Water must flow for
all
I have written about
my obsession with showerheads before, the way I tease the rubberised nipples if
it is restricted or no water flow from any of the teats, this usually due to
calcification.
It is not enough to
stand under the shower, I look up and if just one of the teats is restricted,
it needs to be sorted out. Every teat must be supplying a spray of water at its
optimal capacity. In our apartment, I was met with a little extra difficulty,
the teasing of the nipples did not work on two of the outlets of the innermost circle
of 5.
The overhead shower
which is a Hans Grohe
product, the company founded in 1901 and is probably a global leader in
faucets, showers, and taps with the model ‘Raindance’ of which there are many
variants.
A census of the teats
After a few trials, I
attempted unpicking the teats with a toothpick to no avail. Eventually, I dismantled
the showerhead and found calcified deposits in the feeder assembly that I was
able to unpick with a toothpick. On reassembling the showerhead, all the teats
began working as intended.
Another thing that
had bothered me was finding a simple mathematical formula to calculate the
number of teats on a showerhead. There are diverse types, square, circular,
rectangular, oblong and so on. This determines how the teats are arranged in
the showerhead.
I have mostly
encountered the circular arrangement with concentric circles with a quintuple setting
in the innermost circle radiating out to 6 or 7 concentric circles. On the
basic count, there were 5 on the innermost circle, then 10 on the next and 15
on the following.
A formula is reused
This would suggest an
arithmetic or mathematical series. So, if there were 3 concentric circles based
on multiples of 5 teats in each concentric circle, the total number of teats
would be 5 + 10 + 15 = 30.
What makes this interesting
is the cumulative number of teats and the series developing. On the 1st
circle it is 5 or 5 * 1, for the second it is 15 or 5 * 3 and on the third, it
is 30 or 5 * 6. I well-known series of 1, 3, 6, 10, 15, 21, 28 … is
forming in the process. This, I have learnt is the triangular
number sequence.
The detail from the
link about suggests a formula of n(n + 1)/2. This would deal the determining
the number of teats for regular concentric circles where each consecutive
circle is a multiple in the natural sequence of the innermost circle. The series in
the paragraph above would suffice for where the innermost circle has one teat
and the next concentric circle has 3 using the triangular number sequence.
Hansgrohe Raindance showerhead
All numbers matter
The showerhead in the
picture has m = 5 teats on the innermost circle with n = 6 concentric circles.
For which I now have the formula m * n(n + 1)/2 and whilst the formula
can be decomposed further, it is neater to keep it this way. I would then have 5
* 6(6 +1)/2 = 5 * 6 * 7 / 2 = 105 teats.
On the referenced
blog where the rainfall showerhead at the Royal York Hotel had 7 concentric
circles with 5 being the multiple, the applied formula would result in 5 * 7 *
8 /2 = 140 teats.
With my showerhead conundrum
solved, I will happily bother my head with something obscure and productively
silly as finding out if there are really any insects with moustaches in Cape
Town, this showerhead mystery already fits the bill.
Courtesy of the William Kentridge exhibition at Zeitz MOCAA, Cape Town.
