Pipeline Design

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Pipeline Design

Fluid Flow in Steel Pipes

5.02 - 5.03

Pipeline Sizing - Pressure Loss

5.04 - 5.06

Fittings - Pressure Loss

5.07 - 5.09

Water Flow in Straight Pipes - Pressure Loss

5.10 - 5.19

Useful Pipe Properties

5.20

Valves - Pressure Loss

5.21 - 5.24

Compressible Fluids

5.25 - 5.27

Steam

5.28 - 5.29

Water Hammer

5.30 - 5.32

ν =

Density and Viscosity for Water

Temperature Density Absolute viscosity °C kg/m3 _{Pa s} 10 1000 1.3 x 10-3

75 975 0.4 x 10-3

150 917 0.2 x 10-3

Fluid Flow in Steel Pipes

The flow of fluids is a complex process, the study of which is known as fluid dynamics. Fluid transport is affected by the physical properties of the fluid, the type of flow, the pipe dimensions and the properties of the pipe material. There are very few transport problems which can be completely solved by the purely mathematical equations of fluid dynamics. For everyday situations the solutions are dependent on

experimentally determined factors, such as the friction factor. Most real problems can be solved using the Darcy formula, which relies on this experimental friction factor.

Physical Properties of Fluids

The properties relevant to fluid flow are summarized below.

Density: This is the mass per unit volume

of the fluid and is generally measured in kg/m3_{. Another commonly used term is}

specific gravity. This is in fact a relative density, comparing the density of a fluid at a given temperature to that of water at the same temperature.

ρ ρ_water

S = specific gravity (dimensionless)

ρ = density of fluid (kg/m3₎

ρ_water = density of water (kg/m3₎

= 1000 at 10° C

Viscosity: This describes the ease with

which a fluid flows. A substance like treacle has a high viscosity, while water has a much lower value. Gases, such as air, have a still lower viscosity. The viscosity of a fluid can be described in two ways.

a) Absolute (or dynamic) viscosity: This

is a measure of a fluid's resistance to internal deformation. It is expressed in pascal seconds (Pa s) or newton seconds per square metre (Ns/m2_).

[1Pas = 1 Ns/m2_]

b) Kinematic viscosity: This is the ratio of

the absolute viscosity to the density

and is measured in metres squared per second (m2_/s).

µ ρ

ν= kinematic viscosity (m2_/s)

µ = absolute viscosity (Pa s or Ns/m2₎

ρ = density (kg/m3₎

Velocity of Fluid

The mean velocity of a fluid is given by: v = Q

A

v = velocity of fluid (m/s)

Q = volume flow rate (m3_/second)

A = pipe cross sectional area (m2₎

Fig. 5.01 Extract from CIBSE Guide C4.3

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Reynolds Number

A useful factor in determining which type of flow is involved is the Reynolds

number. This is the ratio of the dynamic forces of mass flow to the shear resistance due to fluid viscosity and is given by the following formula. vdi

ν

Re = Reynolds number (dimensionless) di = pipe inside diameter (m)

v = velocity of fluid (m/s)

ν = kinematic viscosity (m2_/s)

In general for a fluid like water when the Reynolds number is less than 2000 the flow is laminar. The flow is turbulent for Reynolds numbers above 4000. In between these two values

(2000<Re<4000) the flow is a mixture of the two types and it is difficult to predict the behaviour of the fluid.

Types of Fluid Flow

When a fluid moves through a pipe two distinct types of flow are possible, laminar and turbulent. Laminar flow occurs in fluids moving with small average velocities and turbulent flow becomes apparent as the velocity is increased above a critical velocity. In laminar flow the fluid particles move along the length of the pipe in a very orderly fashion, with little or no sideways motion across the width of the pipe. Turbulent flow is characterised by random, disorganised motion of the particles, from side to side across the pipe as well as along its length. There will, however, always be a layer of laminar flow at the pipe wall - the so-called 'boundary layer'.

The two types of fluid flow are described by different sets of equations. In general, for most practical situations, the flow will be turbulent. Re =

d

v

v

v

Laminar Flow - Re < 2000 Disturbed Turbulent Flow -Re >2000 and -Re <4000

Disturbed Turbulent Flow - Re> 4000

Fig. 5.02

Pipeline Sizing

What size should the pipe be?

The following formula can be used as a first approximation for a given flow rate.

d = 1.13 Q v where v = flow velocity (m/s)

d = inside pipe diameter (m) Q = flow rate (m2_/s)

Normally the flow velocity is unknown and must be approximated. The

following are generally accepted design velocities.

Liquids v = 1.0-3.0 m/s Gases v= 10-30 m/s

Example

What size steel pipe should be used when the flow rate Q = 8 x 10-3_m3_{/s and}

the velocity v = 2m/s?

d =1.13 8 x 10-3

2 = 0.071m = 71mm

In this case a 3'' (DN80) steel pipe can be used, since it ha a nominal bore of 80.9mm. The next size down is 21_/ 2"

(DN65) which has a bore of 68.7mm and would cause a reduction in the required flow rate to 7.45 x 10-3_m3_{/s. If the flow}

rate may be slightly less than 8 x 10-3_m3_{/s, it would be more economical}

to use the smaller pipe.

Pressure Loss

Whenever fluid flows in a pipe there will be some loss of pressure due to several factors:

a) friction- this is affected by the

roughness of the inside surface of the pipe, the pipe diameter, and the physical properties of the fluid.

b) changes in size and shape or

direction of flow

c) obstructions

For normal, cylindrical straight pipes the major cause of pressure loss will be friction. Pressure loss in a fitting or valve is greater than in a straight pipe. When fluid flows in a straight pipe the flow pattern will be the same through out the pipe. In a valve or fitting changes in the flow pattern due to factors (b) and (c) will cause extra pressure drops.

Pressure drops can be measured in a number of ways. The SI unit of pressure is the pascal. However pressure is often measured in bar. To convert from bar to pascals we use:

1 bar = 105_Pa

Another way of measuring pressure drop is in terms of head loss. To convert head loss to pascals we use :

∆p = Hρg

where ∆p = pressure drop in pascals

∆H = head loss in metres

ρ = density of fluid (kg/m3) g = acceleration due to gravity = 9.81m/s2

Pipeline Sizing

-Pressure Loss

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diagram provided the Reynolds number and the relative roughness of the pipe material are known. Values for the relative roughness are given in the table on page 5.20. When considering steel pipes it is not only necessary to allow for pipe roughness, but also possible build up of scale and rusting.

Pipe roughnesses and correction factors, used to account for these, are given in tables on page 5.20.

Equivalent length: this is the length of pipe which will produce a frictional pressure loss of one velocity pressure. It is given by:

le = di

4f

le = equivalent length (m)

di = inside pipe diameter (m)

f = friction factor (dimensionless)

ν = µ = 1.3x10-3 _{=1.3 x10}-6 _m2_/s ρ 1000 Re = vdi = (0.81) x (0.0687) ν 1.3 x10-6 = 4.3x104 Step 2

Use Moody diagram to determine the friction factor. For a Reynolds number of 4.3 x104 _{and a roughness of 6.7 x 10}-4

we find f = 0.006

Step 3

Find head loss in m/m

∆Hpi = 2fv2 =2 x (0.006) x (0.81)2

g di (9.81) x (0.0687) = 0.012 m/m = 12mm/m

Step 4

If necessary change to pascals.

Example

Find the pressure loss per unit length for water flow at 3 l/s through 21_/

2" (DN65)

medium grade BS 1387 steel pipe at 10°C.

