30079_55.pdf

CHAPTER 55

PUMPS AND FANS

William A. Smith

College of Engineering

University of South Florida

Tampa, Florida

55.1

PUMPANDFANSIMILARITY

1681

55.3.5 Modeling of Rotating

Fluid Machines

1691

55.3.6 Summary of Modeling

Laws

55.2 SYSTEM DESIGN: THE FIRST

STEP IN PUMP OR FAN

SELECTION

1691

1682

55.2.1 Fluid System Data

Required

55.4 PUMPSELECTION

1692

1682

55.4.1 Basic Types: Positive

Displacement and

Centrifugal (Kinetic)

55.2.2 Determination of Fluid

Head Required

1682

1692

55.2.3 Total Developed Head of

a Fan

55.4.2 Characteristics of Positive

Displacement Pumps

1684

1692

55.2.4 Engineering Data for

Pressure Loss in Fluid

Systems

55.4.3 Characteristics of

Centrifugal Pumps

1693

1684

55.4.4 Net Positive Suction Head

(NPSH)

55.2.5 Systems Head Curves

1684

1693

55.4.5 Selection of Centrifugal

Pumps

1693

55.3 CHARACTERISTICS OF

ROTATING FLUID

MACHINES

55.4.6 Operating Performance of

Pumps in a System

1694

1687

55.4.7 Throttling versus Variable

Speed Drive

55.3.1 Energy Transfer in

Rotating Fluid

Machines

1695

1687

55.3.2 Nondimensional

Performance

Characteristics of Rotating

Fluid Machines

55.5 FANSELECTION

1696

55.5.1 Types of Fans; Their

Characteristics

1696

1687

55.5.2 Fan Selection

1696

55.3.3 Importance of the Blade

Inlet Angle

55.5.3 Control of Fans for

Variable Volume

Service

1689

55.3.4 Specific Speed

1690

1698

55.1 PUMP AND FAN SIMILARITY

The performance characteristics of centrifugal pumps and fans (i.e., rotating fluid machines) are

described by the same basic laws and derived equations and, therefore, should be treated together

and not separately. Both fluid machines provide the input energy to create flow and a pressure rise

in their respective fluid systems and both use the principle of fluid acceleration as the mechanism to

add this energy. If the pressure rise across a fan is small (5000 Pa), then the gas can be considered

as an incompressible fluid, and the equations developed to describe the process will be the same as

for pumps.

Compressors are used to obtain large increases in a gaseous fluid system. With such devices the

compressibility of the gas must be considered, and a new set of derived equations must be developed

to describe the compressor's performance. Because of this, the subject of gas compressors will be

included in a separate chapter.

Mechanical Engineers' Handbook, 2nd ed., Edited by Myer Kutz.

55.2 SYSTEM DESIGN: THE FIRST STEP IN PUMP OR FAN SELECTION

55.2.1 Fluid System Data Required

The first step in selecting a pump or fan is to finalize the design of the piping or duct system (i.e.,

the "fluid system") into which the fluid machine is to be placed. The fluid machine will be selected

to meet the flow and developed head requirements of the fluid system. The developed head is the

energy that must be added to the fluid by the fluid machine, expressed as the potential energy of a

column of fluid having a height H p (meters). H p is the "developed head." Consequently, the following

data must be collected before the pump or fan can be selected:

1. Maximum flow rate required and variations expected

2. Detailed design (including layout and sizing) of the pipe or duct system, including all elbows,

valves, dampers, heat exchangers, filters, etc

3. Exact location of the pump or fan in the fluid system, including its elevation

4. Fluid pressure and temperature available at start of system (suction)

5. Fluid pressure and temperature required at end of system (discharge)

6. Fluid characteristics (density, viscosity, corrosiveness, and erosiveness)

55.2.2 Determination of Fluid Head Required

The fluid head required is calculated using both the Bernoulli and D'Arcy equations from fluid

mechanics. The Bernoulli equation represents the total mechanical (nonthermal) energy content of

the fluid at any location in the system:

E TW = P 1 V 1 + Z lg + V\I2

(55.1)

where £ r(1 ) = total energy content of the fluid at location (1), J/kg

P 1 = absolute pressure of fluid at (1), Pa

U 1 = specific volume of fluid at (1), m 3 /kg

Z 1 = elevation of fluid at (1), m

g = gravity constant, m/sec 2

V 1 = velocity of fluid at (1), m/sec

The D'Arcy equation expresses the loss of mechanical energy from a fluid through friction heating

between any two locations in the system:

uAPX/j) = f L e (i - j) V 2 /2D

J/kg-m

(55.2)

where u = average fluid specific volume between two locations (i and j) in the system, m 3 /kg

APyfty) = pressure loss due to friction between two locations (i andy) in the system, Pa

/ = Moody's friction factor, an empirical function of the Reynolds number and the pipe

roughness, nondimensional

L e (i ~ j) = equivalent length of pipe, valves, and fittings between two locations i andy in the

system, m

D = pipe internal diameter (i.d.), m

An example best illustrates the method.

