# How to compute the Reynolds number of a fluid without knowing the density?

I am running a simulation with LAMMPS involving a colloid suspended in a fluid. Simple shear is applied creating flow. My question is, how can I calculate the Reynolds number of the fluid given I don't know it's density? The fluid is modeled through LAMMPS only by specifying it's viscosity.

To get the Reynolds number I need to calculate Re = $$\rho u L / \mu$$. $$\rho$$ is the fluid density (unknown), $$u$$ is the flow speed (I'll use the value at the top of the simulation box since this varies), $$L$$ is a characteristic length (the diameter of the colloid particles), and $$\mu$$ is the viscosity of the fluid (which I know).

• Consider to spell out acronyms. Jan 12 at 6:59
• What command are you using for it? For example fix lb/fluid need viscosity and density as inputs (at least in the current documentation), so you should be able to extract the values that you need, isn't it? Jan 12 at 8:28

Kinematic viscosity $$\nu=\mu/\rho$$ is often tabulated separately from dynamic or "regular" viscosity $$\mu$$.
Also, if it's a simulation, can you not simply choose a Reynolds number as an input parameter? You can pick an arbitrary system of units where $$\rho=1$$, and it becomes irrelevant.
The evaluation of the Reynolds number does not require a precise determination of its ingredients. The order of magnitude $$\pm 1$$ is enough. Looking at typical liquid densities under normal conditions, you'll realize that most liquid solvents have a mass density of the same order of magnitude as water density. Therefore, using water mass density should not be critical for evaluating the flux regime through the Reynolds number.