Pipe size 65mm

Inside diameter di = 68.7 x 10-3m

Relative roughness 6.7x10-4

See page 5.20 Useful Pipe Properties

Cross-sectional area A = π x (68.7x103_m/2)2_m2

Volume flow rate Q = 3x10-3 _m3_/s

Absolute viscosity µ = 1.3Pa s x 10-3

Density ρ = 1000kg/m3

(both from Fig. 5.01)

Step 1

Calculate Reynolds number Re = vdi

ν

find flow velocity

v = Q = volume flow rate A cross-sectional area = 3x10-3

Fluid Flow in Straight Pipes

The pressure drop due to friction is given by Darcy's formula:

∆Hpi = 2fv2

gdi

∆Hpi = head loss (m/m)

f = friction factor (dimensionless) v = fluid velocity (m/s)

g = acceleration due to gravity= 9.81m/s2

di = inside pipe diameter (m)

The friction factor (f) is a dimensionles constant which is dependent on the Reynolds number (Re) and the roughness of the pipe material. For turbulent flow (Re > 4000 for water) the friction factor has a very complex formula. However, a practical means of calculating the friction factor is provided by Moody's diagram shown in Fig. 5.03. A value for the friction factor can be read directly from this

Moody’s Diagram

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Fittings - Pressure Loss

There are two general types of fittings. Reducing (or expanding) fittings change the cross sectional area of flow, while deflecting fittings alter the direction of flow (e.g. bends and elbows). Couplings or unions offer no appreciable resistance to flow so may be considered as straight pipe.

The pressure drop for a valve or fitting consists of two parts:

1. The pressure drop we would obtain

for straight pipe of the same length as the fitting.

2. The pressure drop of the fitting itself.

The pressure loss factor (ζ - value) of the fitting is determined experimentally and allows us to calculate the total pressure drop due to both of these factors.

Finding the ζ - value

Fig. 5.05 gives the ζ value for several fittings. For the elbows and bends, the ζ -value can be easily read directly from the table. For example a 90° elbow 11_/

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(DN32) has ζ= 0.7 However the situation may be more complex. In some pipe systems we may have a reduction or enlargement in pipe size. This change in size has a ζ - value which depends on the ratio of the two pipe areas (see example below).

Tees and junctions have ζ - values which vary depending on which branch is being considered. Once the basic ζ -value for the relevant branch has been determined extra factors need to be added on. The first is for the elbow or bend (if the flow is through the straight section of a tee then this is zero). Finally any reduction or enlargement in pipe cross sectional area must be accounted for. 11_{/4" (DN 32) pipe} Reducer 1" (DN 25) pipe Diverging junction (DN 32) Example 1

What is the ζ - value for a system of 1 inch (DN25) diameter with a malleable cast iron elbow and a diverging tee where the flow being considered is along the run of the tee?

Step 1

Find the ζ - value for the malleable cast iron elbow. From the table we see this is 0.8. (Fig. 5.05)

Step 2

Find the ζ - value for the tee junction. The run is the important part so we have flow from A1 to A3 in Fig. 5.05. So we read

the basic ζ3 value of 0.2. We do not need

to add on a reduction or enlargement factor as the pipe bore does not change.

Step 3

Find the total ζ - value

The ζ - value for all the fittings will be:

ζTOTAL = 0.8 + 0.2 = 1.0

Example 2

What is the ζ - value for the following system?

The diverging junction has the effect of a 90° elbow.

Step 1

Find the basic ζ - value for a diverging junction. The table gives ζ2 = 0.5 (Fig. 5.05)

Step 2

Find the contribution due to the 90° elbow. From the elbows and bends table we see for a 32mm 90° elbow we have

ζ = 0.7.

First we find the ratio of the two cross sectional areas.

cross sectional area = π x (radius)2

A1 = π x (32)2 A2 = π x (25)2

4 4 A2 = 0.6

A1

The value corresponding to A2 = 0.6

A1

is ζ = 0.25.

Step 4

Find the total ζ by adding together contributions from the previous three steps.

ζ_TOTAL = 0.5 + 0.7 + 0.25 = 1.45

Lef = ζ di

4 f

Lef = equivalent length of fitting (m)

ζ = pressure loss factor (dimensionless) di = internal pipe diameter (m)

f = friction factor (dimensionless)

For an entire pipe system, the equivalent length of all the fittings is added to the actual length of pipe to give a total effective length. The total pressure loss is then equal to this effective length multiplied by the pressure loss per unit length for the appropriate material and pipe diameter (see Figs. 5.08-5.10).

Calculating pressure loss

Once we have calculated the ζ value we can find the pressure loss in two ways.

Method 1

Here we use the following formula.

∆p_fi = ζ ρ v2

2

∆p_fi = pressure change in fittings (Pa)

ζ = pressure loss factor (dimensionless)

ρ = density (kg / m3₎

v = flow velocity (m/s)

The flow velocity for a given volume flow rate and pipe dimension can be found in the water flow pressure loss tables. The pressure loss for the valves and fittings is simply added to the pressure loss for the straight pipe in a system to find the total pressure loss.

Method 2

Equivalent length

The equivalent length of a fitting is the length of pipe, of the same material and diameter as the fitting, which would give the same pressure loss as the fitting itself. It can be calculated as follows.

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Pressure Loss Factors for Pipe Fittings

(based on velocity pressure of combined flow. Factors refer to the branch indicated by the subscript, e.g. ζ2 is for flow from branch 2).

Diverging ζ2 ζ3 Diverging ζ2

Converging Converging

0.5

+ factor for bend

or elbow as appropriate + factor for enlargement or reduction where bores differ

(

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(

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0.2 + factor for enlargement or reduction where bores differ

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0.5 + factor for bend

or elbow as appropriate + factor for enlargement or reduction where bores differ

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(

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Elbows and Bends

Malleable Cast Iron 90° Elbow

Type

10-25mm 32-50mm 65-90mm >100mm

0.8 0.7 0.6 0.6

Malleable Cast Iron

45° Elbow 0.6 0.6 0.5 0.5

Malleable Cast Iron

Bend 0.7 0.5 0.4 0.4

Malleable Cast Iron

Return Bend 0.9 0.8 0.8 –

Tees and Junctions

Fig. 5.05

Extract from CIBSE Guide, Table 4.36.

Reductions

Based on velocity pressure in smaller pipe

Enlargements

Based on velocity pressure in smaller pipe A2 A1 A2 A1 A1 A2 A1 A2 ζ ζ ζ ζ 0.1 0.55 0.4 0.40 0.2 0.50 0.6 0.25 0.3 0.45 0.8 0.05 0.1 0.80 0.4 0.35 0.2 0.65 0.6 0.15 0.3 0.50 0.8 0.05 DN

Correction factors for rusted steel pipes

Nominal pipe size Pressure loss as read from tables

mm inches 2 5 10 20 50 100 200 500 1000 15 1_/ 2 1.0 3.2 3.2 3.5 3.8 4.1 4.3 4.5 4.7 25 1 2.4 2.7 2.93.1 3.4 3.6 3.7 3.9 4.0 50 2 2.3 2.5 2.7 2.93.1 3.2 3.3 3.4 3.5 100 4 2.3 2.4 2.5 2.7 2.8 2.92.93.1 3.1

Water Flow in Straight Pipes

- Pressure Loss

The following tables (Figs. 5.08-5.10) relate a pressure loss per unit length (in pascals) to the volume flow rate in the pipe. The correction tables which precede them allow compensation for rust and a higher temperature. The value read from the flow tables is multiplied by the appropriate factor from the correction tables.

