def METHOD_NAME(z, H, ext_force_density, dyn_visc):
    """
    Analytical solution for planar Poiseuille flow.
    Parameters
    ----------
    z : :obj:`float`
        Distance to the mid plane of the channel.
    H : :obj:`float`
        Distance between the boundaries.
    ext_force_density : :obj:`float`
        Force density on the fluid normal to the boundaries.
    dyn_visc : :obj:`float`
        Dynamic viscosity of the LB fluid.
    """
    return ext_force_density * 1. / (2 * dyn_visc) * (H**2.0 / 4.0 - z**2.0)