Introduction to Industrial Automation

Example 5.1:  Internal Diameter Calculation of a Pressurized Air Distribution Pipe.

The consumption of pressurized air in a factory is at a level of 800 m

3

/hr. The distribution pipe will 

have a length of 300 m and it will contain six T-connectors, five 90°-curve connectors and one two-

way valve. For this application, the allowable drop of pressure will be 0.04 bar, while the operation 

pressure should be 9 bar.

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  Introduction to Industrial Automation

In the nomogram of Figure 5.1, the first vertical line indicates the length of the pipe, while the 

second line refers to the flow of the pressurized air. The point L = 300 m in the first line and the 

point Q = 800 m

3

/hr in the second line defines a straight line that intercepts Axis 1 at Z

1

. The fourth 

line represents the operational pressure and the fifth line represents the allowable pressure drop. 

Point P = 9 bar in the fourth line and point 

Δ

P = 0.04 bar in the fifth line defines a line that inter-

cepts Axis 2 at the point Z

2

. The previously defined points Z

1

 and Z

2

 in Axes 1 and 2 correspond-

ingly define a line that intersects the third line at one point that expresses the internal diameter of 

the required pipe. Based on all these calculations, the resulting internal diameter of the pressurized 

air distributed pipe is D = 90 mm.

Subsequently, the pressure drop that is created from the various equipment of having a diameter 

equal to the calculated one (D = 90 mm), should be taken into consideration. The nomogram of 

Figure 5.2 provides an equivalent length for the five types of equipment. Each one has an equivalent 

resistance to the one that of a pipe of the same diameter and a length equal to the calculated length. 

The horizontal axis of the nomogram indicates the diameter of the pipe. Thus, for D = 90 mm, we 

have the following:

 

Equivalent length of T-connector

m

=

10 5

.

 

Equivalent two-way valve length

m

=

32

 

Equivalent length of

-curve connector

m

90

1 2

°

=

.

 

Total equivalent length

m

= ×

+

+ ×

=

6 10 5 32 5 1 2 101

.

.

Pipe length

(m)

10

20

50

100

100

100

50

40

10

30

20

20

3

4

5

200

200

200

300

500

500

500

1000

1000

2000

2000

5000

5000

10000

1

2

2

3

4

5

0.03

0.04

0.05

0.1

0.2

0.3

0.4

0.5

1.0

1.5

Air flow

(m

3

/h)

Axis 1

Axis 2

Pipe inside

diameter

(mm)

System

pressure

(bar)

Pressure

drop

(bar)

Z

1

Z2