Correction factors for water at 150°C

Nominal pipe size Pressure loss as read from tables

mm inches 2 5 10 20 50 100 200 500 1000 15 1_/ 2 1.00 1.00 0.91 0.95 0.96 0.97 0.99 1.0 1.0 25 1 0.90 0.90 0.92 0.93 0.95 0.97 0.99 1.0 1.0 50 2 0.90 0.92 0.94 0.96 0.98 1.0 1.0 1.0 1.0 100 4 0.95 0.96 0.97 0.99 1.0 1.0 1.0 1.0 1.0 Example

The pressure drop for water at 10°C, flowing at 1 x 10-3_m3_{/s through heavy}

black 11_/

2 " (DN40) pipe, can be read

from Fig. 5.08 as 220 Pa/m.

However if this pipe were rusted we would need to apply a correction factor. As the nominal pipe size required is not actually listed in Fig. 5.06 we use the next size up, 2" (DN 50). Our pressure loss is about 200 Pa so we read off a

correction factor of 3.3. We multiply our original pressure loss by this factor to find the loss for rusted pipes. 220 x 3.3 gives us 726 Pa/m.

For new pipes the pressure loss is 220 Pa/m, but for rusted pipes it would be

726 Pa/m.

Fig. 5.06

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Pressure loss in steel pipes

The following pages (5.12-5.17) tabulate the pressure loss data for water flowing in different grades of steel pipe at either 10°C or 75°C, for a range of flow rates.

Fig. 5.08 Volume flow 15mm 20 mm 25 mm 32 mm 40 mm _rate 1_/ 2 in 3/4 in 1 in 1 1/4 in 1 1/2 in l/s H G v H G v H G v H G v H G v 0.05 140 175 0.28 25.0 50 0.16 6.5 0.1 2.0 0.8 1.5 0.04 0.10 420 600 0.57 92.5 120 0.32 32.5 50 0.2 8.0 2.5 3.5 0.08 0.15 880 1500 0.85 200 250 0.48 62.5 80 0.3 17.5 0.197.5 0.12 0.20 1500 2250 1.13 320 450 0.64 120 130 0.41 27.5 0.25 12.5 0.16 0.25 3500 1.42 480 700 0.80 160 200 0.51 40.0 50 0.31 20.0 0.20 0.30 5000 1.70 660 1000 0.95 220 275 0.61 52.5 70 0.37 25.0 0.24 0.35 7000 1.98 880 1250 1.11 280 400 0.71 70.0 90 0.44 32.5 0.28 0.40 9000 2.26 1200 1750 1.27 360 500 0.82 87.5 110 0.50 42.5 50 0.32 0.45 11000 2.55 1400 2000 1.43 460 600 0.92 120 140 0.56 50.0 60 0.36 0.50 1700 2750 1.59540 800 1.02 140 175 0.62 62.5 80 0.40 0.55 3000 1.75 640 900 1.12 160 200 0.68 72.5 90 0.44 0.60 3500 1.91 760 1100 1.22 200 225 0.75 85.0 100 0.48 0.65 4500 2.07 880 1250 1.32 220 275 0.81 97.5 120 0.52 0.70 5000 2.23 1000 1500 1.43 240 320 0.87 120 140 0.56 0.75 5500 2.391200 1750 1.53 280 350 0.93 140 160 0.60 0.80 6500 2.56 1300 2000 1.63 320 400 1.00 150 175 0.64 0.85 7000 2.71 1500 2150 1.73 360 450 1.06 160 200 0.68 0.90 8000 2.87 1600 2250 1.83 380 500 1.12 180 225 0.72 0.95 9000 3.03 1800 2500 1.94 420 550 1.18 200 250 0.76 1.00 10000 3.18 2750 2.04 460 600 1.24 220 275 0.80 1.50 7000 3.06 980 1500 1.87 460 600 1.19 2.00 11000 4.08 1700 2250 2.49760 1000 1.60 2.50 3500 3.11 1200 1750 1.99 3.00 5000 3.73 1700 2250 2.39 3.50 7000 4.35 3000 2.79

Pressure loss for water flow at 10°C in steel pipes

with velocity of flow (v), for heavy grade (H) and galvanised (G) steel

Pressure loss per unit length (Pa/m) and velocity of flow (v)

Data extracted and re-arranged (uses volume flow rate rather than mass flow rate) From CIBSE Guide, tables C4-17, C21.

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H G v H G v H G v H G v 0.1 0.8 0.05 0.3 0.03 0.2 0.02 0.2 4.0 0.10 1.5 0.06 0.5 0.04 0.1 0.03 0.3 8.0 0.15 2.5 0.091.0 0.06 0.3 0.04 0.4 15.0 0.20 4.0 0.12 2.0 0.08 0.5 0.05 0.5 20.0 0.25 5.5 0.15 2.5 0.10 0.7 0.06 0.6 27.5 0.31 7.5 0.18 3.5 0.12 1.0 0.08 0.7 35.0 50.0 0.36 9.5 0.21 4.5 0.14 1.3 0.09 0.8 45.0 55.0 0.41 12.5 0.24 5.5 0.16 1.5 0.10 0.955.0 70.0 0.46 15.0 0.27 7.0 0.18 2.0 0.12 1.0 65.0 80.0 0.51 20.0 0.3 8.0 0.20 2.5 0.13 1.5 140 175 0.76 37.5 50.0 0.45 17.5 0.30 4.5 0.19 2.0 240 300 1.02 62.5 80.0 0.60 27.5 0.40 7.5 0.25 2.5 340 450 1.27 92.5 110.0 0.75 42.5 50.0 0.50 12.5 0.32 3.0 480 700 1.53 140.0 175.0 0.90 57.5 70.0 0.60 17.5 0.38 3.5 640 900 1.78 180.0 225.0 1.06 77.5 90.0 0.70 22.5 0.45 4.0 820 1250 2.04 220.0 275.0 1.21 97.5 120.0 0.80 27.5 0.51 4.5 1100 1500 2.29280.0 350.0 1.36 120.0 150.0 0.90 32.5 0.57 5.0 1300 1750 2.55 340.0 450.0 1.51 160.0 175.0 1.00 40.0 50.0 0.64 5.5 1500 2250 2.80 400.0 500.0 1.66 180.0 225.0 1.10 47.0 55.0 0.70 6.0 1800 2500 3.06 480.0 600.0 1.81 220.0 250.0 1.20 55.0 70.0 0.76 6.5 3000 3.31 540.0 700.0 1.96 240.0 300.0 1.29 65.0 80.0 0.83 7.0 3500 3.57 620.0 800.0 2.11 280.0 350.0 1.3972.5 90.0 0.89 7.5 4000 3.82 720.0 1000.0 2.26 320.0 400.0 1.4982.5 100.0 0.96 8.0 4500 4.08 800.0 1100.0 2.41 360.0 450.0 1.5992.5 110.0 1.02 8.5 5000 4.33 900.0 1250.0 2.56 400.0 500.0 1.69 110.0 130.0 1.08 9.0 5500 4.59 1000.0 1350.0 2.71 440.0 550.0 1.79 120.0 140.0 1.15 9.5 6000 4.84 1200.0 1500.0 2.87 500.0 650.0 1.89 130.0 160.0 1.21 10 7000 5.10 1300.0 1750.0 3.02 540.0 700.0 1.99 140.0 175.0 1.27 11 8000 5.61 1500.0 2000.0 3.32 640.0 800.0 2.19180.0 200.0 1.40 12 1800.0 2250.0 3.62 760.0 1000.0 2.39200.0 250.0 1.53 13 2750.0 3.92 880.0 1250.0 2.59 240.0 300.0 1.66 14 3200.0 4.22 1000.0 1350.0 2.79280.0 350.0 1.78 15 3500.0 4.52 1200.0 1500.0 2.99 300.0 400.0 1.91 16 4000.0 4.82 1300.0 1750.0 3.18 340.0 450.0 2.04 17 4500.0 5.13 1500.0 2000.0 3.38 380.0 500.0 2.17 18 5500.0 5.43 1700.0 2250.0 3.58 420.0 550.0 2.29 196000.0 5.73 1800.0 2500.0 3.78 480.0 600.0 2.42 Volume flow 50 mm 65 mm 80 mm 100 mm rate 2 in 2 1_/ 2 in 3 in 4 in l/s

Pressure Loss for water flow at 10°C in steel pipes

With velocity of flow (v), for heavy grade (H) and galvanised (G) steel.

