So, what does the valve do?

[Eregius]

The valve beside to the trap door.

What does it do?

Any special scene related?

[Leaf★]

There isn't any special scenes, no. When you open it, you'll notice when you exit out to the garden that water is gushing out the fountain.

This is helpful later on when you're trying to save David, because it gives you a hint where to find him. Honestly, I didn't even catch this until now!