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The STM numerically solves equation 3 through an iterative process. This can be done using the bisection or Newton-Raphson Method, and is essentially solving for total head at a specified location using equations 4 and 5 by varying depth at the specified location. [5] = Equation 4
A vortex sheet is a term used in fluid mechanics for a surface across which there is a discontinuity in fluid velocity, such as in slippage of one layer of fluid over another. [1] While the tangential components of the flow velocity are discontinuous across the vortex sheet, the normal component of the flow velocity is continuous.
Occasionally the factor β is included before the von Kármán constant in the equation, which is a constant which correlates eddy viscosity to eddy diffusivity. This is generally taken to be equal to 1, and therefore is ignored in actual calculation. However, it should not be ignored when considering the full equation.
The critical velocity for deposition, on the other hand, depends on the settling velocity, and that decreases with decreasing grainsize. The Hjulström curve shows that sand particles of a size around 0.1 mm require the lowest stream velocity to erode. The curve was expanded by Åke Sundborg in 1956.
Dimensionless numbers (or characteristic numbers) have an important role in analyzing the behavior of fluids and their flow as well as in other transport phenomena. [1] They include the Reynolds and the Mach numbers, which describe as ratios the relative magnitude of fluid and physical system characteristics, such as density, viscosity, speed of sound, and flow speed.
The Reynolds and Womersley Numbers are also used to calculate the thicknesses of the boundary layers that can form from the fluid flow’s viscous effects. The Reynolds number is used to calculate the convective inertial boundary layer thickness that can form, and the Womersley number is used to calculate the transient inertial boundary thickness that can form.
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In hydrology, discharge is the volumetric flow rate (volume per time, in units of m 3 /h or ft 3 /h) of a stream.It equals the product of average flow velocity (with dimension of length per time, in m/h or ft/h) and the cross-sectional area (in m 2 or ft 2). [1]