Magnetic Reynolds Number Calculator

This template calculates the magnetic Reynolds number which is the ratio of the advection of a magnetic field by fluid motion to magnetic diffusion. The magnetic Reynolds number is used to characterise the relative importance of magnetic effects to fluid flow effects in electrically conducting fluids, such as plasmas and certain liquid metals.
CalculationInput﻿﻿U 
:2.00m/s​
﻿
﻿﻿L
:5.00m​
﻿
﻿﻿η
:1.00m2/s​
﻿
Output﻿﻿Rm
:10.0​
﻿
﻿
Rm=ULηRm=\dfrac{UL}{η}Rm=ηUL​
Where:
﻿﻿U
 is the characteristic velocity scale of flow, which is the typical speed at which the conducting fluid is moving within the system being analysed ﻿(m/s)
﻿
﻿﻿L
 is the characteristic length scale of flow, which depends on the context of the problem being studied. It could represent the size of the entire system, such as the diameter of a planet, or it could represent a length associated with a part of the system, such as the diameter of a vortex in a turbulent flow ﻿(m)
﻿
﻿﻿η
 is the magnetic diffusivity, which is a property of the conducting fluid. It is a measure of the ability of the fluid to conduct magnetic fields, that is how rapidly magnetic fields can diffuse within the fluid ﻿(m2/s)
﻿
﻿﻿Rm
 is the magnetic Reynolds Number, a dimensionless quantity
ExplanationThe magnetic Reynolds number is the ratio of the advection of a magnetic field by fluid motion to magnetic diffusion. In simple terms, it provides a measure of how well magnetic fields can diffuse (or spread out) within a conducting fluid, compared to how quickly the magnetic field is advected (or transported) by the fluid flow.
The significance of the magnetic Reynolds Number is that when:
﻿﻿Rm<<1
, indicates that magnetic diffusion is dominant over advection, meaning that the magnetic field is easily diffused and does not significantly affect the fluid flow
﻿﻿Rm>>1
, indicates that advection of the magnetic field dominates over magnetic diffusion, suggesting that the magnetic field plays a significant role in the behavior of the fluid flow. 
Related ResourcesMagnetic Reynolds Number Calculator for eddy current braking
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