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Using the expression derived above for the total volumetric flux, , this can be written as ψ ( x , y , t ) = Q ( x , y , t ) b {\displaystyle \psi (x,y,t)={\frac {Q(x,y,t)}{b}}} . In words, the stream function ψ {\displaystyle \psi } is the volumetric flux through the test surface per unit thickness, where thickness is measured perpendicular ...
Right: The reduction in flux passing through a surface can be visualized by reduction in F or dS equivalently (resolved into components, θ is angle to normal n). F•dS is the component of flux passing through the surface, multiplied by the area of the surface (see dot product). For this reason flux represents physically a flow per unit area.
Diagram showing definitions and directions for Darcy's law. A is the cross sectional area (m 2) of the cylinder. Q is the flow rate (m 3 /s) of the fluid flowing through the area A. The flux of fluid through A is q = Q/A. L is the length of the cylinder. Δp = p outlet - p inlet = p b - p a.
Advanced. Specialized. Miscellanea. v. t. e. In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, [1] is a theorem relating the flux of a vector field through a closed surface to the divergence of the field in the volume enclosed. More precisely, the divergence theorem states that the surface ...
Potential flow with zero circulation. In mathematics, potential flow around a circular cylinder is a classical solution for the flow of an inviscid, incompressible fluid around a cylinder that is transverse to the flow. Far from the cylinder, the flow is unidirectional and uniform. The flow has no vorticity and thus the velocity field is ...
In fluid dynamics, potential flow or irrotational flow refers to a description of a fluid flow with no vorticity in it. Such a description typically arises in the limit of vanishing viscosity, i.e., for an inviscid fluid and with no vorticity present in the flow. Potential flow describes the velocity field as the gradient of a scalar function ...
Gaussian surface. A cylindrical Gaussian surface is commonly used to calculate the electric charge of an infinitely long, straight, 'ideal' wire. A Gaussian surface is a closed surface in three-dimensional space through which the flux of a vector field is calculated; usually the gravitational field, electric field, or magnetic field. [1]
Volumetric flux. In fluid dynamics, the volumetric flux is the rate of volume flow across a unit area (m 3 ·s −1 ·m −2), and has dimensions of distance/time (volume/ (time*area)) - equivalent to mean velocity. The density of a particular property in a fluid's volume, multiplied with the volumetric flux of the fluid, thus defines the ...