Pumps theory

There are various means and ways for conveying fluids (both compressible and non-

compressible) and two phase suspensions. Most widely used equipments can be classified as

follows.

� Pumps

� Fans

� Blowers

� Compressors

Out the four machines mentioned above, pumps are mostly used for transporting incompressible

fluids.

Pumps

Before starting detailed discussion on pumps, there are some terms that are commonly

encountered while dealing with pumps, especially centrifugal pumps. These terms will be briefly

discussed below.

HEAD:-

The mechanical energy equation is given below.

Pa/ρ + gZa/gc + αaVa2/2gc + ηWp = Pb/ρ + gZb/gc+ αbVb

2/2gc + hf

Various terms encountered here are given below.

Pa/ρ & Pb/ρ Pressure Heads

gZa/gc & gZb/gc Height Heads

αaVa2/2gc & αbVb

2/2gc Velocity Heads

ηWp Pump Work

Positive Displacement Centrifugal

Reciprocating

Rotary

hf Friction Losses During Flow From Section a

to Section b

The pressure at any point in a liquid can be thought of as being caused by a vertical

column of the liquid which, due to its weight, exerts a pressure equal to the pressure at the point

in question. The height of this column is called the static head and is expressed in terms of feet of

liquid.

The static head corresponding to any specific pressure is dependent upon the weight of

the liquid according to the following formula.

We can predict the approximate head of any centrifugal pump by calculating the

peripheral velocity of the impeller and substituting into the above formula. A handy formula for

peripheral velocity is:

The head developed is approximately equal to the velocity energy at the periphery of the

impeller.

Where

H = Total head developed in feet. v = Velocity at periphery of impeller in feet per sec. g = 32.2 Feet/Sec

2

D = Impeller diameter in inches

V = Velocity in ft./sec

SUCTION LIFT:-

It exists when the source of supply is below the

center line of the pump. Thus the STATIC SUCTION

LIFT is the vertical distance in feet from the centerline of the pump to the

free level of the liquid to be pumped.

Suction Lift – Showing Static Heads in a Pumping System

Where the Pump is Located Above the Suction Tank. (Static Suction Head)

SUCTION HEAD:- It exists when the source of supply is above the centerline of the pump. Thus the STATIC

SUCTION HEAD is the vertical distance in feet from the centerline of the pump to the free level of the liquid to be pumped.

Suction Head – Showing Static Heads in a Pumping System Where the Pump is Located Below the Suction Tank. (Static Suction Head)

SPECIFIC SPEED:-

Specific speed (Ns) is a non-dimensional design index used to classify pump impellers as

to their type and proportions. It is defined as the speed in revolutions per minute at which a

geometrically similar impeller would operate if it were of such a size as to deliver one gallon per

minute against one foot head.

The understanding of this definition is of design engineering significance only, however,

and specific speed should be thought of only as an index used to predict certain pump

characteristics. The following formula is used to determine specific speed:

Where

N = Pump speed in RPM

Q = Capacity in gpm at the best efficiency point

H = Total head per stage at the best efficiency point

CAVITATION:-

Consider that a pump transfers fluid from a section a to section b. The power calculated

from the mechanical energy balance equations dependent upon the inlet and outlet pressures.

Consider a case where the suction or inlet pressure becomes almost equal to or just above the

vapor pressure of the fluid. The fluid sucked in will have bubbles of air entrained in it and this

will be a serious cause of pump capacity and thus efficiency. In other words, when the pressure

of the liquid is reduced to a value equal to or below its vapor pressure the liquid begins to boil

and small vapor bubbles or pockets begin to form. As these vapor bubbles move along the

impeller vanes to a higher pressure area above the vapor pressure, they rapidly collapse. This

phenomenon is termed as cavitation. The collapse or "implosion" is so rapid that it may be heard

as a rumbling noise, as if you were pumping gravel. The accompanying noise is the easiest way

to recognize cavitation. Vibration and mechanical damage such as bearing failure can also occur

as a result of operating in excessive cavitation, with high and very high suction energy pumps.

On the other hand what will happen if the suction pressure falls below the vapor pressure of the

fluid? The answer is that the pump will be unable to suck any fluid and thus no fluid will be

transferred through the pump. In such a case the pump will be vapor locked. This generally

happens when the pump is started to operate. The sure of such a problem is Priming which

means that the operating fluid be manually or mechanically circulated through the pump so that

the pump becomes void of air or vapors and the pump is able to operate on the designed

pressure.

