Characteristics of Ryenold
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Characteristic length is a term commonly used to represent a typical dimension in a fluid flow medium when studying it in fluid mechanics. It can be anything, as long as it is consistent.
For example, if we are investigating internal flows of air (which is a fluid) in a room, then any of the length LL, width WW, or height HH can be chosen as a characteristic length depending on the direction of the flow. Similarly, if we are studying external or internal flows over or inside a circular cylinder, the diameter DD, or maybe the length LL can be chosen as the length scale depending on the flow direction.
For example, let us consider Reynolds numberFrancesco Iovine mentionned. It is known to be a dimensionless number which represents the ratio of momentum forces out of viscous forces.
Re=vLνRe=vLν
where LL represents the characteristic length. In that case, how do we work out the characteristic length LL ?
Well, for shapes such as squares, rectangular or annular ducts where the height and width are comparable, LL would be represented by thehydraulic diameter, which is defined as 4-times the hydraulic radius, ratio between the wetted cross-sectional area over the wetted perimeter.
DH=4RH=4APDH=4RH=4AP
For a fluid moving between two plane parallel surfaces, where the width is relatively much greater than the space between the platen, then LL is twice the distance between the plates. If the flow has a free surface, then the hydraulic radius will be used. For flow around airfoils, then the chord length will be used.
You can take a look at this great answer on how to determine the characteristic length, from a mathematical perspective.
Hope this helps
For example, if we are investigating internal flows of air (which is a fluid) in a room, then any of the length LL, width WW, or height HH can be chosen as a characteristic length depending on the direction of the flow. Similarly, if we are studying external or internal flows over or inside a circular cylinder, the diameter DD, or maybe the length LL can be chosen as the length scale depending on the flow direction.
For example, let us consider Reynolds numberFrancesco Iovine mentionned. It is known to be a dimensionless number which represents the ratio of momentum forces out of viscous forces.
Re=vLνRe=vLν
where LL represents the characteristic length. In that case, how do we work out the characteristic length LL ?
Well, for shapes such as squares, rectangular or annular ducts where the height and width are comparable, LL would be represented by thehydraulic diameter, which is defined as 4-times the hydraulic radius, ratio between the wetted cross-sectional area over the wetted perimeter.
DH=4RH=4APDH=4RH=4AP
For a fluid moving between two plane parallel surfaces, where the width is relatively much greater than the space between the platen, then LL is twice the distance between the plates. If the flow has a free surface, then the hydraulic radius will be used. For flow around airfoils, then the chord length will be used.
You can take a look at this great answer on how to determine the characteristic length, from a mathematical perspective.
Hope this helps
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