Volume flow 15mm 20 mm 25 mm 32 mm 40 mm rate 1_/ 2 in 3/4 in 1 in 1 1/4 in 1 1/2 in litres/sec _{H M v H M v H M v H M v H M v} 0.05 90 65 0.28 20 15 0.16 6.5 5 0.1 2.0 1.5 0.06 0.8 0.7 0.04 0.10 360 240 0.57 70 55 0.32 22.5 20 0.2 5.5 5 0.12 2.5 2.5 0.08 0.15 760 500 0.85 160 120 0.48 47.5 35 0.3 12.5 90.195.5 4.5 0.12 0.20 1300 880 1.13 260 200 0.64 82.5 60 0.41 20 17 0.25 9.0 7.5 0.16 0.25 2000 1400 1.42 400 300 0.80 140 90 0.51 30 25 0.31 15 12.5 0.20 0.30 1900 1.70 560 420 0.95 180 140 0.61 42.5 35 0.37 20 17.5 0.24 0.35 760 560 1.11 240 180 0.71 55 45 0.44 25 22.5 0.28 0.40 960 720 1.27 300 220 0.82 70 55 0.50 35 27.5 0.32 0.45 1200 900 1.43 380 300 0.92 85 70 0.56 40 35 0.36 0.50 1500 1100 1.59460 340 1.02 120 85 0.62 50 40 0.40 0.55 1900 1400 1.75 540 400 1.12 140 100 0.68 60 50 0.44 0.60 1600 1.91 660 480 1.22 160 120 0.75 65 55 0.48 0.65 1900 2.07 780 560 1.32 180 140 0.81 80 67.5 0.52 0.70 2.23 900 660 1.43 200 160 0.87 90 75 0.56 0.75 2.391000 740 1.53 240 200 0.93 100 85 0.60 0.80 2.56 1200 840 1.63 260 220 1.00 120 97.5 0.64 0.85 2.71 1300 980 1.73 300 240 1.06 140 120 0.68 0.90 2.87 1500 1100 1.83 320 260 1.12 160 130 0.72 0.95 3.03 1600 1200 1.94 360 280 1.18 180 140 0.76 1.00 3.18 1900 1300 2.04 400 320 1.24 200 160 0.80 1.50 840 680 1.87 320 1.19 2.00 1500 1200 2.49540 1.60 2.50 1800 3.11 840 1.99 3.00 1200 2.39 3.50 1600 2.79

Pressure loss per unit length (Pa/m) and velocity of flow (v) Pressure loss for water flow at 75°C in

steel pipes

with velocity of flow (v), for heavy grade (H) and medium grade (M) steel

Fig. 5.09

Data extracted and re-arranged (uses volume flow rate rather than mass flow rate) From CIBSE Guide, tables C4-11, C4-12.

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7

8

H M v H M v H M v H M v 0.1 0.8 0.7 0.05 0.3 0.2 0.03 0.2 0.1 0.02 0.2 3.0 2.5 0.10 0.8 0.7 0.06 0.4 0.4 0.04 0.1 0.1 0.03 0.3 6.0 5.0 0.15 2.0 1.5 0.090.7 0.7 0.06 0.2 0.2 0.04 0.4 9.0 8.5 0.20 3.0 2.5 0.12 1.5 2.5 0.08 0.4 0.3 0.05 0.5 15.0 12.5 0.25 1.0 3.5 0.15 2.0 3.5 0.10 0.5 0.5 0.06 0.6 20.0 17.5 0.31 5.5 5.0 0.18 2.5 2.0 0.12 0.7 0.7 0.08 0.7 27.5 25.0 0.36 7.5 6.5 0.21 3.5 3.0 0.14 0.90.8 0.09 0.8 35.0 30.0 0.41 9.5 8.0 0.24 4.5 4.0 0.16 1.2 1.4 0.10 0.942.5 37.5 0.46 12.5 10.0 0.27 5.0 5.0 0.18 1.5 1.5 0.12 1.0 55.0 45.0 0.51 15.0 12.5 0.3 6.5 5.5 0.20 2.0 2.0 0.13 1.5 120 95 0.76 30.0 27.5 0.45 15.0 12.5 0.30 3.5 3.5 0.19 2.0 200 180 1.02 50.0 45.0 0.60 22.5 20.0 0.40 6.0 5.5 0.25 2.5 300 260 1.27 77.5 67.5 0.75 35.0 30.0 0.50 9.0 8.5 0.32 3.0 420 360 1.53 120.0 95.0 0.90 47.5 42.5 0.60 12.5 12.5 0.38 3.5 580 480 1.78 160.0 140.0 1.06 62.5 57.5 0.70 17.5 17.5 0.45 4.0 740 640 2.04 200.0 180.0 1.21 82.5 75.0 0.80 22.5 20.0 0.51 4.5 920 780 2.29 240.0 220.0 1.36 120.0 92.5 0.90 27.5 25.0 0.57 5.0 1200 960 2.55 300.0 260.0 1.51 140.0 120.0 1.00 32.5 30.0 0.64 5.5 1400 1200 2.80 360.0 320.0 1.66 160.0 140.0 1.10 40.0 37.5 0.70 6.0 1700 1400 3.06 420.0 360.0 1.81 180.0 160.0 1.20 47.5 42.5 0.76 6.5 3.31 480.0 440.0 1.96 220.0 20.0 1.29 55.0 50.0 0.83 7.0 3.57 560.0 500.0 2.11 240.0 220.0 1.3962.5 57.5 0.89 7.5 3.82 640.0 560.0 2.26 280.0 260.0 1.4970.0 65.0 0.96 8.0 4.08 720.0 640.0 2.41 320.0 300.0 1.5980.0 72.5 1.02 8.5 4.33 820.0 720.0 2.56 360.0 320.0 1.6990.0 82.5 1.08 9.0 4.59 920.0 820.0 2.71 400.0 360.0 1.79 100.0 90.0 1.15 9.5 4.84 1200.0 880.0 2.87 440.0 400.0 1.89 120.0 100.0 1.21 10 5.10 980.0 3.02 480.0 440.0 1.99 130.0 120.0 1.27 11 5.61 1200.0 3.32 580.0 520.0 2.19150.0 140.0 1.40 12 6.12 1400.0 3.62 680.0 600.0 2.39160.0 160.0 1.53 13 1700.0 3.92 820.0 720.0 2.59 200.0 200.0 1.66 14 1900.0 4.22 920.0 820.0 2.79 240.0 220.0 1.78 15 1100.0 940.0 2.99 280.0 260.0 1.91 16 1200.0 1100.0 3.18 300.0 280.0 2.04 17 1400.0 1200.0 3.38 340.0 320.0 2.17 18 1500.0 1400.0 3.58 380.0 360.0 2.29 191700.0 1500.0 3.78 420.0 400.0 2.42 Volume flow 50 mm 65 mm 80 mm 100 mm rate 2 in 2 1_/ 2 in 3 in 4 in l/s

