1. Why liquid pressure exists
Liquids have weight and can flow, so they press on the container bottom and walls, and within the liquid itself.
What affects liquid pressure
Required: P = ρgh; depth and density; side-hole jets.
Pressure (junior)Solid, liquid, atmospheric pressure and fluids.
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What affects liquid pressure
Liquid pressure: open three side holes at once — deeper holes spray harder and the middle jet flies farthest, because P = ρgh and range x = 2√(h(H−h)). On a realistic 3D tank bench, drag the water level, switch liquids, and watch jets, readouts, and the formula in action.
Memory cue: P = ρgh · depth & density only · range x = 2√(h(H−h)) peaks mid-tank.
Key formulas
P = ρghx = 2√(h(H−h))
How to use
- Find depth h: straight down from the free surface to the point.
- Drag the water level and switch liquids; check the three hole readouts.
- Watch the jets: deeper sprays harder, middle flies farthest — ρ and h in action.
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Related knowledge
Read section by section — adjust height and liquid on the tank, watch the three side jets, and match P = ρgh.
2. Features (from experiment)
- Pressure acts in every direction inside a liquid.
- At the same depth in the same liquid, pressure is equal in all directions.
- Pressure increases with depth.
- Pressure also depends on density: at equal depth, denser liquids press harder.
3. Formula P = ρgh
Imagine a liquid column of base S and height h: V = Sh, m = ρSh, weight G = ρShg. Pressure on the base is p = G/S = ρgh.
Depth h is the vertical distance from the free surface to the point — not an object's height above water, nor the container's height.
p = ρghp in Pa; ρ in kg/m³; g ≈ 9.8 N/kg (often 10 in rough work); h depth in m.
4. What matters
- Depth: deeper → larger pressure in the same liquid.
- Density: at the same depth, denser liquids press harder.
- Shape, base area, and total mass do NOT matter.
5. Pascal's barrel
In 1648 Pascal fitted a tall thin tube to a closed water-filled barrel and poured in only a few cups from a balcony — the barrel burst. Pressure depends on depth: a tall thin column still exerts large pressure.
6. Side holes & jet range
Deeper holes spray faster, but range also depends on height above the floor; the middle hole reaches farthest.
x = 2√(h(H−h))For hole depth h in water of height H, range x = 2√(h(H−h)), maximal at h = H/2.
7. Lab
- Punch three holes in a vertical line and fill the tank, then open them at once.
- Watch ranges: the middle goes farthest — depth controls pressure.
- Try different liquids or water levels to confirm ρ and h.
8. Applications
- Dams are thicker at the base where depth (and pressure) is greatest.
- Divers need pressure-rated suits; deep submersibles (e.g. Jiaolong) must resist huge pressure.
9. Pitfalls
- Liquid pressure ignores container shape — that area idea belongs to solid pressure p = F/S.
- Depth is measured vertically from the free surface, not an object's own height.
- p = ρgh is for liquids only — not for solids.
Applications
- Dams are thicker at the base because liquid pressure grows with depth.
- Divers feel higher pressure at greater depth; side-hole jets show the effect.
FAQ
Why are dams thicker at the bottom?
P = ρgh means pressure grows with depth, so the base must be reinforced to resist the larger pressure.
Does liquid pressure depend on the container shape?
No. It depends only on density and depth — not shape, base area, or total mass. Base-area thinking belongs to solid pressure.
Why does the middle hole jet fly farthest?
Range x = 2√(h(H−h)): too shallow means slow spray, too deep means the water lands early — h = H/2 balances the two.
Does a wider base mean higher liquid pressure?
No. P = ρgh depends on density and depth, not base area.
Do higher side holes spray farther?
Deeper holes usually jet harder; compare depths and head in the lab.