given,

hv =

C. Total head, h

h = hs + hv

D. Air power, Pa

Pa = ɣaQh, KW

Where, Q = fan capacity,

E. Fan efficiency, ef

ef =

F. Static power, Ps

Ps = ɣaQhs

G. Static efficiency, es

es =

H. Fan laws

Variable speed (constant fan size and density)

=

= (

)

= (

)

Variable density (constant fan size and density)

Q1 = Q2

=

=

Where, ρ = density of air

P = power

h = head

N = speed

Exercise #1: A fan draws 1.42 m³ per second of air at

a static pressure of 2.54 cm of water through a duct

300 mm diameter and discharges it through a duct of

275 mm diameter. Determine the static fan efficiency

if total fan mechanical is 75% and air is measured at

25°C and 760 mmHg.

Exercise #2: Calculate the air power of a fan that

delivers 1,200 m³/min of air through a 1 m by 1.5

m oulet. Static pressure is 120 mmHg and density

of air is 1.18 kg/m3.

Exercise #3: The fan has a total head of 190 m and

a static pressure of 20 cmHg. If the air density

is 1.2 kg/m³, what is the velocity of air flowing?

“Give, and you will receive.

Your gift will return to you in full - pressed down, shaken

together to make room for more, running over,

and poured into your lap.

The amount you give will determine the

amount you get back.”

- Luke 6:38 (NLT)

“A man‟s true worth is the good he does in this world.”

- Mohammad

“The true principle of capitalism is,

„The more people I serve, the more effective I become.‟

You must be generous if you want to serve as many

people as possible.

Unfortunately, many people want to be paid more,

do less, and retire early.

Doesn‟t this violate the principle of generosity?”

- RTK

CHAPTER 5

Pumps

Pump - a machine which is used to add energy to a

liquid in order to transfer the liquid from one point

to another point of higher energy level.

Aquifers - deep ground water deposits where

underground water are available for water supply and

irrigation.

Hydraulic gradient - the locus of the elevation which

water will rise in a piezometer tube.

Figure 5.1: Pump System

Types of pumps:

1. Reciprocating pump

Low discharge, high head, self-priming, up to 5 ft.

suction lift, positive displacement pumps:

1. Piston type

2. Plunger type

3. Bellows or diaphragm

Figure 5.2

This is commonly used as Boiler Feed Pump for steam.

Reciprocating pumps can be single-acting or double-

acting.

They can be simplex, duplex, triplex, etc.

Air chamber - is to smoothen the flow due to the

nature of flow of liquid. This can be placed on the

suction side or discharge side of piping

installation.

Relief valve - this should be installed on the

discharge side between pump and any other valve.

Foot valve - should be installed at the end of the

suction pipe.

All losses of capacity given in percentage of the

displacement are referred to as slip: (1 - ev).

In new pumps, the slippage is within 2%.

2. Centrifugal pump

Figure 5.3

High discharge, low head, not self-priming:

1. Radial flow - used for single and souble

suction

2. Axial flow - acting like compressors

3. Mixed flow

Centrifugal pump is used to convert kinetic energy

into pressure energy through diffuser vanes.

Specific speed - is defined as that speed in rpm

at which a given impeller would operate to deliver

1 GPM against a total dynamic head of 1 foot.

Specific speed is constant and is given by the

manufacturer.

Impellers for higher heads usually have low

specific speeds. Impellers for lower heads usually

have higher specific speeds.

For double suction pumps, the Q value is

determined by dividing the given capacity by 2.

3. Rotary pump

Figure 5.4

Positive displacement pumps, low discharge, low

head:

1. vanes

2. screws

3. lobes

4. gear

5. cam and piston

6. shuttle block type

4. Kinetic pump - transform fluid kinetic energy

to fluid static ppressure energy.

1. jet pumps

2. ejector pumps

Figure 5.5

5. Deep well pump

1. Turbine pumps - high suction lift up to 305 m.

2. Plunger pumps - are refinement of the old hand

pumps. This is best suited where the lifts are 7.6 m

or over and capacities up to 190 liters per minute.

3. Ejector - a centrifugal pump used for small

capacities combines a single-stage centrifugal pump

at the top of the well and an ejector or jet located

down in the water.

4. Air lifts - another method of pumping wells is by

compressed air being admitted to the well to lift the

water to the surface.

Classification of pumps based on suction lift

1. Shallow well pump - suction lift up to 25 ft.

2. Deep well pump - sution lift up to 120 ft.

3. Turbine pump - up to 300 ft.

4. Submersible pump - for high head

Cavitation - is the spontaneous vaporization of the

fluid, resulting in a degradation of pump

performance.

Causes of cavitation:

1. Discharge head far below the pump head at peak

efficiency.

2. High suction lift or low suction head

3. Excessive pump speed

4. High liquid temperature

Bad effects of cavitation:

1. Drop in capacity and efficiency

2. Noise and vibration

3. Corrosion and pitting

NPSH (Net Positive Suction Head) - is the difference

between actual suction pressure and saturation vapor

pressure of the liquid.

