is simply the weight of an element of fluid, , times the depth of the flow, . From this, we get the expression for the total pressure, , acting on the bed. Shear stress In order to convert the pressure into a shear stress, it is necessary to determine the component of the pressure that provides shear on the bed. For a channel that is at an angle from horizontal, the shear component of the stress acting on the bed , which is the component acting tangentially to the bed, equals the total pressure times the sine of the angle . In natural rivers, the angle is typically very small. As a result, the small-angle formula states that: The tangent of the angle is, by definition, equal to the slope of the channel, . From this, we can arrive at the final form of the relation between bed shear stress and depth–slope product: Scaling Assuming a single, well-mixed, homogeneous fluid and a single acceleration due to gravity (both are good assumptions in natural rivers, and the second is a good assumption for processes on Earth, or any planetary body with a dominant influence on the local gravitational field), the only two variables that determine the boundary shear stress are the depth and the slope. This is the significance of the name of the formula. For natural streams, in the mks or SI system (units of pascals for shear stress), a typical useful relationship to remember is that: for water with a density of 1000 kg/m3 and approximating the acceleration due to gravity as 10 m/s2 (the error in this assumption is typically much smaller than the error from measurements). Uses Bed shear stress can be used to find: The vertical velocity profile within the fluid flow The ability of the fluid to carry sediment The rate of shear dispersion of contaminants and tracers. See also Sediment Fluid mechanics References Leopold, Wolman, and Miller (1964), Fluvial Processes in Geomorphology, Dover Publications, Mineola, NY, USA, 535 pp. Fluid dynamics Geological techniques Civil engineering Environmental engineering