Pinned by a Pressure Difference
When the water pressure on one side of an opening is higher than on the other — a dam, a valve left open, a pipeline at low pressure, a pool drain — anything that covers the opening is pressed onto it. Divers call it Delta P. Find the force from a height difference, a pressure difference or work back from a reported force.
Why Pulling Doesn’t Help
Water presses on everything in it, and the deeper you go the harder it presses: every metre of fresh water adds about 9.8 kPa. If an opening connects deep water to a place at lower pressure — the other side of a dam, an empty pipe, a pump’s suction — the water rushes through. Whatever covers the opening stops the flow, but not the pressure difference: the full Δp now pushes on the covered area, F = Δp · A.
Because the force grows with the area, even a modest pressure difference on a pipe-sized opening gives the weight of several adults. Rescuers cannot pull against that. The only way out is to remove the pressure difference: close the valve, stop the pump or let the low side fill up. That is why commercial divers only work near openings after every valve and pump has been locked off.
From Pressure to Force, Step by Step
ΔPAssumptions of This Model
| Assumption | In reality… |
|---|---|
| The opening is fully sealed, and the pressure difference acts on exactly its area: F = Δp·A | a partly covered opening keeps flowing and pins with less force; a soft body part pushed into the opening is held over a slightly different area |
| Height difference: the water stands still once the opening is covered, so Δp = ρgΔh with a constant density | while water still flows the pressure at the opening is lower, so the pull is weaker until the opening is covered |
| Reported force: it acted on exactly the area of the opening you enter | if the force was spread over a larger area (a body part partly inside the pipe, a gap that was only partly covered), the real pressure difference and water height were smaller |
| The pressure difference does not change over time | it lasts until a valve closes, a pump stops or the low side fills up; a closed pipe that fills slowly loses its Δp over time |
| Inflow while open: ideal (Torricelli) with a discharge coefficient of 0.61, liquids only | grates, bends and pipe friction lower the inflow |
| “Adults” means 75 kg of weight each | a way to picture the force, not a count of the rescuers it would take |
Key Relations
Hydrostatics: the pressure difference between two connected water levels.
The pressure difference times the covered area. The force grows with the square of the diameter.
A reported force on a known opening tells you the pressure difference and the height of water behind it.
Torricelli: the speed of the water rushing through the opening before anything covers it; 0.61 is the discharge coefficient of a sharp-edged opening. Only for liquids.
Sources & Verification
- Y. A. Çengel & J. M. Cimbala, Fluid Mechanics: Fundamentals and Applications, 4th ed., McGraw-Hill, 2018 — hydrostatic pressure and forces on submerged surfaces (Ch. 3), orifice flow (Ch. 8).
- IMCA (International Marine Contractors Association), safety flashes on differential pressure — e.g. SF 14/11 “Identification of differential pressures subsea during diving operations”.
- Reported cases used for the examples — Lake Oliver Dam, Georgia, 2020 (a diver held by a 10-inch opening, reported as about 850 pounds); the 1654 Magdeburg hemispheres experiment of Otto von Guericke (spheres about 35.5 cm across).
- Model choices — the covered opening carries the full pressure difference; the opening is flat and fully covered; the inflow speed is ideal (Torricelli) with a discharge coefficient of 0.61.
Frequently Asked Questions
What is Delta P in diving?
Delta P (ΔP) is a pressure difference across an opening: deep water on one side, lower pressure on the other, for example behind a dam gate, in an emptied pipe or at a pump intake. Water rushes towards the opening, and whatever covers it is pressed on with F = Δp × A. A 30 cm opening with 10 m of fresh water behind it pushes with about 6.9 kN, the weight of 705 kg.
How do you calculate the suction force on an opening?
First the pressure difference: Δp = ρ × g × Δh, about 9.8 kPa for every metre of fresh water. Then multiply by the area of the opening: F = Δp × A. For a round opening A = π d² / 4, so twice the diameter gives four times the force.
Why can't rescuers pull a pinned diver free?
Because the force is far bigger than people can pull, and it does not get smaller while the opening stays covered. At Lake Oliver Dam in Georgia (2020) a diver was held by a 10-inch opening with a force reported as about 850 pounds; that matches a pressure difference of 74.6 kPa, or 7.6 m of water. The diver did not survive and could only be released after the open valve had been found and closed. The only way to free someone is to remove the pressure difference: close the valve, stop the pump or fill the low side.
How strong is the suction of a pool drain?
It depends on the pump and the size of the opening. As an illustration, a pump suction of 0.3 bar on an uncovered 15 cm drain gives 530 N, the weight of 54 kg, enough to hold a child or long hair under water. That is why pools use anti-entrapment covers, more than one drain and safety systems that shut the pump off.
What were the Magdeburg hemispheres?
In 1654 Otto von Guericke pumped the air out of two copper half-spheres, about 35.5 cm across, and showed that teams of horses could not pull them apart. With a perfect vacuum the outside air presses them together with about 10 kN, the weight of a tonne. It is the same physics as Delta P under water: a pressure difference times an area.