Density

The most basic property of the oil — mass per unit volume. Small and almost constant, but it sets the oil's inertia and ties dynamic viscosity to the kinematic one.

Source: Rabie, Fluid Power Engineering, Ch. 2.

Before you start

What you need first

The oil's jobs (Topic 6).

What you'll be able to do

Use $\rho=\dfrac{m}{V}$ both ways.
Quote a typical oil density and relative density.
Say why density matters and how it shifts with temperature.

Start here · the definition

Density = mass ÷ volume

$$\rho = \dfrac{m}{V}$$

where:
Symbol	Meaning	SI unit
$\rho$	density	kg/m³
m	mass of oil	kg
V	volume of oil	m³

Hydraulic mineral oil is about $\rho \approx 850\!-\!900~\text{kg/m}^3$ — a little lighter than water (1000 kg/m³). A handy round value is 870 kg/m³.

Relative density (specific gravity)

Relative density compares the oil with water — useful because it is dimensionless:

$$\text{RD} = \dfrac{\rho_{\text{oil}}}{\rho_{\text{water}}}$$

For $\rho_{\text{oil}}=870$ and $\rho_{\text{water}}=1000$, $\text{RD}=0.87$. That is why oil floats on water — handy to remember when water contaminates a tank: it sinks to the bottom, where the drain is.

Why density matters

It sets the kinematic viscosity — $\nu=\mu/\rho$ (Topic 9) and so the Reynolds number $\mathrm{Re}=vD/\nu$ later.
It is the oil's inertia — a fast-reversing column of oil has mass that must be accelerated and stopped; denser oil resists more.
It sets the pressure of a standing oil column — the "head." A column of oil of height $h$ presses down at its base with $p=\rho g h$ (here $g=9.81~\text{m/s}^2$ is gravity and $h$ is the column height in metres). That column-pressure is what engineers call the head; denser oil gives more of it, which matters at the pump suction.

Density falls a little as the oil heats

Heat the oil and it expands, so the same mass fills more volume — density drops (roughly 0.6–0.7% per 10 °C for mineral oil). The change is small, but real.

Because density barely moves while viscosity changes a lot with temperature (Topic 9), it is the viscosity — not the density — that dominates how oil behaves across the working range. We treat the expansion itself in Topic 11.

✏️ Try it yourself — no numbers needed

Two oils have the same dynamic viscosity $\mu$, but oil A is denser than oil B. Which has the higher kinematic viscosity $\nu$, and which would turn turbulent at a lower speed?

Higher ν: oil B (the lighter one). Since $\nu=\mu/\rho$, a smaller $\rho$ gives a larger $\nu$ for the same $\mu$. Turbulent sooner: oil A (the denser one) has the lower $\nu$, so $\mathrm{Re}=vD/\nu$ is larger — it reaches the turbulent threshold at a lower speed.

Common mistakes to avoid

Mistake	Fix
Using water's density (1000) for oil	Oil is lighter — about 870 kg/m³.
Quoting volume in litres inside $\rho=m/V$	Convert to m³ first: $1~\text{L}=10^{-3}~\text{m}^3$.
Expecting density to swing like viscosity	Density changes only slightly with temperature; viscosity changes a lot.

Recap — the whole topic on one screen

$$\rho=\dfrac{m}{V}\qquad \rho_{\text{oil}}\approx 870~\text{kg/m}^3\qquad \text{RD}=\dfrac{\rho_{\text{oil}}}{\rho_{\text{water}}}\approx 0.87$$

Idea	What you own now
Density	$\rho=m/V$; oil ≈ 870 kg/m³ (lighter than water)
Relative density	≈ 0.87 → oil floats on water
Why it matters	Sets $\nu=\mu/\rho$, inertia, and head

Next topic

Kinematic viscosity & oil grading

Now that you have both $\mu$ and $\rho$, we combine them into the kinematic viscosity $\nu=\mu/\rho$ — the one datasheets quote, and how oil is graded and chosen.

→ Kinematic viscosity & oil grading

Mistake	Fix
Using water's density (1000) for oil	Oil is lighter — about 870 kg/m³.
Quoting volume in litres inside \(\rho=m/V\)	Convert to m³ first: \(1~\text{L}=10^{-3}~\text{m}^3\).
Expecting density to swing like viscosity	Density changes only slightly with temperature; viscosity changes a lot.

Idea	What you own now
Density	\(\rho=m/V\); oil ≈ 870 kg/m³ (lighter than water)
Relative density	≈ 0.87 → oil floats on water
Why it matters	Sets \(\nu=\mu/\rho\), inertia, and head