Should I make 2 applications to the same university I apply for a PhD position, with my own research proposal, at one university and receive an offer already. However, as I cannot fund myself, I have to wait for the scholarship whose result will be announced at the end of April. In the mean time, a university is advertising an industrial funded PhD project whose deadline is the end of March. My background matches the requirements for the project which is quite interesting to me as well. I wonder if I should apply for a project as if I am accepted and receive a scholarship from the first offer, I have to choose one of them.

Update: I'm asking this question as I'm worried if making 2 applications to 2 supervisors from the same research group may impact the outcome of both applications, i.e. whether I receive scholarship from the first application and/or be accepted into the 2nd project. Since, I believe both supervisors are not very happy if they know about it.
There is no right answer to this and it depends on the institution that you are in and the people you are dealing with. You are the only one who can decide on this. 

In principal I don't see any problem with this if you manage it correctly. IMHO talking with the first guy to understand the consequence of your action and then making the decision is the right course. Second guy has the money and that makes the situation entirely different for him. The reality is that if you are good people will always assume that you have your own interest in mind and will try to get the best offer. So thats not new. What matters is how you play your cards and behave. 

So, what I would say is go to the first guy talk about the scholarship situation and your prospects, see what he says, if you feel its right bring up the other project ask him "given the uncertainty of the situation and what would you do if you were in my shoes". and take it from there... 

If he says something on the lines of well i am not sure what will happen with scholarship and nothing is guaranteed then go ahead and apply for the second one but if he is saying its a tough situation and you have to make your own mind it kinda indicates that his is not going to be happy about it and is really not understanding you/caring. 

I think right now you need to test the waters first and need to do it very delicately...