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Plume shapes can be influenced by flow in the ambient fluid (for example, if local wind blowing in the same direction as the plume results in a co-flowing jet). This usually causes a plume which has initially been 'buoyancy-dominated' to become 'momentum-dominated' (this transition is usually predicted by a dimensionless number called the ...
Mathematically, mass flux is defined as the limit =, where = = is the mass current (flow of mass m per unit time t) and A is the area through which the mass flows.. For mass flux as a vector j m, the surface integral of it over a surface S, followed by an integral over the time duration t 1 to t 2, gives the total amount of mass flowing through the surface in that time (t 2 − t 1): = ^.
The convection–diffusion equation can be derived in a straightforward way [4] from the continuity equation, which states that the rate of change for a scalar quantity in a differential control volume is given by flow and diffusion into and out of that part of the system along with any generation or consumption inside the control volume: + =, where j is the total flux and R is a net ...
The Gaussian air pollutant dispersion equation (discussed above) requires the input of H which is the pollutant plume's centerline height above ground level—and H is the sum of H s (the actual physical height of the pollutant plume's emission source point) plus ΔH (the plume rise due to the plume's buoyancy).
The area required to calculate the mass flow rate is real or imaginary, flat or curved, either as a cross-sectional area or a surface, e.g. for substances passing through a filter or a membrane, the real surface is the (generally curved) surface area of the filter, macroscopically - ignoring the area spanned by the holes in the filter/membrane ...
The Amazon River plume is an example of a river plume in which the Earth's rotation does not play a role. Due to the high discharge, the corresponding momentum of the outflow, and the equatorial latitude, the dynamics of the plume are mainly characterized by the internal Froude number. Ambient currents transport the plume away from the mouth.
The weight of the displaced fluid can be found mathematically. The mass of the displaced fluid can be expressed in terms of the density and its volume, m = ρV. The fluid displaced has a weight W = mg, where g is acceleration due to gravity. Therefore, the weight of the displaced fluid can be expressed as W = ρVg.
The above equations calculate the steady state mass flow rate for the pressure and temperature existing in the upstream pressure source. If the gas is being released from a closed high-pressure vessel, the above steady state equations may be used to approximate the initial mass flow rate. Subsequently, the mass flow rate decreases during the ...