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A Graetz number of approximately 1000 or less is the point at which flow would be considered thermally fully developed. [ 2 ] When used in connection with mass transfer the Prandtl number is replaced by the Schmidt number , Sc, which expresses the ratio of the momentum diffusivity to the mass diffusivity.
[4] [5] [6] A generalized model of the flow distribution in channel networks of planar fuel cells. [6] Similar to Ohm's law, the pressure drop is assumed to be proportional to the flow rates. The relationship of pressure drop, flow rate and flow resistance is described as Q 2 = ∆P/R. f = 64/Re for laminar flow where Re is the Reynolds number.
A laminar flow reactor (LFR) is a reactor that uses laminar flow to study chemical reactions and process mechanisms. A laminar flow design for animal husbandry of rats for disease management was developed by Beall et al. 1971 and became a standard around the world [9] including in the then-Eastern Bloc. [10]
For laminar flow Chilton and Stainsby [7] provide the following equation to calculate the pressure drop. The equation requires an iterative solution to extract the pressure drop, as it is present on both sides of the equation.
In the case of laminar flow, for a circular cross section: =, =, where Re is the Reynolds number, ρ is the fluid density, and v is the mean flow velocity, which is half the maximal flow velocity in the case of laminar flow. It proves more useful to define the Reynolds number in terms of the mean flow velocity because this quantity remains well ...
In turbulent flow the flow rate is proportional to the square root of the pressure gradient, as opposed to its direct proportionality to pressure gradient in laminar flow. Using the definition of the Reynolds number we can see that a large diameter with rapid flow, where the density of the blood is high, tends towards turbulence.
If the formula for laminar flow is f = 16 / Re , it is the Fanning factor f, and if the formula for laminar flow is f D = 64 / Re , it is the Darcy–Weisbach factor f D. Which friction factor is plotted in a Moody diagram may be determined by inspection if the publisher did not include the formula described above: Observe the ...
The Dean number (De) is a dimensionless group in fluid mechanics, which occurs in the study of flow in curved pipes and channels.It is named after the British scientist W. R. Dean, who was the first to provide a theoretical solution of the fluid motion through curved pipes for laminar flow by using a perturbation procedure from a Poiseuille flow in a straight pipe to a flow in a pipe with very ...