Effect of Surface Roughness on the Pressure Drop of Liquid Flow in Micro-Channels

Experimental results in the literature of the surface roughness effect on pressure drop of liquid flow in mini and micro channels were examined. Also, three prominent theories, which are the constricted flow model, the constricted model considering roughness distribution, and the roughness viscosity model are reviewed based upon this broad data base. It is found that all the normalized data of fRe can be predicted, within an error of about ±15%, by the classical pressure drop theory with the channel dimension using the constricted flow model. On the other hand, it appears that the viscosity model is difficult to use generally and the roughness distribution information is frequently hard to obtain for natural rough-surfaces. However, the data, which supports these two theories, can also be predicted well by the constricted flow method at a similar accuracy. It is possible that the viscosity model and the constricted model with roughness distribution can be further developed to become easier to use, for the time being the simple constricted flow model could be a general and reliable method for mini and micro channel pressure drop predictions.

Calculations of Pressure Drop in a Circular Duct Using the Traditional Method Compared to That Using the Constricted Flow Diameter

The traditional method of calculating pressure drop in a pipe that conveys a fluid involves use of the Moody Diagram. This diagram is a correlation of data with friction factor plotted as a function of Reynolds number and relative roughness. A new graphical representation of these data has been formulated, and makes use of what is known as the constricted flow diameter. The background for this new correlation is based on using a pipe diameter less twice the average roughness height. A new “modified” Moody Diagram has been produced based on the constricted flow diameter. The presence of roughness features on the inside pipe wall has an effect on the flow along the pipe surface which is not accounted for in the traditional Moody diagram. The new diagram accounts for this effect. To demonstrate the use of the new diagram, several example problems have been formulated and solved using the traditional and the modified diagrams. Calculations indicate that at the smaller pipe sizes, the use of the constricted flow diameter yields significantly different results from those obtained in the traditional way. These results have a major influence on modeling flows in mini- and in micro-channels. Laminar and turbulent flows are both affected.