NET POSITIVE SUCTION HEAD (NPSH):-

The Hydraulic Institute defines NPSH as the total suction head in feet absolute,

determined at the suction nozzle and corrected to datum, less the vapor pressure of the liquid in

feet absolute. Simply stated, it is an analysis of energy conditions on the suction side of a pump

to determine if the liquid will vaporize at the lowest pressure point in the pump.

A liquid increases greatly in volume when it vaporizes. One cubic foot of water at room

temperature becomes 1700 cu. ft. of vapor at the same temperature. It is obvious from this

example that if we are to pump a fluid effectively, we must keep it in liquid form. NPSH is

simply a measure of the amount of suction head present to prevent this vaporization at the lowest

pressure point in the pump.

As the liquid passes from the pump suction to the eye of the impeller, the velocity

increases and the pressure decreases. There are also pressure losses due to shock and turbulence

as the liquid strikes the impeller. The centrifugal force of the impeller vanes further increases the

velocity and decreases the pressure of the liquid. The NPSH Required is the positive head in feet

absolute required at the pump suction to overcome these pressure drops in the pump and

maintain the majority of the liquid above its vapor pressure. The NPSH Required varies with

speed and capacity within any particular pump. Pump manufacturer's curves normally provide

this information.

Net Positive Suction Head (NPSH) NPSH Available is a function of the system in which

the pump operates. It is the excess pressure of the liquid in feet absolute over its vapor pressure

as it arrives at the pump suction. Fig shows four typical suction systems with the NPSH

Available formulas applicable to each. It is important to correct for the specific gravity of the

liquid and to convert all terms to units of "feet absolute" in using the formulas. Various terms

used are

PB = Barometric pressure in feet absolute.

VP = Vapor pressure of the liquid at maximum pumping temperature, in feet absolute.

P = Pressure on surface of liquid in closed suction tank, in feet absolute.

Ls = Maximum static suction lift in feet.

LH = Minimum static suction head in feet.

hf = Friction loss in feet in suction pipe at required capacity

In an existing system, the NPSH Available can be determined by a gauge on the pump

suction. The following formula applies:

Where

Gr = Gauge reading at the pump suction expressed in feet (plus if above atmospheric,

minus if below atmospheric) corrected to the pump centerline.

hv = Velocity head in the suction pipe at the gauge connection, expressed in feet.

SUCTION SPECIFIC SPEED:-

In designing a pumping system, it is essential to provide adequate NPSH available for

proper pump operation. Insufficient NPSH available may seriously restrict pump selection, or

even force an expensive system redesign. On the other hand, providing excessive NPSH

available may needlessly increase system cost. Suction specific speed may provide help in this

situation.

Suction specific speed (S) is defined as:

Where

N = Pump speed RPM

GPM = Pump flow at best efficiency point at impeller inlet (for double suction

impellers divide total pump flow by two).

NPSHR = Pump NPSH required at best efficiency point.

An example:

Flow 2,000 GPM; head 600 ft. What NPSHA will be required?

Assume: at 600 ft., 3500 RPM operation will be required.

SUCTION ENERGY:-

The amount of energy in a pumped fluid, that flashes into vapor and then collapses back

to a liquid in the higher pressure area of the impeller inlet, determines the extent of the noise

and/or damage from cavitation. Suction Energy is defined as:

Suction Energy = De x N x S x Sg

Where

D e = Impeller eye diameter (inches)

Sg = Specific gravity of liquid (Sg - 1.0 for cold water)

AFFINITY LAWS:-

The affinity laws express the mathematical relationship between the several variables

involved in pump performance. They apply to all types of centrifugal and axial flow pumps.

They are as follows:

1. With impeller diameter D held constant:

2. With speed N held constant

Where:

Q = Capacity, GPM

H = Total Head, Feet

BHP = Brake Horsepower

N = Pump Speed, RPM

FUNDAMENTAL FORMULAE FOR CENTRIFUGAL PUMPS:-

Where

GPM = gallons per minute

CFS = cubic feet per second

Lb. = pounds

Hr. = hours

BBL = barrel (42 gallons)

Sp.Gr. = specific gravity

H = head in feet

psi = pounds per square inch

In. Hg. = inches of mercury

hv = velocity head in feet

V = velocity in feet per second

g = 32.16 ft/sec2 (acceleration of gravity)

A = area in square inches

I.D. = inside diameter in inches

BHP = brake horsepower

Eff. = pump efficiency expressed as a decimal

Ns = specific speed

N = speed in revolutions per minute

v = peripheral velocity of an impeller in feet per second

D = Impeller in inches

Nc = critical speed

f = shaft deflection in inches

P = total force in pounds

L = bearing span in inches

m = constant usually between 48 and 75 for pump shafts

E = modules of elasticity, psi - 27 to 30 million for steel

CONSTRUCTION OF CENTRIFUGAL PUMPS:-

As a rule, the casing for the liquid end of a pump with a single-suction impeller is made

with an end plate that can be removed for inspection and repair of the pump. A pump with a

double-suction impeller is generally made so one-half of the casing may be lifted without

disturbing the pump.

