English equivalent to Dutch "Mopping while the tap is running"?

There is a great phrase in Dutch that translates roughly as "Mopping the floor while the tap is running".

I.e. working to fix a problem but having no impact and not even able to keep up.

Is there an English equivalent that conveys the same meaning?

I've found "Mopping while the tub overflows", but I've only found a single usage of that phrase. Is there a better one?

EDIT:

"Coals to Newcastle" et. al. suggest something that is pointless or even silly. While I agree there's some overlap, I feel the phrase "dweilen met de kraan open", suggests you are desperately trying to catch up with a problem.

Maybe something more along the lines of addressing the symptoms, not the cause?

Solution 1:

I would suggest 'bailing out a sinking ship'.

He knew the time was right to cut one's losses, when it was better to find a new boat than to keep bailing out a sinking ship. And with Rydell, the Sherwood boys, and that reporter running free, that ship wasn't just sinking, it was about to be torpedoed into smithereens.

From The Sign, by Raymond Khoury

Solution 2:

One expression for a task that is never-ending is like painting the Forth Bridge.

In the early days of the Forth Rail Bridge, the tale was that by the time the workers had finished painting the bridge, the older paint had started to deteriorate to such an extent that they had to start all over again.

This doesn't quite convey the "running tap" concept of the Dutch expression, because there's no "tap" that could be switched off, unless you count advances in paint technology.

Solution 3:

We do have "Pushing water uphill". No matter how much you push, it comes back down past you.

A similar answer has been given in another ELU question.

It also keeps your watery reference.