Flowresistance

Flowresistance is the opposition to the movement of a fluid through a channel, pipe, or porous medium. It arises from viscous forces in the fluid and from geometric constraints that convert kinetic energy into heat, and is often quantified by the pressure drop needed to sustain a given volumetric flow rate.

In internal flows within pipes or ducts, flowresistance is described by several formulations. For laminar flow in a circular pipe, Poiseuille's law gives ΔP = (8 μ L Q) / (π r^4). For more general conditions, the Darcy–Weisbach equation ΔP = f (L/D) (ρ v^2 / 2) relates pressure drop to length, diameter, fluid density, velocity, and a friction factor f that depends on Reynolds number and surface roughness. The friction factor equals 64/Re for laminar flow and increases with roughness at higher Re. These relations connect flowresistance to material, surface finish, and flow regime.

In porous media, flowresistance is often described by Darcy's law, Q = - (k A / μ) ∇P, or equivalently ΔP = (μ L / (k A)) Q. Here k is permeability; flowresistance is higher in less permeable media or with higher viscosity. The concept can be represented as a resistance coefficient R = ΔP / Q with units of Pa·s/m^3.

Flowresistance is central in engineering applications such as water supply, HVAC, microfluidics, and groundwater hydrology. It is assessed through measurements of pressure drop and is modeled using circuit analogies that relate pressure drop to flow rate through an equivalent resistance.

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