When should I give up on hearing back from a potential PhD supervisor? I am really interested in a position at this particular university and the deadline for applications is the 30th of April. On their website, they say not to contact more than one potential supervisor at a time. 

Anyway, I wrote to one of their lecturers who is currently accepting PhD students two weeks ago and haven’t heard back. To me, he was the best fit for my research. However, there are other academics at the university who I think will be capable of supervising me. 

My question is, as time is running out, should I give the lecturer I already emailed a little more time or should I forget about him at this point and ask someone else?
It might have just slipped through the cracks. Politely follow up and let him know that his position is your first choice. Include whatever attachments you sent the first time so that he doesn't have to hunt for them. If you don't hear back in a few days, move on.