Two relations, and they only mean anything side by side: one says what a pipe can hold, the other says what the water will throw at it.

Barlow's formula, $P = \dfrac{2 S t}{D}$ — P equals two S t over D. $P$ is the internal pressure the wall can contain, $S$ is the hoop stress the material is allowed to carry (its yield strength divided by a code safety factor), $t$ is the wall thickness and $D$ the outside diameter. Keep $t$ and $D$ in the same unit and their ratio is bare, so the answer comes out wearing whatever unit $S$ wore — MPa in, MPa out. The 2 is not decoration: it comes from balancing the pressure across a diameter against two wall sections, one on each side. Read the shape of it and the trade lore falls out — thicker wall, proportionally more pressure; bigger bore, proportionally less. That is why large mains are the expensive ones.

Joukowsky's equation, $\Delta P = \rho\, a\, \Delta v$ — delta-P equals rho a delta-v. $\Delta P$ is the surge pressure ABOVE line pressure in pascals, $\rho$ the fluid density in kg/m³, $\Delta v$ the velocity destroyed in m/s, and $a$ the wave celerity — the speed the pressure wave travels back up the pipe, roughly 1200–1400 m/s in steel, but only 300–500 m/s in thermoplastic, because a plastic wall stretches as the wave passes and takes the edge off it.

Look at what is NOT in that equation: the length of the pipe, and the pressure already in it. Length decides only whether the closure counts as sudden; the peak itself does not care. And the surge rides on top of whatever the line was carrying — the wall feels the sum, which is exactly the sum a verdict has to be made against.

Run the numbers once and the fear becomes useful. Water at 2 m/s in steel, stopped dead: $1000 \times 1200 \times 2 = 2.4\ \mathrm{MPa}$, which is 24 bar of surge on a line that may never see 4 bar in service. A quarter-turn ball valve closed by an enthusiastic apprentice does this. The three remedies are slower closure, a surge vessel, and lower velocity — and only the last one is free, because it was a sizing decision all along.