Depending on the viscosity model and pipe friction model selected, the calculation of pressure drop in a pipe differs.

Darcy-Weisbach Loss Model

AFT Impulse utilizes the Darcy-Weisbach loss model to relate the Darcy Friction Factor, the pipe geometry, fluid density, and fluid velocity to pressure drop in the pipe. The Darcy Friction Factor differs from the Fanning Friction Factor by a factor of 4.

This model requires the calculation of a friction factor, as described below.

• Roughness-Based Methods - This method calculates the friction factor based on the roughness of the pipe wall. Different equations are used based on flow regime - laminar flow uses the standard laminar relationship, while turbulent flow uses the implicit Colebrook-White equation. In the transition range between laminar and turbulent flow, a linearly interpolated value is used. The default transition Reynold's Numbers can be modified in Analysis Setup window.

• Absolute Roughness (default) - The absolute average roughness height ε is specified directly.

• Relative Roughness - The roughness is specified as a ratio ε/D.

• Hydraulically Smooth - The ratio ε/D is set equal to zero.

• Explicit Friction Factor - The friction factor to be used in the Darcy-Weisbach equation is specified directly

Frictionless

The pipe will not have any pressure drop across it. This is inherently unrealistic behavior, but can be useful for troubleshooting purposes.

Resistance

The pipe resistance relates head loss to volumetric flow rate. In equation form, the head loss is:

Using standard relationships, the friction pressure drop is related to volumetric and mass flow rate as follows:

Non-Newtonian Pressure Loss

The pressure loss behavior for Non-Newtonian fluids depends on the specific viscosity model selected in the Viscosity Model panel. See Non-Newtonian fluids for more information.

Hazen-Williams Method

AFT Impulse also offers the Hazen-Williams method of specifying irrecoverable loss information. The Solver converts the Hazen-Williams factor to a Darcy-Weisbach friction factor (Walski 1984,37Walski, T. M., Analysis of Water Distribution Systems, Van Nostrand Reinhold Company, New York, NY, 1984.). This allows a consistent solution approach to be used for all pipe system models, while retaining the flexibility of the two approaches to account for losses.

where V is in ft/s and D is in ft.

MIT Equation for Crude Oil

The MIT Equation is appropriate for crude oil and is given by the following equation (Pipe Line Rules of ThumbPipe Line Rules of Thumb Handbook, Gulf Publishing, Houston, TX.):

where:

• dP        = pressure drop (psi)

• L        = length (miles)

• f        = friction factor, MIT

• Q        = volumetric flow rate (barrels/hour)

• s        = specific gravity

• d        = inside diameter (inches)

• ν        = kinematic viscosity (centistokes)

The friction factor calculated by the MIT equations is not the same as the Darcy friction factor. Once the pressure drop (dP) in the pipe is determined, AFT Impulse uses the Darcy equation to back calculate the equivalent Darcy friction factor.

The MIT equation defines the lower bound for the laminar equation as r=0.1, but offers no explanation as to the validity of calculations below this point. AFT Impulse continues to use the laminar flow equation for Reynolds numbers below 0.1.  The older version of the MIT equations did not have this lower limit, and the results from AFT Impulse 10 agree closely with values from the older equations at these lower Reynolds number values.

For Reynolds numbers in the Indeterminate flow regime, the value for the MIT friction factor is determined by linearly interpolating between the friction factors for the highest laminar Reynolds number and the lowest turbulent Reynolds number.

Miller Turbulent Method

The Miller Turbulent method is appropriate for light hydrocarbons and is given by the following equation (Pipe Line Rules of ThumbPipe Line Rules of Thumb Handbook, Gulf Publishing, Houston, TX.):

where:

• dP        = pressure drop (psi)

• L        = length (miles)

• Q        = volumetric flow rate (barrels/hour)

• ρ        = density (lbm/ft3)

• ρwater= density of water (62.3 lbm/ft3)

• d        = diameter (inches)

• μ        = dynamic viscosity (centipoise)

Design Factors

In each pipe you can specify a Design Factor for the pipe friction. This is a multiplier that is applied to the friction factor calculated with the preceding methods.