Pressure loss for water flow at 75°C in steel pipe

with velocity flow (v ) for heavy grade (H) and medium grade (M) steel

Pressure loss per unit length (Pa/m) and velocity of flow (v)

Pressure loss for water flow at 75°C in steel pipe

with velocity flow (v), for galvanised (G) steel Volume flow 15mm 20mm 25mm 32mm 40mm rate 1_/ 2in 3_/ 4 in 1 in 1 1_/ 4 in 1 1_/ 2 in litres/second G v G v G v G v G v 0.05 140 0.28 50 0.16 0.10 550 0.57 100 0.32 50 0.2 0.15 1250 0.85 225 0.48 70 0.3 0.20 2250 1.13 400 0.64 110 0.41 0.25 3500 1.42 600 0.80 175 0.51 50 0.31 0.30 5000 1.70 900 0.95 250 0.61 55 0.37 0.35 7000 1.98 1250 1.11 350 0.71 70 0.44 0.40 9000 2.26 1500 1.27 450 0.82 100 0.50 0.45 11000 2.55 2000 1.43 550 0.92 120 0.56 50 0.36 0.50 2250 1.49700 1.02 140 0.62 70 0.40 0.55 2750 1.75 800 1.12 175 0.68 80 0.44 0.60 3500 1.91 1000 1.22 200 0.75 90 0.48 0.65 4000 2.07 1250 1.32 250 0.81 110 0.52 0.70 4500 2.23 1350 1.43 275 0.87 120 0.56 0.75 5000 2.391500 1.53 325 0.93 140 0.60 0.80 6000 2.56 1750 1.63 350 1.00 165 0.64 0.85 7000 2.71 2000 1.73 400 1.06 175 0.68 0.90 7500 2.87 2250 1.83 450 1.12 200 0.72 0.95 8000 3.03 2500 1.94 500 1.18 225 0.76 1.00 9000 3.18 2750 2.04 550 1.24 250 0.80 1.5 6000 3.06 1250 1.87 550 1.19 2.0 11000 4.08 2250 2.491000 1.60 2.5 3500 3.11 1500 1.99 3.0 5000 3.73 2250 2.39 3.5 7000 4.35 3000 2.79 4.0 9000 4.98 4000 3.18 4.5 11000 5.60 5000 3.58 5.0 6000 3.98 5.5 7000 4.38 6.0 9000 4.78 6.5 10000 5.18 7.0 11000 5.57

Pressure loss per unit length (Pa/m) and velocity of flow (v)

Fig. 5.10

Data extracted and re-arranged (uses volume flow rate rather than mass flow rate) From CIBSE Guide, tables C4-16.

1

2

3

4

5

6

7

8

Pressure loss per unit length (Pa/m) and velocity of flow (v)

0.8 50 0.41 0.955 0.46 1.0 70 0.51 1.5 150 0.76 50 0.45 2.0 275 1.02 70 0.60 2.5 400 1.27 100 0.75 50 0.50 3.0 600 1.53 140 0.90 60 0.60 3.5 800 1.78 200 1.06 80 0.70 4.0 1000 2.04 250 1.21 110 0.80 4.5 1500 2.29350 1.36 130 0.90 5.0 1750 2.55 400 1.51 175 1.00 5.5 2000 2.80 500 1.66 200 1.10 50 0.70 6.0 2250 3.06 550 1.81 250 1.20 60 0.76 6.5 2750 3.31 700 1.96 275 1.29 70 0.83 7.0 3250 3.57 800 2.11 350 1.3980 0.89 7.5 3500 3.82 900 2.26 400 1.49 90 0.96 8.0 4000 4.08 1000 2.41 450 1.59100 1.02 8.5 4500 4.33 1100 2.56 500 1.69120 1.08 9.0 5000 4.59 1250 2.71 550 1.79 130 1.15 9.5 6000 4.84 1350 2.87 600 1.89 140 1.21 10.0 6500 5.10 1500 3.02 700 1.99 160 1.27 11.0 8000 5.61 1850 3.32 800 2.19200 1.40 12.0 2250 3.62 900 2.39 225 1.53 13.0 3750 3.92 1150 2.59 275 1.66 14.0 3000 4.22 1250 2.79300 1.78 15.0 3500 4.52 1500 3.00 350 1.91 16.0 4000 4.82 1750 3.18 400 2.04 17.0 4500 5.13 2000 3.38 450 2.17 18.0 5000 5.43 2100 3.58 500 2.29 19.0 5500 5.73 2250 3.78 550 2.42 20.0 6000 6.03 2500 4.00 700 2.55

Pressure loss for water flow at 75°C in steel pipes

with velocity of flow (v), for galvanised (G) steel Volume flow 50mm 65mm 80mm 100mm rate 2 in 2 1_/ 2 in 3 in 4 in litre/ second G v G v G v G v Fig. 5.10 (contd.)

The internal pipe diameters are (pipe diameter Fig. 5.14)

For 2" pipe di = 51.3 x 10-3m

11_/

4 " pipe di = 34.4 x 10-3m

First calculate the flow velocities. v = Q = flow rate (m3_/s) A cross-sectional area (m2₎ for 2" pipe v = 1x10-3 π x (57.3 x10-3 ₎2 4 = 0.39m/s for 11_/ 4" pipe v = 1x10-3 π x (34.3 x10-3₎2 4 = 1.08m/s Pipe losses

The total amount of straight pipe in the system is as follows:

3m of 2" pipe 2m of 11_/

4" pipe

From Fig. 5.08 we read off the following values for pressure loss per metre:

2" pipe 65Pa/m 11_/

4" pipe 460 Pa/m

So the total pressue loss due to straight pipe is

∆ppi = 3x65 + 2x460 = 1115 Pa

Fitting losses

We need to split the fitting losses into two sections, one for the 2" pipe fittings and the other for the11_/

4" pipe fittings.

Reductions or enlargements, connecting pipes of different diameters, are included in the section for the smaller pipe. So here the reduction is included in the 11_/

4"

fittings.

2" Pipe Fittings

The only fitting to be considered here is

the diverging junction. We read its basic

ζ - value from table 2 as 0.5.

Then we add a factor for a 90° elbow which is 0.7

So we have ζTOTAL = 0.6 + 0.7 = 1.3

The pressure loss is calculated from :

∆p = ζ ρ v2 2 = 1.3 x (1000 )x (0.39)2 2 = 99 Pa 11_/ 4" Fittings

Here we have a reduction and a 45° elbow to consider.

For the 45° elbow we have ζ = 0.6. For the reduction we need to find A2/A1

π x (34.4x10-3₎2

A1 = 4 = 0.45

A2 π x (51.3x10-3)2

4

This is between the values for ζ=0.40 and ζ=0.25, so we take the larger value.

