### Pipe Friction Calculations Within Pipe For Fluid Flow

**Fluid Flow Table of Contents
Hydraulic and Pneumatic Knowledge
Hazen-Williams Method for Pipe Friction and Pressure Drop **

Pipe Friction drives the pipe size requirements within a fluid flow system and is dependant on the piping system design requirements. The sizing for any piping system consists of two basic components fluid flow design and pressure integrity design. Fluid flow design determines the minimum acceptable diameter of the piping necessary to transfer the fluid efficiently. Pressure integrity design determines the minimum pipe wall thickness necessary to safely handle the expected internal and external pressure and loads.

The primary elements in determining the minimum acceptable diameter of any pipe network are system design flow rates and pressure drops. The design flow rates are based on system demands that are normally established in the process design phase of a project.

Before the determination of the minimum inside diameter can be made, service conditions must be reviewed to determine operational requirements such as recommended fluid velocity for the application and liquid characteristics such as viscosity, temperature, suspended solids concentration, solids density and settling velocity, abrasiveness and corrosivity. This information is then used to determine the minimum inside diameter of the pipe for the network.

For normal liquid service applications, the acceptable velocity in pipes is 2.1 ± 0.9 m/s (7 ± 3 ft/s) with a maximum velocity limited to 2.1 m/s (7 ft/s) at piping discharge points including pump suction lines and drains. As stated, this velocity range is considered reasonable for normal applications. However, other limiting criteria such as potential for erosion or pressure transient conditions may overrule. In addition, other applications may allow greater velocities based on general industry practices; e.g., boiler feed water and petroleum liquids.

Pressure drops throughout the piping network are designed to provide an optimum balance between the installed cost of the piping system and operating costs of the system pumps. Primary factors that will impact these costs and system operating performance are internal pipe diameter (and the resulting fluid velocity), materials of construction and pipe routing.

Pressure drop, or head loss, is caused by friction between the pipe wall and the fluid, and by minor losses such as flow obstructions, changes in direction, changes in flow area, etc. Fluid head loss is added to elevation changes to determine pump requirements.

A common method for calculating pressure drop is the Darcy-Weisbach equation:

or

Where:

h_{L} = head loss, m (ft)

f = friction factor

L = length of pipe, m (ft)

D_{i} = inside pipe diameter, m (ft)

L_{e} = equivalent length of pipe for minor losses, m
(ft)

K = loss coefficients for minor losses

V = fluid velocity, m/s (ft/sec)

g = gravitational acceleration, 9.81 m/sec^{2} (32.2
ft/sec^{2} )

The friction factor, f, is a function of the relative roughness of the piping material and the Reynolds number, R_{e} .

Where:

R_{e} = Reynolds number

D_{i} = inside pipe diameter, m (ft)

V = fluid velocity, m/s (ft/s)

= kinematic viscosity, m^{2}/s (ft^{2} /s)

If the flow is laminar (R < 2,100), then f is determined by:

where:

R_{e} = Reynolds number

f = friction factor|

If the flow is transitional or turbulent (R_{e} > 2,100), then f is determined from a **Moody Diagram**. The appropriate roughness curve on the diagram is
determined by the ratio /D_{i} where , is the specific
surface roughness for the piping material (see **Pipe Roughness Coefficients**) and D_{i} is the inside pipe diameter.

The method of equivalent lengths accounts for minor losses by converting each valve and fitting to the length of straight pipe whose friction loss equals the minor loss. The equivalent lengths vary by materials, manufacturer and size. The other method uses loss coefficients. This method must be used to calculate exit and entrance losses. The coefficients can be determined from **Estimated Pressure Drop for Thermoplastic Lined Fittings and Valves** .

Another method for calculating pressure drop is the **Hazen-Williams Method for Pipe Friction and Pressure Drop**.