> Hertz is for periodic phenomena
> The applicable SI unit therefore is just the reciprocal second, s^(-1).
That's the hertz.
> The applicable SI unit therefore is just the reciprocal second, s^(-1).
That's the hertz.
When you use hertz meaning ‘cycles per second’ it’s far more natural to associate it with an angular velocity of 2pi radians per second - which throws a bit of a spanner in the dimensionless works, and makes it feel like using 1/2pi as a radian makes more sense.
Score another point for tau I guess.
The Becquerel is also s^-1.
It's not algebraically incorrect, but it contains something dangerously wrong connotations about what kind of data it is.
A watt is just a joule per second. Making 1 kWh === 3.6 MJ.
In the US we use miles per gallon, which is the inverse - a ‘per area’.
You see this problem pop up all the time in chemistry, where a mole of some substance and a mole of some other substance are incompatible units. There is no such unit as "mole", only "mole of [whatever]". But there are people who would like to believe that "mole" is a unit.
(In contrast, there is such a unit as "liter", but it isn't used in fuel efficiency ratings.)
If my engine consumes 10lGas/100km when traveling at 100km/h, that means it uses 10lGas/h, or .002778 lGas/s.
If the pipe feeding my engine has a cross sectional area of 10^-6m^2, how fast is the gasoline flowing through that pipe?
Naively I would expect I could divide flow rate by area to get mean velocity. But I’m expecting the result to be in m/s. But if I divide .002778 lGas/s by 10^-6m^2 I get 2778lGas/sm^2.
Unless an lGas is 10^-3mGas^3 and I can measure gas area in mGas^2, so I can get my gas speed in mGas/s?
If you want a mathematical way to capture ‘of gasoline’ the right way to think of it is not as a unit dimension but rather as a basis vector, kinda like ‘up’ or ‘across’.
1m * up is the vector quantity ‘1m up’, which has dimension ‘length’. 1m * across is the vector quantity ‘1m across’ which also has dimension length (we call it a displacement, but it’s a vector in the length dimension). We can add them together even though they point in different directions because they share the same dimension. The result is the vector quantity ‘1m up and 1m across’ and it is also a length.
Similarly 1l * of gas is a vector quantity ‘1l of gas’ with dimension ‘volume’. I can add it to ‘1l of air’ to get ‘1l of gas plus 1l of air’ which is still a vector volume. It might describe the contents of my fuel tank when it’s half empty for example.
This is one of the most salient ways in which different types of power plants differ; it's something that people are very concerned with.