# 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, 2023 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, 2023 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.