Thermal expansion & trapped-oil pressure

Oil expands a lot when heated. If it is trapped and cannot expand, that pull toward expansion turns into enormous pressure — a real burst hazard.

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

Before you start

What you need first

Bulk modulus $B$ — the oil's stiffness (Topic 10).

What you'll be able to do

Use $\Delta V = \alpha\,V\,\Delta T$ for free expansion.
Use $\Delta P = \alpha\,B\,\Delta T$ for trapped oil.
Explain why a trapped, heated line is dangerous — and how to protect it.

Start here · free expansion

Oil expands when heated

Free to grow, a warmed volume of oil expands by:

$$\Delta V = \alpha\,V\,\Delta T$$

where:
Symbol	Meaning	SI unit
$\Delta V$	volume increase	m³
$\alpha$	cubical (volume) expansion coefficient	1/°C
V	original volume	m³
$\Delta T$	temperature rise	°C (or K)

For hydraulic oil $\alpha \approx 7\times10^{-4}~/°\text{C}$ — about ten times more than steel. That is why a reservoir must leave an air gap, and why the oil level rises as a machine warms up.

Trap it, and the pressure rockets

Now seal the oil so it cannot expand (a length of line shut between two closed valves). Heating still "wants" to expand it by $\alpha\,\Delta T$ — but that expansion is suppressed by compressing the oil, which needs a pressure rise of stiffness $B$ times that strain:

$$\Delta P = \alpha\,B\,\Delta T$$

Put numbers in and it is alarming: with $\alpha=7\times10^{-4}$, $B=1.7~\text{GPa}$, just $\Delta T = 20\,°\text{C}$ gives $\Delta P \approx 238~\text{bar}$. Notice it does not depend on the volume — a short trapped line is just as dangerous as a long one.

Sealed oil + heat → the "wanted" expansion is converted into a steep pressure rise, $\Delta P=\alpha B\,\Delta T$.

How to protect against it

Never fully trap a service line that can be heated — fit a small thermal-relief valve that cracks open and bleeds a little oil to tank.
Leave expansion room: a reservoir air gap, an accumulator, or a relief path.
Beware closed-centre valves locking oil in a sun-heated cylinder (recall Topic 5) — that is a classic trapped-volume case.

✏️ Try it yourself — no numbers needed

A filled hydraulic line is shut at both ends on a cool morning, then sits in the midday sun. Why is this dangerous, and what single change removes the danger?

Danger: the oil cannot expand, so the temperature rise converts to a large pressure rise ($\Delta P=\alpha B\,\Delta T$) — easily hundreds of bar from a modest warming, enough to burst a hose or fitting. Fix: give the oil somewhere to go — a small thermal-relief valve (or an accumulator / expansion path) so the expansion bleeds off instead of building pressure.

Common mistakes to avoid

Mistake	Fix
Thinking a short trapped line is "too small to matter"	$\Delta P=\alpha B\,\Delta T$ has no volume in it — length doesn't reduce the risk.
Using $B$ in GPa with $\Delta T$ but forgetting the result is in Pa	$\alpha B\,\Delta T$ gives pascals; ÷$10^5$ for bar.
Confusing free expansion with trapped pressure	Free → $\Delta V=\alpha V\Delta T$; trapped → $\Delta P=\alpha B\Delta T$.

Recap — the whole topic on one screen

$$\Delta V=\alpha V\,\Delta T \qquad \Delta P=\alpha B\,\Delta T\qquad \alpha\approx 7\times10^{-4}~/°\text{C}$$

Idea	What you own now
Free expansion	$\Delta V=\alpha V\Delta T$; oil expands ~10× steel
Trapped pressure	$\Delta P=\alpha B\Delta T$ — huge, volume-independent
Protection	Thermal relief / expansion room; mind closed-centre traps

Next topic

Cavitation, vapour pressure & aeration

We've squeezed and heated the oil. Next, the opposite danger: where the pressure drops too low, the oil boils or sucks in air — and the bubbles wreck pumps.

→ Cavitation, vapour pressure & aeration

Symbol	Meaning	SI unit
\(\Delta V\)	volume increase	m³
\(\alpha\)	cubical (volume) expansion coefficient	1/°C
V	original volume	m³
\(\Delta T\)	temperature rise	°C (or K)

Mistake	Fix
Thinking a short trapped line is "too small to matter"	\(\Delta P=\alpha B\,\Delta T\) has no volume in it — length doesn't reduce the risk.
Using \(B\) in GPa with \(\Delta T\) but forgetting the result is in Pa	\(\alpha B\,\Delta T\) gives pascals; ÷\(10^5\) for bar.
Confusing free expansion with trapped pressure	Free → \(\Delta V=\alpha V\Delta T\); trapped → \(\Delta P=\alpha B\Delta T\).

Idea	What you own now
Free expansion	\(\Delta V=\alpha V\Delta T\); oil expands ~10× steel
Trapped pressure	\(\Delta P=\alpha B\Delta T\) — huge, volume-independent
Protection	Thermal relief / expansion room; mind closed-centre traps