We discuss a hydrodynamical model for the dispersal of protoplanetary discs around young , low mass ( < 1.5 M _ { \odot } ) stars by photoevaporation from the central object ’ s energetic radiation , which considers the far-ultraviolet as well as the X-ray component of the radiation field . We present analytical scaling relations and derive estimates for the total mass-loss rates , as well as discussing the existence of similarity solutions for flows from primordial discs and discs with inner holes . Furthermore , we perform numerical calculations , which span a wide range of parameter space and allow us to provide accurate scalings of the mass-loss rates with the physical parameters of the systems ( X-ray and FUV luminosity , stellar mass , disc mass , disc temperature and inner hole radius ) . The model suggest that the X-ray component dominates the photoevaporative mass-loss rates from the inner disc . The mass-loss rates have values in the range from 10 ^ { -11 } to 10 ^ { -7 } M _ { \odot } yr ^ { -1 } and scale linearly with X-ray luminosity , with only a weak dependence on the other parameters explored . However , in the case of high FUV to X-ray ( L _ { FUV } / L _ { X } > 100 ) luminosity ratios , the FUV constricts the X-ray flow and may dominate the mass-loss . Simulations of low mass discs with inner holes demonstrate a further stage of disc clearing , which we call ‘ thermal sweeping ’ . This process occurs when the mid-plane pressure drops to sufficiently low values . At this stage a bound , warm , X-ray heated region becomes sufficiently large and unstable , such that the remaining disc material is cleared on approximately dynamical time-scales . This process significantly reduces the time taken to clear the outer regions of the disc , resulting in an expected transition disc population that will be dominated by accreting objects , as indicated by recent observations .