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Ratio, proportion & rates of change · Compound units & rates

Chapter 1 · 4

The idea

Density and pressure

Why density is mass packed into one unit of volume and pressure is force spread over one unit of area, how to rearrange both formulas by sense rather than by triangle, and why a mixture's density is never the average of the two densities.

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Ratio, proportion & rates of change · Compound units & rates

Density and pressure

Why density is mass packed into one unit of volume and pressure is force spread over one unit of area, how to rearrange both formulas by sense rather than by triangle, and why a mixture's density is never the average of the two densities.

Why it works

Two more rates

Density and pressure are both rates, exactly like speed — just with different ingredients. Speed packs metres into one second; density packs mass into one unit of volume; pressure spreads force over one unit of area. Read any of them as "per one", and the arithmetic tells you itself whether to multiply or divide.

Density: mass packed into volume

Density is how much mass is packed into one unit of volume:

density=massvolume\text{density} = \frac{\text{mass}}{\text{volume}}

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