ME3311 · Hydraulic & Pneumatic

Theme 2 · The fluid

Kinematic viscosity & oil grading

Datasheets and ISO grades never quote $\mu$. They quote kinematic viscosity. Here is what that second viscosity means, and how oil is graded and chosen.

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

Before you start

What you need first

Dynamic viscosity $\mu$ in Pa·s (Topic 7).
Density $\rho=\tfrac{\text{mass}}{\text{volume}}$ (Topic 8).

What you'll be able to do

Use $\nu=\dfrac{\mu}{\rho}$ and convert cSt ↔ m²/s.
Read an ISO VG grade and a viscosity index (VI).
Pick a grade for a temperature range.

Start here · the motivation

Why a second "viscosity"?

The instruments that measure oil viscosity simply time how long a fixed volume takes to drain through a cup. That draining is driven by the oil's own weight and resisted by its internal friction — so what they measure is viscosity relative to density. That ratio has its own name: kinematic viscosity.

Recall from the previous topic: $\rho$ is mass per unit volume, and hydraulic oil is about $\rho\approx 870~\text{kg/m}^3$. That is the number we now use to connect the two viscosities.

Kinematic viscosity $\nu = \mu/\rho$

$$\nu = \dfrac{\mu}{\rho}$$

where:
Symbol	Meaning	SI unit
$\nu$	kinematic viscosity	m²/s
$\mu$	dynamic viscosity	Pa·s
$\rho$	density	kg/m³

Read it as: $\nu$ is the oil's "thickness" weighed against its own inertia. It is the viscosity that decides flow regime — it is exactly what goes into the Reynolds number later ($\mathrm{Re} = vD/\nu$).

The SI unit (m²/s) is huge, so grades use the centistokes (cSt):

$$1~\text{cSt} = 10^{-6}~\text{m}^2/\text{s} = 1~\text{mm}^2/\text{s}$$

ISO VG — the grade number is just $\nu$ at 40 °C

An ISO Viscosity Grade is defined simply: the grade number is the oil's kinematic viscosity in cSt at 40 °C. So "ISO VG 46" means $\nu = 46~\text{cSt}$ at 40 °C.

Grade	ν at 40 °C (cSt)	Typical use
ISO VG 32	32	Light/indoor systems, cooler running
ISO VG 46	46	The general-purpose default for industrial hydraulics
ISO VG 68	68	Heavier duty, warmer climates

Viscosity falls as the oil heats — the VI tells you how much

Oil thins as it warms. How steeply it thins is the viscosity index (VI) — a high VI means the viscosity stays steadier across the temperature range.

A high-VI oil is thick enough to seal when hot, yet still thin enough to pump when cold — vital for machines that see both a cold start and hot running.

VI is raised with VI-improver additives (Topic 6); a "multigrade" oil is a high-VI oil.

Both oils thin when hot, but the high-VI oil holds its viscosity far better across the range.

Choosing the grade

A pump is happy only inside a viscosity band (often roughly 16–36 cSt at the working temperature, with wider start/stop limits). So:

Pick the VG so the oil sits in that band at the machine's working temperature.
Pick a high VI if the temperature swing is wide (cold start to hot running).

VG is always quoted at 40 °C, but the machine rarely runs at 40 °C — so you must think about viscosity at the real operating temperature, which is where the VI matters.

✏️ Try it yourself — no numbers needed

A machine starts on a cold winter morning and then runs hot all day. Two oils share the same ISO VG 46 grade, but one has a low VI and the other a high VI. Which would you choose, and what goes wrong with the other?

Choose the high-VI oil. It keeps a usable viscosity across the whole range — pumpable when cold, still sealing when hot. The low-VI oil: far too thick on the cold start (hard to pump, cavitation risk) and too thin when hot (leaks, poor film). Same VG at 40 °C — but very different behaviour where it actually runs.

Common mistakes to avoid

Mistake	Fix
Mixing up $\mu$ and $\nu$	$\nu=\mu/\rho$: divide dynamic viscosity by density.
Leaving $\nu$ in cSt inside a formula	Convert: $1~\text{cSt}=10^{-6}~\text{m}^2/\text{s}$.
Thinking VG is the viscosity at the running temperature	VG is measured at 40 °C only; use the VI to judge other temperatures.

Recap — the whole topic on one screen

$$\nu=\dfrac{\mu}{\rho}\qquad 1~\text{cSt}=10^{-6}~\text{m}^2/\text{s}\qquad \text{ISO VG} = \nu~[\text{cSt}]~\text{at }40\,^\circ\text{C}$$

Idea	What you own now
Kinematic viscosity	$\nu=\mu/\rho$; what cups measure; drives Reynolds
ISO VG	Grade number = ν in cSt at 40 °C
VI	How steady ν stays with temperature; high VI for wide swings

Next topic

Compressibility & bulk modulus

Oil seems "solid" — but it does compress, just a little. Next we measure that stiffness with the bulk modulus, and see why a few air bubbles wreck it.

→ Compressibility & bulk modulus

Kinematic viscosity & oil grading

Before you start

What you need first

What you'll be able to do

Why a second "viscosity"?

Kinematic viscosity \(\nu = \mu/\rho\)

ISO VG — the grade number is just \(\nu\) at 40 °C

Viscosity falls as the oil heats — the VI tells you how much

Choosing the grade

Common mistakes to avoid

Recap — the whole topic on one screen

Compressibility & bulk modulus

Symbol	Meaning	SI unit
\(\nu\)	kinematic viscosity	m²/s
\(\mu\)	dynamic viscosity	Pa·s
\(\rho\)	density	kg/m³

Mistake	Fix
Mixing up \(\mu\) and \(\nu\)	\(\nu=\mu/\rho\): divide dynamic viscosity by density.
Leaving \(\nu\) in cSt inside a formula	Convert: \(1~\text{cSt}=10^{-6}~\text{m}^2/\text{s}\).
Thinking VG is the viscosity at the running temperature	VG is measured at 40 °C only; use the VI to judge other temperatures.

Idea	What you own now
Kinematic viscosity	\(\nu=\mu/\rho\); what cups measure; drives Reynolds
ISO VG	Grade number = ν in cSt at 40 °C
VI	How steady ν stays with temperature; high VI for wide swings