How to calculate pipe size for pulp stock and water?

 

Objective:

To Calculate Pipe size for process lines such as Pulp stock and Water for Pulp & Paper Industry design

Inputs required:

Fluid nature  : Pulp stock, Water etc
Flow             : in m³/sec
Velocity        : in m/sec

 

Formula-1:

Where

A – Cross Sectional Area of Pipe (m²)
Q – Flow (m³/sec)
V – Velocity (m/sec)

 

Formula-2:

Where

D – Diameter of the pipe required (mm)
A – Cross Sectional Area of Pipe (m²) calculated from Formula-1

 

Importance of choosing the correct velocity:

When calculating the pipe size, velocity plays major role. Velocity has to be chosen considering factors like fluid nature, application point, delivery pressure requirement, pipe types and pipe pressure rating etc.

1. Fluid nature - Though the specific gravity for Pulp stock and Water is same, stock and water impart different friction in pipes due to difference in viscosity; hence the velocity to be considered for stock is lesser than water
2. Application point - means the pipe location and origin & destination (Eg: Pump suction pipe, Pump discharge pipe, Equipment accepts pipe, rejects pipe, gravity pipe, long running pipe etc). Based on these points and its pressure requirement, velocity has to be chosen.
3. When velocity kept at higher side, pipe size will get reduced but it will impart higher friction in pipe and in-turn higher energy for pumping. Hence optimum velocity is to be considered to optimize the pipe size as well as energy.
4. Equipment manufacturers recommends pressure ranges / velocity ranges for various applications which should be followed.
5. Pipe manufacturer offer standards which shows frictional loss (in m/100 m of pipe) for every pipe size against the flow which can be referred to find the right pipe size
6. In some cases, pipe size is calculated by checking the pressure drop (between origin to delivery point) which is predominant factor over velocity. Long running pipes over pipe racks between process building to building are chosen by checking the pressure drop.
7. Pump suction pipe sizes are kept matching the pump suction nozzle size or higher
8. For every pump delivery pipe line, overall pressure drop is to be calculated like pipe frictional losses, pressure drop due to equipment and valves etc to optimize the velocity and pipe size
9. Pipe Types - Depending upon the nature of pipe (like SS, MS, Galvanized, PVC etc), the frictional losses slightly vary for the same pipe size among them. Based on the fluid nature and its reaction with pipe; and application purpose, pipe type is chosen.
10. Pressure rating - Eg: 5 bar, 10 bar etc of the pipes should be checked to ensure the internal fluid pressure not exceeding the pipe rating when choosing the pipes for higher pressure applications such High pressure showers

Steps:

1. Once correct velocity is identified, calculate the Cross-sectional area required for the pipe in m² using the above Formula-1
2. Convert the Cross-sectional area into diameter for the pipe required using the Formula-2

Choosing Pipe size:

1.   The Diameter calculated from the Formula-2 may not be the exact internal diameter of the Standard pipes. Hence by using the calculated value, we need to choose the closest pipe internal diameter

2.   With the chosen pipe’s internal diameter, the actual velocity can be calculated by reorganizing Formula-1 to ensure the velocity is not deviating from the standard range

 

Example:

Q – 0.25 m³/sec
V – 2.0 m/sec

= 0.25 ÷ 2.0

A = 0.125 m²

D = 399 mm

The closest standard pipe size for calculated pipe size is 400 mm pipe. If we choose Stainless steel pipe; according to the ANSI standard, the outer diameter is 406.4 mm and wall thickness is 4.19 mm

The internal diameter can be calculated as follows

 

ID = 406.4 – (4.19 x 2)

    = 398.2 mm

Hence, the 400 mm pipe can be chosen. In most cases the closest standard pipe size can be chosen directly; however, when calculating pipe size for velocity sensitive applications, it is advisable to check the actual velocity by using the internal diameter of the chosen pipe.

 

General Velocity ranges:

The following table shows the typical velocity range recommendations generally followed in the industry; the above velocity factors to be considered while choosing the right velocity

Fluid	Velocity ranges (m/sec)
Stock (< 1% consistency)	1.5	2.5
Stock (1 - <2% consistency)	1.3	2.3
Stock (2 - 4% consistency)	1.2	2.0
Stock under gravity	0.6	1.2
Water	1.0	3.0
Water under gravity	1.0	2.2
Pump suction	0.6	1.2
Velocity ranges follows pipes from lower size to 250 mm Pipe size and for above 250 mm pipe, the maximum in velocity range can be followed