ζTOTAL = 0.6 + 0.4 =1.0

The pressure loss here is

∆p = ζ ρ v2 _{= 1.0 x (1000) x (1.08)}2

2 2 = 583 Pa

So the total pressure loss due to fittings is

∆pfi = 583 +99 = 682 Pa

Total Loss

The total pressure loss will be

∆ppi + ∆pfi = 1115 + 682 = 1797 Pa

The total pressure loss is 1.8 kPa

Example 1

What is the pressure loss for the system below, made of heavy grade steel pipe, when water flows at 10°C? The flow rate is 1litre/second.

Fig 130 Fig 240 Fig 41

3m 1m 2" (DN 50) pipe Reducer 45° Elbow 11_{/4" (DN 32)} 90° Diverging Junction 11 /4_{" (DN 32)} 1m Fig. 5.11

1

2

3

4

5

6

7

8

So Re = 0.28 x (0.067) 1.3x10-6 = 14430

The roughness is given in Fig. 5.13 as 6.9x10-4 _{and we combine this with our}

Reynolds number in the Moody diagram to find the friction factor (f).

f = 0.0075 So the equivalent length is:

lef = 2.4 x 0.067

4 x 0.0075 = 5.36

Now we add this equivalent length to the real length of straight pipe to get an effective length.

Effective length = 25m + 5.36m = 30.36m The pressure loss per unit length for 65mm pipe with a flow rate of 1l/s is 20Pa/m. So we multiply this value by our effective length to get a total pressure loss.

∆pTOTAL = 20•30.36 = 607.2 Pa

So we lose 607.2 Pa of pressure in this part of the system.

Example 2

Consider part of a system of 21_/ 2"

(DN65) heavy grade steel pipe as shown below. Water is flowing at a rate of 1 litre per second at 10°C.

Let's approach this problem from the perspective of equivalent lengths. Pipe: There is 25m of straight pipe. Fittings: There are four 90° elbow fittings 21_/

2" (DN65), which each have a ζ of 0.6.

So,

ζTOTAL = 2.4

To find the equivalent length of these fittings we use

lef = ζdi

4f

We need to find the Reynolds number to use this formula.

Re = vdi

ν

The flow velocity for 21_/

2" (DN65) pipe

with a flow rate of 1 litre per second is found below. v = Q = flow rate (m3_/s) A cross-sectional area (m2₎ = 1 x 10-3 π x (67 x 10-3₎2 4 = 0.28 m/s 5m Fig 90 5m 5m 5m 5m Fig. 5.12

Internal Diameters of Pipes

Nominal pipe size Mean internal diameter/mm Mild Steel BS 1387

mm inches Medium black Heavy black Heavy Galvanised

Useful Pipe Properties

Relative Roughness

Nominal pipe size Relative roughness Mild steel BS 1387

mm inches Medium black Heavy black Heavy Galvanised 10 3_/ 8 3.7x10-3 4.1x10-3 1.4x10-2 15 1_/ 2 2.9 x 10-3 3.1 x 10-3 1.4 x 10-2 20 3_/ 4 2.1x10-3 2.2x10-3 7.5x10-3 25 1 1.7x10-3 _1.8x10-3 _5.9x10-3 32 1 1_/ 4 1.3x10-3 1.3x10-3 4.4x10-3 40 1 1_/ 2 1.1x10-3 1.1x10-3 3.8x10-3 50 2 8.7x10-4 _9.0x10-4 _2.9x10-3 65 2 1_/ 2 6.7x10-4 6.9x10-4 2.3x10-3 80 3 5.7x10-4 _5.8x10-4 _1.9x10-3 100 4 4.4x10-4 _4.5x10-4 _1.5x10-3 10 3_/ 8 12.4 11.3 10.8 15 1_/ 2 16.1 14.914.4 20 3_/ 4 21.6 20.4 19.9 25 1 27.3 25.7 25.2 32 11_/ 4 36.0 34.4 33.9 40 11_/ 2 41.940.3 39.8 50 2 53.0 51.3 50.8 65 21_/ 2 68.7 67.0 66.5 80 3 80.7 79.1 78.6 100 4 105.1 103.5 102.8

Pipe Wall Thicknesses

Nominal pipe size Wall Thickness/mm Mild Steel BS 1387

mm inches Medium black Heavy black

10 3_/ 8 2.3 2.9 15 1_/ 2 2.6 3.2 20 3_/ 4 2.6 3.2 25 1 3.2 4.0 32 11_/ 4 3.2 4.0 40 11_/ 2 3.2 4.0 50 2 3.6 4.5 65 21_/ 2 3.6 4.5 80 3 4.0 5.0 100 4 4.5 5.4

Extract from CIBSE Guide Table C4.5. Fig. 5.13

Fig. 5.14

Fig. 5.15 Extract from CIBSE Guide Table C4.4.

1

2

3

4

5

6

7

8

Valves - Pressure Loss

Flow rate/ Flow factor

The flow value or kv factor is a

convenient means of calculating flow rates in hydraulics. It allows for all internal resistances and for practical purposes is regarded as reliable.

The kv factor is defined as the flow rate

of water in litres per minute with a pressure drop of 1 kg/cm2 _{across the}

valve.

The relationships between kv factor, flow

rate (Q) and pressure drop (∆p) are given in the following formulae.

Liquids with kinematic viscosity less than 22 centistokes (22 x 10-6 _m2_/s)

e.g. water, hydraulic oil

kv = Q or Q = kv

or ∆p = ρ x Q2

where Q = flow rate (litres per minute)

ρ = density of the liquid (kg/dm3₎

∆p = pressure drop (kg/cm2 ₎

Liquids with kinematic viscosity greater than 22 centistokes

The effect of viscosity, caused by friction between the particles of the fluid, is no longer negligable, and the flow rate is reduced. The flow factor must be multiplied by a correction factor, c, to give a new flow factor, kvn.

kvn = kv x c

The correction factor is given by: kv2

Gases

Qg = 30.8 kv

valid for ∆p < only where

Qg = flow rate (m3 / hour)

kv = flow factor for water

(dimensionless)

∆p = pressure drop (kg / cm2₎

= p1-p2

p1 = absolute inlet pressure (bar)

p2 = absolute outlet pressure (bar)

ρ = density of gas at 0°C (kg/m3₎

T = absolute temperature (Kelvin) = 273 + t

t = temperature in Celsius (°C) where ν = kinematic viscosity

(centistokes)

kv= flow factor for water

(dimensionless)

Q = flow rate (litres/minute)

p₁ 2 ρ ∆p ∆p ρ ∆p x p₂ ρx T

Where there are several flow factors in series, the resultant k_v factor is

Where the flow factors are in parallel, the resultant k_v factor is

kvx = kv1 + kv2 + kv3 + …… + kvn

kvx2 kv12 kv22 kv32 kvn2

= + + + …+ 1 1 1 1 1

Flow Value Conversion Table

kv 1 14.28 17.09

kv Cv f

All references are in metric (kv) units. For

imperial (f) or american (cv) units the following conversions may be used:

Given Q = 300 litres/min ρ = 1 kg/dm3 ∆p = p1 – p2 = 0.5 – 0 = 0.5 kg/cm2 kvp = ? kvp = Q = 424 Solution to part 2

First it is necessary to calculate the kv

factor for the total system (kvt).

The kv factor for the valve (kvv) can now

be established by subtracting the kv

factor for the pipline (kvp) from the kv

factor for the total system (kvt). For this

purpose, the formula for calculating flow factors in series should be used, which is

thus

=7.98 ×10-6_{– 5.56} ×₁₀-6

= 2.42 ×10-6

kvv =

= 643

In this example, the kv factor for the valve

has been determined by calculation. It may also be found by the simpler method of reading off the nomograph,

Fig. 5.20.

kvv2 kvt2 kvp2

Part1

What is the kv factor for a 11/4" water

pipeline with a flow of 300 litres/min, an inlet pressure of 0.5 bar and an outlet pressure of 0 bar?

