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If the Reynolds number exceeds 2000, the flow in a tube always becomes unstable and eventually becomes fully turbulent. As a result, it is no longer possible to use the viscous laminar flow approximation that gives rise to the Hagen-Poiseuille law, and an alternative model is required.



The model that describes a flow where viscosity is irrelevant is the one that gives rise to Bernoulli's equation. However, this model assumes that energy density is conserved. An alternative is to assume that turbulence leads to mixing in such a way that energy density is not conserved but remains constant. In this case, the flow can be modeled using an equation similar to Bernoulli's, but with a correction to account for homogenization due to mixing effects.

>Model

ID:(1970, 'ky')

Description

If the Reynolds number exceeds 2000, the flow in a tube always becomes unstable and eventually becomes fully turbulent. As a result, it is no longer possible to use the viscous laminar flow approximation that gives rise to the Hagen-Poiseuille law, and an alternative model is required. The model that describes a flow where viscosity is irrelevant is the one that gives rise to Bernoulli's equation. However, this model assumes that energy density is conserved. An alternative is to assume that turbulence leads to mixing in such a way that energy density is not conserved but remains constant. In this case, the flow can be modeled using an equation similar to Bernoulli's, but with a correction to account for homogenization due to mixing effects.

ID:(1970, 0)