Flow deceleration as a method of determining drag coefficient over roughened flat beds

Abstract

The drag coefficient (CD) is a fundamental parameter in the determination of shear stress or the drag force between a fixed object and fluid moving over it. In natural settings, conventional methods of defining it are largely impractical and so either smooth‐bed CD or constant values are used irrespective of bed roughness or flow strength. This paper deals with the determination of CD over naturally roughened beds. The work was carried out in two annular flumes of known, constant water mass. In an otherwise balanced system, flow deceleration is a manifestation of the total drag force exerted at the rigid boundaries (Newton's second law). The inversion of this relationship is used to yield the bed drag coefficients. The advantages of this method include its accurate use over rough and irregular beds, as shown by experiments over patchy and homogeneous gravel beds and over a wide range of Reynolds numbers. The value of CD was found to converge to the constant value of 3 × 10−3 determined by Sternberg [1968] at intermediate velocities, and a reduction in the drag coefficient occurred at high velocities. Results showed that patch spacing did not influence the shear stress value in the case of one‐grain‐thick gravel patches. A modification of the equipment for field use may give advantages where traditional methods fail due to difficulties in obtaining accurate velocity profile measurements.