How to perform wudhu with a cup of water

If our sins are washed away when we perform wudhu, what happens when we commit sins during wudhu?

I’m currently staying in a city struggling with a major water shortage.

And every time I go for salah, I see Muslims leaving the taps on full while they haphazardly slap water into their mouths, up their noses and so on.

When I say water shortage, the mosque h…