Rather than ask for the job, I suggest you demonstrate interest by asking how the interview process will proceed and how you might remain part of it. In other words, as a savvy employment candidate you should be intuitive enough to know if the interview went well. If so, ask for a follow up commitment.
Ask for a follow up date; if it feels right, put the date and time in your calendar right there and then. If corporate protocol dictates your deferral to HR; on your way out of the interview stop at HR and ask for a follow up commitment, time and date.
Let's not read too much in to this. An interview is simply a meeting between two pros with a common cause. Common is the key!
Therefore, use the same keen common sense that got you where you are today to get you where you want to be tomorrow!
If you are applying for a sales position; remember what Zig Ziglar used to say; telling aintselling asking is! For you engineers and IT folk, come out of the comfort zone just enough to ask for a follow up commitment. As you should already know, once you leave the first interview, they will soon forget you! Make sure they don't!