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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 speed-density relationship is linear with a negative slope; therefore, as the density increases the speed of the roadway decreases. The line crosses the speed axis, y, at the free flow speed, and the line crosses the density axis, x, at the jam density. Here the speed approaches free flow speed as the density approaches zero.
where is the absolute pressure at the inlet, is the average velocity at the inlet, is the fluid density, is the acceleration of gravity and is the vapor pressure of the fluid. Note that NPSH is equivalent to the sum of both the static and dynamic heads – that is, the stagnation head – minus the equilibrium vapor pressure head, hence "net ...
ρ = fluid mass density; u is the flow velocity vector; E = total volume energy density; U = internal energy per unit mass of fluid; p = pressure
Given the density of the operating fluid, mass flow rate (ṁ) can also be used to obtain the volume flow rate. The relationship between the mass flow rate and volume flow rate (also known as the capacity) is given by: ˙ = Where ρ is the operating fluid density.
In fluid dynamics, dynamic pressure (denoted by q or Q and sometimes called velocity pressure) is the quantity defined by: [1] = where (in SI units): q is the dynamic pressure in pascals (i.e., N/m 2, ρ (Greek letter rho) is the fluid mass density (e.g. in kg/m 3), and; u is the flow speed in m/s.
SG is the specific gravity of the fluid (for water = 1), Δ P is the pressure drop across the valve (expressed in psi). In more practical terms, the flow coefficient C v is the volume (in US gallons) of water at 60 °F (16 °C) that will flow per minute through a valve with a pressure drop of 1 psi (6.9 kPa) across the valve.
In fluid dynamics, the Darcy–Weisbach equation is an empirical equation that relates the head loss, or pressure loss, due to friction along a given length of pipe to the average velocity of the fluid flow for an incompressible fluid.