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In many engineering applications the local flow velocity vector field is not known in every point and the only accessible velocity is the bulk velocity or average flow velocity ¯ (with the usual dimension of length per time), defined as the quotient between the volume flow rate ˙ (with dimension of cubed length per time) and the cross sectional area (with dimension of square length):
u is the local flow velocity with respect to the boundaries (either internal, such as an object immersed in the flow, or external, like a channel), and; c is the speed of sound in the medium, which in air varies with the square root of the thermodynamic temperature. By definition, at Mach 1, the local flow velocity u is
Flow in phase space specified by the differential equation of a pendulum.On the horizontal axis, the pendulum position, and on the vertical one its velocity. In mathematics, a flow formalizes the idea of the motion of particles in a fluid.
The Froude number is based on the speed–length ratio which he defined as: [2] [3] = where u is the local flow velocity (in m/s), g is the local gravity field (in m/s 2), and L is a characteristic length (in m). The Froude number has some analogy with the Mach number.
u is the local flow velocity of the continuum, c p is the constant-pressure local specific heat of the continuum, Δ T {\displaystyle \Delta T} is the difference between wall temperature and local temperature.
Superficial velocity (or superficial flow velocity), in engineering of multiphase flows and flows in porous media, is a hypothetical (artificial) flow velocity calculated as if the given phase or fluid were the only one flowing or present in a given cross sectional area. Other phases, particles, the skeleton of the porous medium, etc. present ...
The definition above relied on the physical nature of a fluid current; however, no laws of physics were invoked (for example, it was assumed that a lightweight particle in a river will follow the velocity of the water), but it turns out that many physical concepts can be described concisely using the material derivative.
Thus, the Cauchy Number is defined as the ratio between inertial and the compressibility force (elastic force) in a flow and can be expressed as =, where = density of fluid, (SI units: kg/m 3) u = local flow velocity, (SI units: m/s)