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).

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).