Since an impeller rotates at high speed, it must be carefully

machined to minimize friction. An impeller must be balanced to

avoid vibration. A close radial clearance must be maintained

between the outer hub of the impeller and that part of the pump

casing in which the hub rotates. The purpose of this is to minimize

leakage from the discharge side of the pump casing to the suction

side.

Centrifugal pump impellers.

A. Single-suction. B. Double-suction

In most centrifugal pumps, the shaft is fitted with a replaceable sleeve. The advantage of

using a sleeve is that it can be replaced more economically than the entire shaft.

Seal piping (liquid seal) is installed to cool the mechanical seal. Most pumps in saltwater

service with total head of 30 psi or more are also fitted with cyclone separators. These separators

use centrifugal force to prevent abrasive material (such as sand in the seawater) from passing

between the sealing surfaces of the mechanical seal. There is an opening at each end of the

separator. The opening at the top is for "clean" water, which is directed though tubing to the

mechanical seals in the pump. The high-velocity "dirty" water is directed through the bottom of

the separator, back to the inlet piping for the pump.

OPERATION OF CENTRIFUGAL PUMP:-

Liquid enters the rotating impeller on the suction side of the casing and enters the eye of

the impeller. Liquid is thrown out through the opening around the edge of the impeller and

against the side of the casing by centrifugal force. This is where the pump got its name. When

liquid is thrown out to the edge of the casing, a region of low pressure (below atmospheric) is

created around the center of the impeller; more liquid moves into the eye to replace the liquid

that was thrown out. Liquid moves into the center of the impeller with a high velocity (speed).

Therefore, liquid in the center of the impeller has a low pressure, but it is moving at a high

velocity.

Liquid moving between the blades of the impeller spreads out, which causes the liquid to

slow down. (Its velocity decreases.) At the same time, as the liquid moves closer to the edge of

the casing, the pressure of the liquid increases. This change (from low pressure and high velocity

at the center to high pressure and low velocity at the edge) is caused by the shape of the opening

between the impeller blades. This space has the shape of a diffuser, a device that causes the

velocity-pressure relationship of any fluid that moves through it to change.

A centrifugal pump is considered to be a nonpositive-displacement pump because the

volume of liquid discharged from the pump changes whenever the pressure head changes. The

pressure head is the combined effect of liquid weight, fluid friction, and obstruction to flow. In a

centrifugal pump, the force of the discharge pressure of the pump must be able to overcome the

force of the pressure head; otherwise, the pump could not deliver any liquid to a piping system.

The pressure head and the discharge pressure of a centrifugal pump oppose each other. When the

pressure head increases, the discharge pressure of the pump must also increase. Since no energy

can be lost, when the discharge pressure of the pump increases, the velocity of flow must

decrease. On the other hand, when the pressure head decreases, the volume of liquid discharged

from the pump increases. As a general rule, a centrifugal pump is usually located below the

liquid being pumped. (NOTE: This discussion assumes a constant impeller speed.).

When a centrifugal pump is started, the vent line must be opened to release entrained air.

The open passage through the impeller of a centrifugal pump also causes another problem. It's

possible for liquid to flow backwards (reverse flow) through the pump. A reverse flow, from the

discharge back to the suction, can happen when the pressure head overcomes the discharge

pressure of the pump. A reverse flow can also occur when the pump isn't running and another

pump is delivering liquid to the same piping system. To prevent a reverse flow of liquid through

a centrifugal pump, a check valve is usually installed in the discharge line.

With a check valve in the discharge line, whenever the pressure above the disk rises

above the pressure below it, the check valve shuts. This prevents liquid from flowing backwards

through the pump.

