Deeper is Harder

Why it matters

Dam walls are always thicker at the bottom. Divers' ears hurt more the deeper they go. Water keeps a strict account of depth — and pays it out as pressure.

The idea in plain words

The depth tax. Tap the terms.

P = h ρ g

Pressure of water 10 m down (ρ = 1000, g = 10)?

100,000 Pa — one full atmosphere, every 10 m of water

• metre: h — depth BELOW the free surface — the only distance that matters
• kg/m³: ρ — density of the liquid — mercury taxes ~13.6× harder than water
• the liquid laws: laws — same depth → same pressure in all directions; independent of vessel SHAPE and total amount
• P = hρg = 10 × 1000 × 10

Predict first

Three holes in a bottle's side: top, middle, bottom. Which jet lands farthest?

P = hρg: pressure grows with DEPTH below the surface. The bottom hole feels the tallest column and shoots hardest.

• the bottom one — most water above it, most pressure — correct
• the top one — least water to hold it back
• all equal — same water

What you do

Tap your prediction, then raise the water level and watch every jet obey h.

Check yourself

Liquid pressure at a point depends on…

A thin 10 m pipe and a 10 m lake press equally hard at the bottom — h is everything.

Dam walls are built thicker at the base because…

P = hρg made concrete: engineering drawn to the shape of the equation.

At the same depth, a liquid pushes…

That upward push at depth is the seed of the next chapter: upthrust.

• depth and density (and g) — NOT the vessel's shape or width — correct
• the total amount of liquid
• the container's shape
• pressure rises with depth — the base takes the hardest push — correct
• the base carries the wall's weight
• it looks stable
• equally in ALL directions — even upward — correct
• only downward
• only sideways