Part 2

If a valve has to be fitted and the minimum acceptable flow rate in the pipline is 250 litres/min, which type of valve should be used?

Part 3

Having established which type of valve should be used, what will be the true flow rate of the system?

Solution to part 1

Calculate the kv for the pipeline (kvp)

Example 2 1 kvx2 kv12 kv22 = + kvv2 354 2 424 2 = = -Given Q =250 litres/min ρ = 1kg/dm3 ∆p = p1 – p2 = 0.5 – 0 = 0.5 kg/cm2 kvt= ? = 300 ρ ∆p 1 0.5 0 .5 1 2.42 ×10-6 kvt = 250 kvt = 354 1 1 1 1 1 1 1 1 1 Fig. 5.18 Fig. 5.17

1

2

3

4

5

6

7

8

The section of the nomograph

reproduced above allows us to read off the reciprocals of the squares of the flow factors.

kvt=354 gives 8.5 x10-6 and

kvp=424 gives 6 x10-6

We find the reciprocal of kvv by

subtracting these two values. 8.5 x10-6 _{- 6 x10}-6 _{= 2.5 x10}-6

The value for the flow factor

corresponding to 2.5×10-6 _{can also be}

read from the nomograph. Thus, kvv = 640

The valve used must therefore be one with a minimum kv100 factor of 640.

A typical value for a ball valve, which could be used in this example is kvv = 800

(kv valves are supplied by valve

manufacturers).

by using the nomograph:

= 6 x10-6 _{+ 1.5 x 10}-6

= 7.5 x10-6

kvt = 365

The true flow for the system can now be calculated as follows: Q = kv = 365 = 258 litres/min 1 kvt2 1 1 1 kvt2 kvp2 kv 2(ball valve) = + Solution to part 3

First, calculate the k_v factor for the pipline with the 11_{/4" ball valve installed.}

∆p

ρ

0.5 1

Nomogram for valve losses

Fig. 5.20

ρ

(kg/dm3₎

1

2

3

4

5

6

7

8

3. Connect the point on reference line F

to the working pressure (line E). Extend this line to line G.

4. Read the value of the pressure drop at

this intesection point.

Example

The problem below is solved by the dotted lines on the nomogram.

Pipe length = 300m

Free air flow = 175 litres/second Pipe inner diameter = 90mm Working pressure = 9 bar

Following the steps above we draw the 3 lines shown on the nomogram. The final line intersects line G at approximately 0.04. So the pressure drop is 0.04 bar. A general rule is that the velocity of compressed air must be less than 6 m/s . Using this restriction we find maximum flow values through medium grade steel as given in Fig. 5.21.

Maximum Recommended Flow of Compressed Air at 7 bar

Compressible Fluids

Fluids such as air and steam are compressible. A force acting on them may decrease the fluid volume (increasing its density) rather than causing movement of the fluid. This density change will lead to a pressure drop. If this drop in pressure is less than 10% of the inlet pressure we can treat the fluid as incompressible. If this is not the case then new equations must be used to describe the flow depending on the type of fluid and the surrounding conditions.

Compresssed Air

Pipe Losses

For compressed air the pressure drop can be found from the following equation

∆p = 1.6 x 108 _{x V} 1.85 _{x L}

d5 _{x P}

∆p= pressure drop (bar) V = free air flow (m3_/s)

L = pipe length (m)

d = inside pipe diameter (mm) P = initial pressure (bar)

Values can be inserted directly into this formula, or the nomogram (Fig. 5.22) can be used. The nomogram gives the free air flow in litres/second and the pressure drop in bar. Conversions to cubic metres per second and pascal are given below. m3_{/s = l/s x 10}-3

bar = 105 _Pa

To use the nomogram, follow these steps:

1. Connect pipe length (line A) to free air

flow (line B). Extend this line to the first reference line (line C).

2. Connect the point found on this

10 5 15 10 20 17 25 25 32 50 40 65 50 100 65 180 80 240 100 410

Nominal bore Rate of air flow (mm) (litres/second)

Air Flow through Black Iron Pipes

1

2

3

4

5

6

7

8

90° Elbow 0.2 0.3 0.4 0.6 0.8 1.3 1.6 Bend 0.1 0.2 0.3 0.5 0.6 1.0 1.2

Run of Tee Junction 0.2 0.3 0.5 0.8 1.0 1.6 2.0

Branch of Tee Junction 0.6 1.0 1.5 2.4 3.0 4.8 6.0

Reducer - 0.3 0.5 0.7 1.0 2.0 2.5

15 20 25 40 50 80 100

Fitting Losses

For compressed air the pressure loss for a system is most easily calculated using equivalent lengths. The following table gives the equivalent lengths for fittings of various pipe sizes.

Now we can use the nomogram (Fig. 5.22) to find the pressure drop.

Effective pipe length = 23.6 Free air flow = 0.2m3_{/s = 200 l/s}

Nominal Pipe diameter = 40mm Working pressure = 10 bar The pressure drop is found to be approximately 0.4 bar.

Fig. 5.23

1_/

2 3/4 1 11/2 2 3 4

Example

A compressed air system where air flows at 0.2m3_{/s has a working pressure of 10}

bar (10 x105_{Pa) and consists of 20m of}

11_/

2" (DN 40) straight pipe with the

following fittings: 2 x 90° elbow

1 x tee: air flows through the branch of the tee

First we find the equivalent length of the fittings.

The 90° elbow has an equivalent length of 0.6m.

The tee has an equivalent length of 2.4m. So the total equivalent length of the fittings

Fitting Equivalent pipe length (m) pipe diameter

Nom. Size DN

lef = 2 x 0.6 + 2.4 = 3.6m

Adding the length of straight pipe to this value gives the effectve length of the system. 3.6 + 20 = 23.6 Fig 130 11_/ 2 5m Fig 90 11_/ 2

Pressure Loss - Equivalent Pipe Lengths

di = pipe inside diameter (m)

V = volume flow rate (m3_/s)

f = friction factor

Applying the method used in the analysis of water flow we calculate the friction factor (f) from the Reynolds number.

Re = vdi

ν

Values for the friction factor are given in the table Fig.5.26 below:

10 3_/ 8 0.035 0.0290.027 0.027 25 1 0.033 0.025 0.023 0.023 50 2 0.032 0.022 0.020 0.019 80 3 0.032 0.021 0.018 0.017 100 4 0.031 0.020 0.017 0.016

Pressure Loss

Pipe losses

The pressure loss for steam flowing in a straight pipe is given by:

∆p = 6.48 fρ V2

di 100000

∆p = pressure loss per unit length (Pa/m)

ρ = density (kg/m3₎

Steam

Steam is another compressible fluid which behaves in a similar way to compressed air. Two important factors to remember when laying steam piping are that temperature changes can lead to expansion or contraction, which must not put any excessive stress on the system, and that no water should be allowed to collect anywhere in the system. Each time the system is started from cold there will be water of condensation to dispose of. Another consideration is that if the velocity exceeds about 60 m/s the system may become intolerably noisy. The volume flow rate corresponding to a velocity of 60m/s is given below for various pipe sizes.

