Pressure Drop in Pipes Detailed Discussion
Depending on the pipe friction model selected, the calculation of pressure drop in a pipe differs.
Darcy-Weisbach Loss Model
Note: The pressure drop for compressible flow depends on several equations, as discussed in Review of Compressible Flow Theory. The effect of pipe friction is taken into account as part of the full compressible method. The Darcy-Weisbach pressure loss equation for incompressible flow is shown below for simplicity.
AFT Arrow 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, accomplished by various methods as described below.
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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 the Environmental Properties panel.
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Absolute Roughness (default) - The absolute average roughness height ε is specified directly.
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Relative Roughness - The roughness is specified as a ratio ε/D.
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Explicit Friction Factor - The friction factor to be used in the Darcy-Weisbach equation is specified directly.
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Weymouth Equation - A model for natural gas pipelines under fully turbulent flow, using pipe diameter to characterize pressure loss. The full form of the Weymouth equation relates flow to pressure drop, specific gravity, pipe length, and temperature. CraneCrane Co., Flow of Fluids Through Valves, Fittings, and Pipe, Technical Paper No. 410, Crane Co., Joliet, IL, 1988. (page 1-8) presents an equivalent form using friction factor:
Note: Crane indicates that this friction factor is "identical to the Moody friction factor in the fully turbulent range for 10-inch I.D. pipe only. Weymouth friction factors are greater than Moody factors for sizes less than 20-inch, and smaller for sizes larger than 20-inch."
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Panhandle Equation - A model for natural gas pipelines, using Reynolds Number to characterize pressure loss. Valid for pipes 6 to 24 inch diameter, Reynolds Numbers 5E6 to 14E6 and specific gravity of 0.6. The full form relates flow to a flow efficiency factor, diameter, pressure drop, and pipe length. Similar to the Weymouth model, Crane (page 1-8) presents an equivalent form using friction factor:
Note: Crane indicates: "In the flow range to which the Panhandle formula is limited, this results in friction factors that are lower than those obtained from either the Moody data or the Weymouth friction formula."
Frictionless
The pipe will not have any pressure drop across it. This is inherently unrealistic behavior, but can be useful for troubleshooting purposes.
Helical Tubes
For helical tubes the pressure drop is modified from the equivalent "straight pipe" pressure drop via the following relationship (Ito 1959Ito, H., “Friction factors for pipe flow,”Journal of Basic Engineering, Vol. 81, pp. 123-126, 1959.):
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.
