I'm not a plumber but from what I remember of the physics I learnt in school...

The velocity of a liquid ('fluid' includes gases as well as liquids) has nothing to do with pressure (at least not in the true senses of the words 'velocity' and 'pressure').

Velocity means the rate (and direction) of movement; pressure is force per unit area.

I suspect nothing you do to the cross sectional area of your pipe is likely to affect the pressure of the water (though it may affect flow rate) - pressure is determined by force being applied to the water, either because of a pump or the effect of gravity making any water above press down.

Flowrate will, I reckon, be mainly determined by a) pressure and b) the narrowest point (smallest cross-sectional area) in the tube delivering the water (though I guess it might also be affected by friction in the tube).

Okay...that's not of much practical help, I know.

I do know that the pressure reading on our combi boiler gradually, over every few months, creeps down towards 1 bar and occasionally I need to open a tap in a pipe that runs up into the boiler for a few seconds in order to get the pressure gauge to go back up to about 1.5, where it is supposed to be for optimum operation.

Someone in the boiler manufacturer's helpline call centre talked me through how to do that.

Not sure whether that affects the flow rate through the shower though. Doesn't seem to, though I never really thought about it until now.