The base Durand equation is given in Perry’s, and uses gravity (*g*), pipe diameter (*D*), and solid:liquid density ratio (*s*). This equation also has an empirical constant (*F*_{L}) from Figure 6-33 in Perry’s. I’ve made a curve fit equation to estimate F_{L}, but the chart should be consulted when available.

The Wasp modification includes correction for particle size (which I think is very important!). This calculation does not have a modification for liquid viscosity.

Using data from vertical upflow example, the horizontal carrying velocity for the 3 mm particle is 1.15 m/s (3.8 ft/s). This is greater than the vertical velocity value, and both values are well below the normal velocity in produced water piping (e.g. typically 2-3 m/s)

Combining Erosive Limit (previous article) and Saltation Limit give the boundary flow rates for our example;

- Minimum flow rate is 1.2 m/s (V
_{MT-H}) - Maximum flow rate is 4.7 m/s (V
_{e})

While I use the Durand-Wasp equation almost exclusively, there are a few other methods of calculation as shown in the following graphic. The first equation is the combined Durand-Wasp. The next equation is the Oroskar-Turian from the Davies 1987 reference. This attempts to correct Durand-Wasp with a kinematic viscosity term. Lastly is shown the Wilson Nomograph taken from the Wilson et al. reference. While not useable for spreadsheet calculations, the nomograph is handy when in the field without a calculating device.