ROTARY PUMPS:-

A number of types are included in this classification, among which are the gear pump, the

screw pump, and the moving vane pump. Unlike the centrifugal pump, which we have discussed,

the rotary pump is a positive displacement pump. This means that for each revolution of the

pump, a fixed volume of fluid is moved regardless of the resistance against which the pump is

pushing. As you can see, any blockage in the system could quickly cause damage to the pump or

a rupture of the system. You, as a pump operator, must always be sure that the system is properly

aligned so a complete flow path exists for fluid flow. Also, because of their positive

displacement feature, rotary pumps require a relief valve to protect the pump and piping system.

The relief valve lifts at a preset pressure and returns the system liquid either to the suction side of

the pump or back to the supply tank or sump.

Rotary pumps are also different from centrifugal pumps in that they are essentially self-

priming. As we saw in our discussion of centrifugal pumps, the pump is located below the liquid

being pumped; gravity creates a static pressure head which keeps the pump primed. A rotary

pump operates within limits with the pump located above the source of supply.

A good example of the principle that makes rotary pumps self-priming is the simple

drinking straw. As you suck on the straw, you lower the air pressure inside the straw.

Atmospheric pressure on the surface of the liquid surrounding the straw is therefore greater and

forces the liquid up the straw. The same conditions basically exist for the gear and screw pump

to prime itself.

In the tank must be vented to allow air into the tank to provide atmospheric pressure on

the surface of the liquid. To lower the pressure on the suction side of the pump, the clearances

between the pump parts must be close enough to pump air. When the pump starts, the air is

pumped through the discharge side of the pump and creates the low-pressure area on the suction

side, which allows the atmospheric pressure to force the liquid up the pipe to the pump. To

operate properly, the piping leading to the pump must have no leaks or it will draw in air and can

lose its prime.

Rotary pumps are useful for pumping oil and other heavy viscous liquids. In the engine

room, rotary pumps are used for handling lube oil and fuel oil and are suitable for handling

liquids over a wide range of viscosities.

Rotary pumps are designed with very small clearances between rotating parts and

stationary parts to minimize leakage (slippage) from the discharge side back to the suction side.

Rotary pumps are designed to operate at relatively slow speeds to maintain these clearances;

operation at higher speeds causes erosion and excessive wear, which result in increased

clearances with a subsequent decrease in pumping capacity.

Classification of rotary pumps is generally based on the types of rotating element. Some

types have been briefly mentioned below.

1- GEAR PUMPS:-

The simple gear pump has two spur gears that mesh together and revolve in opposite

directions. One is the driving gear, and the other is the driven gear. Clearances between the gear

teeth (outside diameter of the gear) and the casing and between the end face and the casing are

only a few thousandths of an inch. As the gears turn, the gears unmesh and liquid flows into the

pockets that are vacated by the meshing gear teeth. This creates the suction that draws the liquid

into the pump. The liquid is then carried along in the pockets formed by the gear teeth and the

casing. On the discharge side, the liquid is displaced by the meshing of the gears and forced out

through the discharge side of the pump.

Simple gear pump

2- SCREW PUMPS:-

Several different types of screw pumps exist. The differences between the various types

are the number of intermeshing screws and the pitch of the screws. Figure shows a double-screw,

low-pitch pump; and figure 9-11 shows a triple-screw, high-pitch pump. Screw pumps are used

aboard ship to pump fuel and lube oil and to supply pressure to the hydraulic system. In the

double-screw pump, one rotor is driven by the drive shaft and the other by a set of timing gears.

In the triple-screw pump, a central rotor meshes with two idler rotors.

In the screw pump, liquid is trapped and forced through the pump by the action of

rotating screws. As the rotor turns, the liquid flows in between the threads at the outer end of

each pair of screws. The threads carry the liquid along within the housing to the center of the

pump where it is discharged.

Most screw pumps are now equipped with mechanical seals. If the mechanical seal fails,

the stuffing box has the capability of accepting two rings of conventional packing for emergency

use.

3- SLIDING VANE PUMPS:-

The sliding-vane pump figure below has a cylindrically bored housing with a suction

inlet on one side and a discharge outlet on the other side. A rotor (smaller in diameter than the

cylinder) is driven about an axis that is so placed above the center line of the cylinder as to

provide minimum clearance between the rotor and cylinder at the top and maximum clearance at

the bottom.

The rotor carries vanes (which move in and out as the rotor rotates) to maintain sealed

spaces between the rotor and the cylinder wall. The vanes trap liquid on the suction side and

carry it to the discharge side, where contraction of the space expels liquid through the discharge

line. The vanes slide on slots in the rotor. Vane pumps are used for lube oil service and transfer,

tank stripping, bilge, aircraft fueling and defueling and, in general, for handling lighter viscous

liquids.