Assume we have some velocity data given in km/h:
$$ \mathrm{velocity} = [10, 25, 40, 55, 70, 90, 105, 120] $$
and the corresponding fuel consumption given in liters/10km:
$$ \mathrm{fuel} = [2.2, 1.5, 0.83, 0.81, 0.78, 0.75, 0.87, 0.99] $$ I want to find fuel used per hour. Here's what I have done
$$ \mathrm{distance\ per\ hour} = \frac{10}{\mathrm{velocity}/60} $$ (time it takes to travel 10 km at a given velocity)
$$ \mathrm{fuel\ per\ hour} =\frac{\mathrm{fuel\ consumption}}{\mathrm{distance\ per\ hour}} $$
so we can calculate fuel/hour
However, what I obtain is:
$$ \mathrm{fuel\ per\ hour} = \\ [0.03666667, 0.0625, 0.05533333, 0.07425, 0.091, 0.1125, 0.15225, 0.198] $$
And it does not look very realistic, I think the numbers are too small. Have I done anything wrong?
When converting different units, I like to think of them as fractions, as I find this a convenient way to actually visualise what is going on there (even though the notation does seem a bit off, but again, this is only to get the intuition behind the calculations). So, the first thing I’d do is convert $l/10 km$ to $l/km$; one can imagine this as follows: $$x \frac{l}{10\,km}=\frac{x}{10}\frac{l}{km}$$ Hence, a fuel consumption of $2.2\,l/10\,km$ is the same as $0.22\,l/km$. Now, we need to figure out how to calculate the fuel consumption over time, that is, how to get $l/h$ as a unit. We see that $$x\frac{l}{km}\cdot y\frac{km}{h}=xy\frac{l}{h}$$ by simply thinking of the units as fractions; then, the $km$'s cancel out, and we are left with what we wanted, that is $l/h$. So to sum it up, if your car uses $x\,l/10 km$ at $y\,km/h$, the fuel consumption in liters per hour is calculated as follows: $$x\frac{l}{10\,km}y\frac{km}{h}=\frac{xy}{10}\frac{l}{h}$$ So, for the first car driving at $10\,km/h$ with fuel consumption $2.2\,l/10\,km$, you’d get $$2.2\frac{l}{10\,km}\cdot10\frac{km}{h}=\frac{2.2\cdot10}{10}\frac{l}{h}=2.2\frac{l}{h}$$ So, the resulting consumption in $l/h$ would be [2.2 3.75 3.32 4.455 5.46 6.75 9.135 11.88], which also seems a bit more realistic. Hope this helps :)