The toilet physic?

I am confused on how a toilet tap works.Probably because of insufficient sex these days. Kiddin’. You see when you open the tap bigger, you get larger flow rate. Correct. It directly means that the valve has bigger opening. Correct.

Try to see where i go wrong here.
When the valve opening is bigger, you get lesser pressure drop and provided that the flow rate is constant, the velocity of the water increase. OK but the fact is the flow rate is not constant ( water comes out more with larger valve opening), in fact it increases with the bigger valve opening. So is this due to compressible flow effect that for larger valve opening you get smaller pressure drop but higher flow velocity and flow rate. HELLO still with me? correct me. i knwo i am wrong somewhere.