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The kinematic viscosity of water at 20 °C is about 1 cSt. The most frequently used systems of US customary, or Imperial , units are the British Gravitational (BG) and English Engineering (EE). In the BG system, dynamic viscosity has units of pound -seconds per square foot (lb·s/ft 2 ), and in the EE system it has units of pound-force -seconds ...
where ε is the average rate of dissipation of turbulence kinetic energy per unit mass, and; ν is the kinematic viscosity of the fluid.; Typical values of the Kolmogorov length scale, for atmospheric motion in which the large eddies have length scales on the order of kilometers, range from 0.1 to 10 millimeters; for smaller flows such as in laboratory systems, η may be much smaller.
For kinematic viscosity, the SI unit is m^2/s. In engineering, the unit is usually Stoke or centiStoke, with 1 Stoke = 0.0001 m^2/s, and 1 centiStoke = 0.01 Stoke. For liquid, the dynamic viscosity is usually in the range of 0.001 to 1 Pascal-second, or 1 to 1000 centiPoise. The density is usually on the order of 1000 kg/m^3, i.e. that of water.
A simple and widespread empirical correlation for liquid viscosity is a two-parameter exponential: = / This equation was first proposed in 1913, and is commonly known as the Andrade equation (named after British physicist Edward Andrade). It accurately describes many liquids over a range of temperatures.
This functional relationship is described by a mathematical viscosity model called a constitutive equation which is usually far more complex than the defining equation of shear viscosity. One such complicating feature is the relation between the viscosity model for a pure fluid and the model for a fluid mixture which is called mixing rules.
The turbulent Schmidt number is commonly used in turbulence research and is defined as: [3] = where: is the eddy viscosity in units of (m 2 /s); is the eddy diffusivity (m 2 /s).; The turbulent Schmidt number describes the ratio between the rates of turbulent transport of momentum and the turbulent transport of mass (or any passive scalar).
The shallow-water equations in unidirectional form are also called (de) Saint-Venant equations, after Adhémar Jean Claude Barré de Saint-Venant (see the related section below). The equations are derived [ 2 ] from depth-integrating the Navier–Stokes equations , in the case where the horizontal length scale is much greater than the vertical ...
The in the equation above, which represents specific volume, is not the same as the in the subsequent sections of this derivation, which will represent a velocity. This partial relation of the volume expansion coefficient, β {\displaystyle \mathrm {\beta } } , with respect to fluid density, ρ {\displaystyle \mathrm {\rho } } , given constant ...