Maximum Flow rates corresponding to a velocity of 60m/s at 100°C

Nominal size Max. volume flow rate mm inches (l/s) 10 3_/ 8 6.1 20 3_/ 4 19.6 25 1 31.0 32 11_/ 4 55.6 40 11_/ 2 76.3 50 2 121.2 65 2 1_/ 2 211.3 80 3 294.1 100 4 504.2

The density and viscosity of steam at various temperatures is given in Fig. 5.27

(Properties of Saturated Steam).

Pipe size Reynolds no. mm in 104 ₁₀5 ₁₀6 ₁₀7

Fitting losses

The pressure loss due to the fitting is found using:

∆p = ζρ v2

2

where ∆p = pressure loss (Pa)

ζ = pressure loss factor (dimensionless)

ρ = density (kg/m3₎

v = velocity (m/s)

Fig. 5.25

The pressure loss can now be calculated.

Fig. 5.26

1

2

3

4

5

6

7

8

bar Pressure Temperature Density Kinematic Viscosity kPa ° C kg/m3 ρ _(m2_/s) ν

Properties of Saturated Steam

0.5 50 81.35 0.3095.2 x 10-5 1.0 100 99.63 0.590 2.7 x 10-5 1.5 150 111.37 0.863 1.9 x 10-5 2.0 200 120.23 1.1291.4 x 10-5 2.5 250 127.43 1.391 1.2 x 10-5 3.0 300 133.54 1.650 1.0 x 10-5 3.5 350 138.88 1.908 4.0 400 143.63 2.165 8.4 x 10-6 4.5 450 147.92 2.415 6.6 x 10-6 5.0 500 151.85 2.667 6.0 x 10-6 6.0 600 158.84 3.165 5.1 x 10-6 7.0 700 164.96 3.663 4.4 x 10-6 8.0 800 170.41 4.167 3.8 x 10-6 9.0 900 175.36 4.651 3.4 x 10-6 10.0 1000 179.88 5.155 3.1 x 10-6 12.0 1200 187.96 6.135 2.6 x 10-6 14.0 1400 195.04 7.092 2.3 x 10-6 18.0 1800 207.10 9.091 1.8 x 10-6 20.0 2000 212.37 10.000 1.6 x 10-6 22.0 2200 217.24 10.989 1.5 x 10-6 24.0 2400 221.78 12.048 1.3 x 10-6 28.0 2800 230.04 14.085 1.1 x 10-6 Fig. 5.27

The pressure waves travel along at speeds limited by the speed of sound in the medium, causing the pipe to expand and contract. The energy carried by the wave is dissipated and the waves are progressively damped. (see Figure ?) The pressure excess due to water hammer must be considered in addition to the hydrostatic load, and this total pressure must be sustainable by the pipng system. In the case of oscillatory surge pressures extreme caution is needed as surging at the harmonic frequency of the system could lead to catastrophic damage.

Water Hammer

Water hammer, or surge pressure, is a term used to describe dynamic surges caused by pressure changes in a piping system. They occur whenever there is a deviation from the steady state, i.e. when the velocity of the fluid is increased or decreased, and may be transient or oscillating. Waves of positive or

negative pressure may be generated by any of the following:

1. opening or closing of a valve 2. pump start up or shut down 3. change in pump or turbine speed

4. wave action in a feed tank 5. entrapped air

The maximum positive or negative addition of pressure due to surging is a function of fluid velocity, bulk modulus of elasticity of the fluid, pipe dimensions and the modulus of elasticity of the pipe material. It can be calculated using the following steps.

Pressure Change

Wavelength

Damped pressure wave

Step 1

Determine the velocity of the pressure wave

Vw =

where

Vw= velocity of pressure wave (m/s)

K = bulk modulus of elasticity of fluid (Pa) ρ = fluid density (kg/m3₎ ρ x (1 + ) K K x di t x E

E = modulus of elasticity of pipe wall (Pa)

d_i = pipe inner diameter (mm) t = pipe wall thickness (mm)

1

2

3

4

5

6

7

8

Step 4

Compare the maximum total pressure due to water hammer, calculated in step 3, with the maximum allowable pressure

Step 2

Calculate maximum pressure change due to surging.

∆p = Vw x ∆v x ρ x 10-5

where ∆p = maximum pressure change (bar)

Vw = velocity of pressure wave

(m/s) (see step 1)

∆v = change in fluid velocity (m/s) = (v1-v2)

v1 = velocity of fluid before

change (m/s) v2 = velocity of fluid after

change ( m/s)

ρ = density of fluid (kg/m3₎

NB. All pressure rises induced by a flow reduction will have a corresponding reflected pressure drop (vacuum). If this exceeds the expected static minimum operation pressure it must not exceed the collapsing pressure for safe operation of the system.

Step 3

Calculate the maximum and minimum total pressures

pmax = P + ∆p

pmin = P – ∆p

where pmax = maximum total pressure

(bar)

pmin = minimum total pressure

(bar)

P = expected operating pressure (bar)

∆p = change due to surge pressure (calculated in step 2)

withstand this water hamer pressure instantaneously. As long as the

calculated maximum total pressure due to water hammer is within the maximum allowable pressure for a system the effects of water hammer will not be serious. The exception to this rule is when the pressure surges are oscillatory (e.g. from a positive displacement pump). In this case the system must be treated as if a load equal to the maximum total pressure, Pmax, exists throughout the

lifetime of the pipe.

If the total pressure due to water hammer does not fall within these limits an

increase in pipe diameter should be considered, or measures should be taken to reduce surge occurance (i.e. actuated valves, surge tanks, slow start-up pumps). When using actuated valves it is

common to design valves with closure times greater than the critical period Tc to

reduce water hammer. The critical period is the time taken by the pressure wave to complete one circuit of the pipeline.

2L Vw

where Tc = critical period

L = pipe length (m)

Vw = pressure wave velocity

(m/s) Tc =

Step 2

Find velocity of fluid before change

v1 =

=

= 0.32 m/s

assume water velocity goes to zero after the valve is closed i.e. ∆v = 0.32m/s Find pressure change

∆p = 1286 x (0.32) x 1000 x 10-5

= 4.12 bar

Example

Water piping from a storage tank is connected to a primary shut-off valve, which is hydraulically actuated with an electrical remote control. The water flow rate is Q= 10m3_{/h. The working pressure}

is 6 bar.

The pipe details are:

material medium grade steel

Nom. size 100 inner diameter 105 mm wall thickness 4.5 mm pipeline length 500m operating temp. 40°C Modulus of elasticity E = 200 x 109 other information: water density ρ = 1000 kg/m3 bulk modulus of water K = 2.05 GPa Step 1

Find velocity of pressure wave Vw =

= 1286 m/s

Step 3

Find maximum pressure

Pmax = 6 + 4.12 = 10.12 bar

∆p < p so the minimum pressure is positive. If the minimum pressure was negative (i.e. ∆p > p), then we would need to ensure that all the components in the system could withstand the negative pressure. 1000 x 1 +105 x 2.05 x 109

)

4.5 x 200 x 109 2.05 x109

(

cross-sectional area volume fluid flow

π (0.105 / 2 )2 _m2

10/60 x 60 m3_/s

Step 4

The maximum total pressure due to water hammer is 10.12 bar. If this value is less than the maximum allowable

instantaneous pressure in our system then the effects of water hammer are acceptable. If it is not, adjustments need to be made to pipe dimensions, or valve closing time, to reduce water hammer.

What is the critical period? Tc = 2L = 2 x 500

Vw 1286

= 0.78s

If we use an actuated valve with a closing time greater than this critical period ( e.g. a closing time of 1.5s) this will help to reduce water hammer.