fluid dynamics - How do we define capillary number in 2D (two dimensions)

In 3D the capillary number $Ca$ is defined as:

$$Ca=\frac{\nu \rho U}{\gamma}$$ where $\nu$ is the kinematic viscosity ($m^2/s$), $U$ is the velocity ($m/s$)and $\gamma$ is the interfacial tension ($N/m$) and $\rho$ is the density in $kg/m^3$ . However in 2D I will have $\rho$ in units of $kg/m^2$ (2D simulation), so how to find capillary number?