Welcome to Gaia! ::

Ok, so last Tuesday, because the education system is so productive and rather than actually follow the syllabus or do work as planned, we were brought onto an interesting tangent (to be fair, I'm not complaining - principles of fission are only exciting for a bit), I found myself posed, by my teacher, with a question on power showers. This is purely for fun, and I'm mostly posting here to under the principle that if I can explain it to people who don't hang on a science forum; I may be understanding assertions rather than clinging to jargon;
Essentially, we were bemusedly trying to figure out why, despite no force change by the shower itself, with a decrease in holes in use on the shower head, there was greater force when water impacted (it may seem common sense but who cares for that?);

I started with Bernoulli's principle;
(v^2)/2 + gz + P/ϱ = C
v=velocity, g=accel. due to gravity, z=elevation relevant to a plane, P=pressure, ϱ=density of fluid, C=An arbitrary constant.

Thusly, there'd be no change in g or z because there wasn't a height change (and I'm damn sure accel. due to gravity has been 9.80665 for a long time now - well, ok - about that, It actually varies on global position but anyways...). Nor would density change (water being a liquid and thusly pretty damn hard to compress).

Thusly, (v^2)/2 = P/ϱ + (C-gz)
Given though, that pressure operates on a per area basis and the quantity really changing was volume to travel through (which v operated under), that and the whole (v^2)/2 made me think of integrals which lead onto the thought first, admittedly - it seemed correct to differentiate the left side and perform the changes in function on the right.
Therefore;
v= 2*√[P/ϱ + (C-gz)]
In a more mx+c version (although it wouldn't really be a straight line)
v= √(2/ϱ) * √P + √[2(C-gz)]
(v = m * x + c)

Ergo, pressure increase leads to velocity increase. Which made sense since the Bernoulli principle (the thing I started with) claims that potential energy decreases cause a velocity increase since in the case of higher pressure on the travelling liquid, it leaving the shower head meant a greater change in pressure upon leaving and ergo, greater velocity because of greater potential energy decreases.
And since the force of impact is going to be;
F= m(v-u)/t. With v-u (change in velocity on impact) being higher for the situation of less holes to pass through, a greater force is felt.

So basically, I'm just wondering if that makes sense to people.
And of course, the more social question belies here; is this a bit of a waste of time?

Science forum that bad...actually, yeah - must admit it somewhat doesn't feel like a particularly exciting discussion grounds.
However, actually - it's more just some offhand physics. I'm not actually a university student...yet (currently doing a-levels to put that to easier explanation) - so I'm somewhat bemused by the assumption of someone enrolled as a physics major since I believe that's a term of American universities, isn't it?
That aside; it's simply a physics course; fluid dynamics not even coming up. I simply went at the question and mathematics in pure idle self occupation.