Example 55.1

A piping system is designed to provide 2.0 m 3 /sec of water (Q) to a discharge header at a pressure

of 200 kPa. Water temperature is 2O 0 C. Water viscosity is 0.0013 N-sec/m 2 . Pipe roughness is 0.05

mm. The gravity constant (g) is 9.81 m/sec 2 . Water suction is from a reservoir at atmospheric

pressure (101.3 kPa). The level of the water in the reservoir is assumed to be at elevation 0.0 m. The

pump will be located at elevation 1.0 m. The discharge header is at elevation 50.0 m. Piping from

the reservoir to the pump suction flange consists of the following:

1 20 m length of 1.07 m i.d. steel pipe

3 90° elbows, standard radius

2 gate valves

1 check valve

1 strainer

Piping from the pump discharge flange to the discharge header inlet flange consists of the fol-

lowing:

1 100 m length of 1.07 m i.d. steel pipe

4 90° elbows, standard radius

1 gate valve

1 check valve

Determine the "total developed head," H p (m), required of the pump.

Solution:

Let location (1) be the surface of the reservoir, the system "suction location."

Let location (2) be the inlet flange of the pump.

Let location (3) be the outlet flange of the pump.

Let location (4) be the inlet flange to the discharge header, the system "discharge location."

By energy balances

E r(1 ) - VbPf(I - 2) = E T(2}

E T(2 ) + Ep = E T py

E T{3} - uAP/3 - 4) = E TW

where E p is the energy input required by the pump. When E p is described as the potential energy

equivalent of a height of liquid, this liquid height is the "total developed head" required of the pump.

H p = E p /gm

where H p = total developed head, m.

For the data given, assuming incompressible flow:

P 1 - 101.3 kPa Z 2 - +1.Om

U 1 - 0.001 m 3 /kg = constant Z 3 = +1.Om

Z 1 = 0.0 m Z 4 = +50.0 m

V 1 - 0.0 m/sec P 4 - 200 kPa

A p = internal cross sectional area of the pipe, m 2

V 2 = Q/A = (2.0)(4)/ir(1.07) 2 = 2.22 m/sec

Assume V 3 = V 4 = V 2 = 2.22 m/sec

Viscosity (JUL) = 0.0013 N • sec/m 2

Reynolds number = D V/V[L

= (1.07)(2.22)/(0.001)(0.0013) - 1.82 X 10

Pipe roughness (e) = 0.05 mm

e/D - 0.05/(1000)(1.07) = 0.000047

From Moody's chart, / = 0.009 (see references on fluid mechanics)

From tables of equivalent lengths (see references on fluid mechanics):

Fitting

Equivalent Length, L 6 (m)

Elbow

1.6

Gate valve (open)

0.3

Check valve

0.3

Strainer

1.8

L e (l-2) - 20 + (3)(1.6) + 2(0.3) + 0.3 + 1.8 - 27.5 m

4(3-4) = 100 + (4)(1.6) + 0.3 + 0.3 = 107.0 m

uAP(l-2) - (0.009)(27.5)(2.22) 2 /(2)(1.07) = 0.57 J/kg

uAP(3-4) = (0.009)(107.0)(2.22) 2 /(2)(1.07) - 2.21 J/kg

E TW = P 1 V 1 + Z l§ + Vf/2

- (101,300)(0.001) + O + O - 101.30 J/kg

E Tm = E r( i> - uAP/1-2)

= 101.3 - 0.57 - 100.7 J/kg

E r(4 ) = P 4 V 4 + Z 4 g + V 2 4 /2

= (200,000)(0.001) + (50.0)(9.81) + (2.22) 2 /2

- 692.9 J/kg

ET-O) = ETW + "AP/3-4)

- 692.9 + 2.21 - 695.1 J/kg

E p = £7-( 3 ) ~~ E r(2 )

- 695.1 - 100.7 = 594.4 J/kg

H p = E p /g = 594.4/9.81 - 60.6 m of water

It is seen that a pump capable of providing 2.0 m 3 /sec flow with a developed head of 60.6 m of

water is required to meet the demands of this fluid system.

55.2.3 Total Developed Head of a Fan

The procedure for finding the total developed head of a fan is identical to that described for a pump.

However, the fan head is commonly expressed in terms of a height of water instead of a height of

the gas being moved, since water manometers are used to measure gas pressures at the inlet and

outlet of a fan. Consequently,

H fw = (p s / P JH fg

where H fw = developed head of the fan, expressed as a head of water, m

H fg = developed head of the fan, expressed as a head of the gas being moved, m

p g = density of gas, kg/m 3

p w = density of water in manometer, kg/m 3

As an example, if the head required of a fan is found to be 100 m of air by the method described

in Section 55.2.2, the air density is 1.21 kg/m 3 , and the water density in the manometer is 1000

kg/m 3 , then the developed head, in terms of the column of water, is

H fw = (1.21/100O)(IOO) - 0.121 m of water

In this example the air is assumed to be incompressible, since the pressure rise across the fan

was small (only 0.12 m of water, or 1177 Pa).

55.2.4 Engineering Data for Pressure Loss in Fluid Systems

In practice, only rarely will an engineer have to apply the D'Arcy equation to determine pressure

losses in fluid systems. Tables and figures for pressure losses of water, steam, and air in pipe and

duct systems are readily available from a number of references. (See Figs. 55.1 and 55.2.)

55.2.5 Systems Head Curves

A systems head curve is a plot of the head required by the system for various flow rates through the

system. This plot is necessary for analyzing system performance for variable flow application and is

desirable for pump and fan selection and system analysis for constant flow applications.

The curve to be plotted is H versus Q, where

H=[E T(3} -E T(2} ]/g (55.3)

Assume that V 1 = O and V = V 4 in Eqs. (55.1) and (55.2), and letting V = Q/A, then Eq. (55.3)

reduces to

Fig. 55.1 Friction loss for water in commercial steel pipe (schedule 40). (Courtesy of American Society of Heating, Refrigerating and Air Conditioning Engineers.)

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