Context : Observations indicate that stars generally lose their protoplanetary discs on a timescale of about 5 Myr .
Which mechanisms are responsible for the disc dissipation is still debated .

Aims : Here we investigate the movement through an ambient medium as a possible cause of disc dispersal .
The ram pressure exerted by the flow can truncate the disc and the accretion of material with no azimuthal angular momentum leads to further disc contraction .

Methods : We derive a theoretical model from accretion disc theory that describes the evolution of the disc radius , mass , and surface density profile as a function of the density and velocity of the ambient medium .
We test our model by performing hydrodynamical simulations of a protoplanetary disc embedded in a flow with different velocities and densities .

Results : We find that our model gives an adequate description of the evolution of the disc radius and accretion rate onto the disc .
The total disc mass in the simulations follows the theoretically expected trend , except at the lowest density where our simulated discs lose mass owing to continuous stripping .
This stripping may be a numerical rather than a physical effect .
Some quantitative differences exist between the model predictions and the simulations .
These are at least partly caused by numerical viscous effects in the disc and depend on the resolution of the simulation .

Conclusions : Our model can be used as a conservative estimate for the process of face-on accretion onto protoplanetary discs , as long as viscous processes in the disc can be neglected .
The model predicts that in dense gaseous environments , discs can shrink substantially in size and can , in theory , sweep up an amount of gas of the order of their initial mass .
This process could be relevant for planet formation in dense environments .