NPSHR (Net Positive Suction Head Required) - is a

function of the pump, and will be given by the pump

manufacturer as part of the pump available at the

name plate.

NPSHA (Net Positive Suction Head Available) - is the

actual fluid energy at the inlet.

If NPSHA is less than NPSHR, the fluid will cavitate.

Preventing cavitation:

1. Increasing the height of the fluid source.

2. Reducing friction and minor losses by shortening

the suction line or using larger pipe size.

3. Reducing the temperature of the fluid at the pump

entrance.

4. Pressurizing the fluid supply tank.

5. Reducing the flow rate or velocity.

Pump head:

1. Friction head - head required to overcome

resistance to flow in the pipe, fittings and

valves.

2. Velocity or dynamic head - specific kinetic

energy of the fluid.

3. Static suction head - the vertical distance

above the centerline of the pump inlet to the free

level of water source.

4. Static suction lift - the vertical distance

from pump certerline to the free level of water

source below the pump inlet.

5. Static discharge head - is the vertical

distance from pump centerline to the free level of

the fluid in the discharge tank.

6. Total suction head - is the head that includes

static head, velocity head and friction head at

the suction side.

7. Total discharge head - is the head that

includes static head, velocity head and friction

head at the discharge side.

8. Head - refers to all the head both at suction

and discharge.

9. Drawdown - is the difference between static

water level and operating water level.

10. For duplex pumps:

Pump dimensions: Ds x Dw X L

Ds = steam diameter

Dw = water diameter

L = length of stroke

11. Pump slip

For positive slip, the coefficient of discharge

(Cd) is less than 1 (decreases).

For negative slip, the coefficient of discharge

(Cd) is more than 1 (decreases).

12. Series pump

To increase the head, connect the pump in series.

The head of pump in series is h1 + h2.

The volume flow is Q1 = Q2.

Figure 5.6

13. Parallel pump

To increase the discharge, connect the pump in

parallel.

The discharge of pump in parallel is Q1 + Q2.

The heads, h1 = h2.

Figure 5.7

14. To increase the head of submersible pump,

increase the number of stages of number of impeller.

Formulas:

Figure 5.8

A. Volume flow rate of water, Q

Q = Av

B. Pressure head, hp

hp =

C. Velocity head, hv

hv =

D. Total head of pump, h

h = (hp2 - hp1) + (hv2 - hv1) + (z2 - z1) + (hf1 + hf2)

Where, z1 is negative if source is below pump center

line.

Ps is negative if it is a vacuum.

E. Water power, PW

PW = ɣwQh, KW

Where, ɣw = specific weight of water

F. Pump efficiency, ep

ep =

G. Head as determined from two pressure readings:

h =

+

+ z

Where, P1 is negative if vacuum

Figure 5.9

H. Friction head, hf

Darcy’s Equation: hf =

Morse Equation: hf =

I. Specific speed, Ns

Ns = √

Where, N = speed, rpm

Q = discharge, gpm

h = head, ft

J. Similar pumps:

√

= √

=

K. For the same pump:

Constant impeller diameter, variable speed:

=

= (

)

= (

)

Constant speed, variable impeller diameter:

= (

)

= (

)

= (

)

Constant speed, variable fluid density:

=

=

=

L. Characteristics of Reciprocating pumps:

Figure 5.9.1

1. Piston Displacement:

Piston rod neglected: VD = 2(

),

Piston rod considered: VD =

+

,

2. Slip = VD - Q

3. %slip =

x 100%

4. volumetric efficiency, ev =

= 1 - Slip

Exercise #1: A 4 m³/hr pump delivers water to a

pressure tank. At the start, the gage reads 138 KPa

until it reads 276 KPa and then the pump was shut

off. The volume of the tank is 180 liters. At 276

KPa, the water occupied 2/3 of the tank volume.

Determine the volume of water that can be taken out

until the gage reads 138 KPa.

Exercise #2: If a 1/3 horsepower pump runs for 20

min, what is the energy used?

Exercise #3: A double suction centrifugal pump

delivers 20 ft³/sec of water at a head of 12 m

and running at 650 rpm. What is the specific

speed of the pump?

“Generosity is the key to succes. What are our schools

teaching our children? Are they giving them fish to eat,

keeping them needy and, often, greedy? Or do they teach kids

to fish, to be self-reliant, innovative, and responsible enough

to feed themselves? Needy people become greedy people.

Greedy people become desperate people. And desperate

people do desperate things.

I believe genius is found at Maslow‟s fifth level. At that level

are found powerful and beautiful words, values, and abilities

essential for today‟s world. The words are:

1. Morality: you don‟t have to cheat people to be rich

2. Creativity: tap into your genius

3. Spontaneity: live without the fear of making mistakes

4. Problem solving: focus on solutions

5. Lack of prejudice: having a wider context on life

6. Acceptance of fact: not afraid to face the truth”

- RTK