# Scaling of Navier Stokes equations

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Hello, I have implemented a Navier-Stokes solver for a fluid simulation. However, I have assumed that all measures are performed in SI-units. I am not sure how exactly I have to adapt the NS-equations so I can simulate smaller volumes, such as 10cmx10cmx10cm. Do I have to adjust the constants density and viscosity? Which part of the NS-equation do I have to adapt and how? Thanks, Icebraker

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You need to decide on what units you are using and use them throughout. It's not a matter of scaling.

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So if I get you correctly I can just change the gravity, density and viscosity from meter to centimeter and get the simulation for a cm x cm x cm cube?

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Maybe I'm an idiot but... can't you just move a decimal? 1 m = 100 cm = 1000 mm = .001 km?

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Icebraker, I think you've got it right, but I will try to add some clarification.

The idea, introduce by the other responses, is that you can use whatever system of units you want, and the equations will work. They key thing is, you must not mix different units, e.g., if you have decided to model water and so your initial density values are for water at 20 degrees Celcius at sea level, and the density value is in kilograms per square meter, then if you change your mesh to be represented in centimeters, you MUST convert your density to be kilograms per square centimeter. Similarly, if you want your density to be represented using kilogram, then you must make sure your specific heat, used in the energy conservation equation bits, is defined in terms of kilograms, not grams. So, the rule is that everything must the exact same set of units, and you cannot mix kilo/deci/centi/etc...

If you have a mesh that is 1 meter wide and you decide that you really wanted it to be 1 centimeter, then you can use the same coordinates for your mesh...just now calling them centimeters, and it is the conversion of the physical coefficients and property values to centimeters that will cause the fluid to behave properly for the smaller volume.

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