The Effect Of Surface Roughness On Fluid Flow Through Narrow Rectangular Passages
Authors: Veatch Ralph W. , Helander Donald P. , Guerrero E.T. 
Published: December 2007

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Abstract
A laboratory study was made of surface roughness effects on fluid flow through narrow rectangular passages to investigate parameters applicable to flow through fault planes or fractured media. The work presents several new concepts and methods for predicting the effects of both passage geometry and surface roughness on flow.
Flow tests were run through rectangular passages of various size and roughness. Some 1200 data points were run on eleven passage sizes. Passage widths ranged from 0.010 to 0.140 inches which corresponded to aspect ratios between 100 and 7.15, respectively. Four surface roughnesses were studied. Tests were made for each passage and surface roughness with four different fluids.
Friction factor and Reynolds number were correlated to evaluate experimental data. Reynolds numbers ranged from 50 to 14,000 permitting investigation of the laminar, critical and Blasius turbulent flow regions. Relative roughness index was used to define surface roughness. Hydraulic diameter and aspect ratio were the defining parameters for passage cross section.
Experimental data is presented graphically to illustrate particular flow characteristics in the laminar, critical, and turbulent regions. Empirical equations were developed for laminar flow and for the Blasius region of turbulent flow. Equations were also developed for incipience points of critical and turbulent flow. These equations express the effect of flow passage geometry, and surface roughness on fluid flow.
Conclusions derived from analysis of the experimental data are as follows:
The general friction factor and Reynolds number equations are applicable to fluid flow in rectangular passages. However, both aspect ratio and hydraulic diameter are required to adequately describe passage cross section. Equations can be established relating flow passage parameters (hydraulic diameter, aspect ratio, and relative roughness index) with f, and Re to predict flow conditions for any size passage or roughness. The friction factor-Reynolds number relation is independent of roughness in laminar flow, and depends only on passage geometry. Inturbulent flow, both geometry and roughness are a factor. The Reynolds number at which transition from laminar to critical flow, and transition from critical to turbulent flow occurs is a function of both surface roughness and hydraulic diameter.

Introduction
Very little has been published on fluid flow through fractured or faulted media. As the need for more refined secondary recovery techniques increases, knowledge of hydrodynamics in fractures or fault planes is becoming more important.