Once, by the Darcy law, the flux of a fluid with viscosity $\mu$ in a porous media with permeability $K$ between the points $a,b$ (with distance $L$) is given by
$$Q=-\dfrac{K}{\mu}(p_b-p_a)\dfrac{A}{L}$$
I think the velocity of Darcy is given by
$$u=-\dfrac{K}{\mu}(p_b-p_a)\dfrac{1}{L}$$ (it's interesting for me mantain the $L$ at expression)
But my dimensional analysis is not good:
$$\dfrac{\bigg[\frac{m}{s}\bigg]}{\bigg[\frac{N\cdot s}{m^2}\bigg]}\bigg[\frac{N}{m^2}\bigg]\bigg[\dfrac{1}{m}\bigg]=\dfrac{1}{s^2}$$
It might be $m/s$. What is the problem?
Many thanks.