Pipe Line Sizing Calculations In Details with Example

Line sizing is defined as the process calculation which is used to calculate the appropriate diameter (size) for pipes or pipelines to ensure that they can carry a specific fluid flow rate in accordance with engineering criteria (i.e. Pressure drop and Velocity limits). Line Sizing is a crucial step in designing fluid transport systems to ensure efficient and safe operations.

Note: Velocity and pressure drop criteria depend upon the phase of the fluid (liquid, Vapor, or gas) being transported through the pipeline. Please refer to the below general guidelines:

Liquid Phase:

1. Velocity: Recommended velocity range is between 1 to 3 meters per second (3.28 to 9.84 feet per second). This Velocity range helps to prevent excessive frictional pressure losses and minimizes the loss due to erosion or corrosion within the pipe.
2. Pressure Drop: The pressure drop occurring in liquid pipelines is usually limited to a certain percentage of the initial pressure. This percentage can vary based on different factors such as the fluid’s viscosity, the length of the pipeline (fluid transport system), and the specific application. Typically, pressure drops of around 5% to 10% of the initial pressure are common in many cases.

LIQUID	Nominal Pipe Size	Max Velocity (m/s)	Max ΔP (bar/100m)
Pump suction	Lower than 8″	1	0.1
Pump suction	Higher than 8″	2	0.1
Pump discharge	Lower than 8″	2	0.5
Pump discharge	Higher than 8″	3.5	0.5

Gas Phase:

1. Velocity: In gas pipelines, the recommended velocity range is generally on the higher side than in liquid pipelines due to the lower density of gases. The recommended velocity for gas pipelines is between 10 to 30 meters per second (32.81 to 98.43 feet per second). This Velocity range helps ensure prevents the risk of excessive pressure drop due to friction and erosion.
2. Pressure Drop: Pressure drop in gas pipelines is also affected by factors such as pipeline length, gas density, and flow rate. Pressure drop limits in gas pipelines might be specified in terms of pressure per unit length (e.g., 1 psi per 100 feet) or as a percentage of the initial pressure.

GAS & VAPOR	Operating Pressure	Max Velocity (m/s)	Max ΔP (bar/100m)
Gas	Lower than 7 barg	30	0.1
Gas	Higher than 7 barg	30	0.4
Steam	LPS (Low Pressure)	12√d​ (Pipe diameter in Inch)	0.1
Steam	MPS (Medium Pressure)	9√d​ (Pipe diameter in Inch)	0.5

TWO PHASE	Max Velocity (m/s)	Max ΔP (bar/100m)
High pressure flow	Ve	0.45
Low pressure flow	0.65 Ve	0.45

Pressure Drop Calculation:

The most common equation used for pipe sizing depends on fluid flow rates and pressure drop considerations. The Darcy Weisbach equation, often used in conjunction with the Moody chart, is commonly employed for this purpose.

The Darcy Weisbach equation for pressure drop in a pipe is:

ΔP = f * (L / D) * (ρ * V²) / 2

Where:
– ΔP is the pressure drop across the pipe (Pa)
– f is the friction factor (dimensionless) based on the flow regime and pipe characteristics
– L is the length of the pipe (m)
– D is the diameter of the pipe (m)
– ρ is the density of the fluid (kg/m³)
– V is the velocity of the fluid (m/s)

The friction factor (f) varies depending on fluid region laminar, turbulent, or transition.

The Moody chart graphical representation is used for friction factor based on Reynolds number and relative roughness (ε/D) in case of turbulent flow or alternatively Colebrook – White equation can be used for friction factor calculation.

• Where, (f) is the friction factor (dimensionless)
• (ε) is the pipe roughness (m)
• (D) is the hydraulic diameter of the pipe (m)
• Re is the Reynolds number (dimensionless)
• Relative roughness is a dimensionless quantity that is used to measure the roughness of the inner surface of a pipe. It is defined as the ratio of the absolute roughness of the pipe (ε) to the inside diameter of the pipe (D).

In Case of laminar flow, the friction factor can be directly calculated using the Hagen-Poiseuille equation (f = 16 / Re). Hagen-Poiseuille equation in details as given below for better understanding

Hagen-Poiseuille equation describes the pressure drop (Delta P) across a pipe due to laminar flow. It applies to situations where the flow is characterized by smooth, orderly movement of fluid layers. The equation is given as:

ΔP = {8 * μ * L* Q} / {pi R^4}

Where:
– (Delta P) is the pressure drop (Pa)
– (μ) is the dynamic viscosity of the fluid (Pa·s)
– (L) is the length of the pipe (m)
– (Q) is the volumetric flow rate (m3/s)
– (R) is the radius of the pipe (m)

For circular pipes, the radius (R) is half the diameter (D).

Here’s an example:
Let’s say you’re transporting a viscous fluid with a dynamic viscosity (μ) of 0.02 Pa·s through a pipe of length (L) 2 meters and radius (R) 0.02 meters. You want to know the pressure drop for a volumetric flow rate (Q) of 0.001 m3/s.

Substitute the given values into the Hagen-Poiseuille equation:
Delta P = {8 * 0.02 * 2 * 0.001} / {pi * (0.02)^4}

= 636.61 Pa ~ 637 Pa

So, in this example, the pressure drop across the pipe due to laminar flow is approximately 637 Pa.

Line Size Calculation Procedure:

Line Size can be calculated by the equations:

Q = V * A

Where, Q is the Volumetric Flow rate in m3/s

V is the Allowable velocity for the fluid in m/s (differs in each phase of fluid or as per Project requirement / design basis)

A is the Area of Circular Pipe or duct through which fluid is flowing in m2

Let’s understand this with an Example as given below:

Fluid is water (density ρ = 1000 kg/m³, dynamic viscosity μ = 0.001 kg/(m·s)) flowing through a circular pipe with a diameter D = 0.05 m and a length L = 10 m. The flow velocity V is 0.1 m/s.