Physics · Fluids

Pressure and Hydrostatic Pressure

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Wrap-up

What you learned

Recommended next: Open concept testCheck whether the core ideas are ready without leaving this concept.
Read next: Continuity EquationMove from static pressure to steady flow

Key takeaway

Surface pressure from the piston is $P_{s} = F / A$ , so the same force gives less pressure when it is spread over a larger area.
In a resting connected fluid, pressure at one point acts equally in all directions.

Common misconception

Fluid pressure only pushes downward because the fluid above the point has weight.

The fluid above a point explains why pressure increases with depth, but the pressure at that point acts equally in all directions.

Carry this into buoyancy and fluids

Keep this idea moving

Open the next concept, route, or track only when you want the current model to widen into a larger branch.

Move from static pressure to steady flowFluids

Continuity Equation

Keep one steady stream tube on screen and use Q = Av to connect cross-sectional area, flow speed, and the same volume flow rate through narrow and wide sections.

Add speed-pressure tradeoffsFluids

Bernoulli's Principle

Follow one steady ideal-flow pipe and see how pressure, speed, and height trade within the same Bernoulli budget while continuity keeps the flow-rate story honest.

Carry pressure into buoyancyFluids

Buoyancy and Archimedes' Principle

Use one immersed-block bench to connect pressure difference, displaced fluid, and the density balance behind floating, sinking, and neutral buoyancy.

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Reference and support

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Equation snapshotPressure from a surface load · Hydrostatic pressureShow 2 equations

Pressure from a surface load
$P_{s} = \frac{F}{A}$
The same force gives less pressure when it is spread over a larger area.
Hydrostatic pressure
$P_{h} = ρ g h$
Deeper points have more fluid above them, so hydrostatic pressure increases with depth.

Why it behaves this way

Explanation

Pressure tells you how much force is applied to each unit area. If the same force is spread over a larger area, the pressure is smaller. The piston at the fluid surface lets you see that $P_{s} = F / A$ idea directly before depth is added.

A resting fluid transmits pressure through the connected fluid, and at one point that pressure acts equally in all directions. The probe arrows are not only downward. The fluid above explains why pressure increases with depth, but the pressure at a point is still the same in every direction at that point.

Depth adds hydrostatic pressure because deeper points have more fluid above them. On this page, the probe reads the surface pressure from the piston plus the depth-dependent part $h o g h$ . That gives one clear chain to follow: change force or area to change $F / A$ , change depth, density, or gravity to change the hydrostatic part, then read how both pieces combine in the graphs and the probe.

Key ideas

01Surface pressure from the piston is

P_{s} = F / A

, so the same force gives less pressure when it is spread over a larger area.

02In a resting connected fluid, pressure at one point acts equally in all directions.

03At the same depth in the same resting fluid, the hydrostatic pressure is the same.

04Hydrostatic pressure increases linearly with depth because each extra meter adds the same pressure increment.

05Density and gravity set the slope of the pressure-depth graph, so denser fluids or stronger gravity make pressure rise faster with depth.

Worked examples

Pressure worked examples

Open examples when you want to see the same idea walked through step by step.

Frozen walkthrough

Step through the frozen example

Frozen walkthrough

Use the current tank values. First separate the probe reading into surface pressure and hydrostatic pressure, then see how an extra depth change affects the total.

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Example 1 of 2

Frozen valuesUsing frozen parameters

For the current tank with $F = 720$ , $A = 0.15$ , $h o = 1 e 3$ , $g = 9.8$ , and $h = 1$ , what surface pressure, hydrostatic pressure, and total probe pressure should you expect?

F

Surface force

720 N

A

Piston area

0.15 m²

ρ

Fluid density

1e3 kg/m³

g

Gravity

9.8 m/s²

h

Probe depth

1 m

1. Convert the piston force into surface pressure with $P_s = F/A$

The piston sets

P_{s} = F / A = 4.8 kPa

, so the same force is currently being spread across a moderate piston area.

2. Calculate the extra pressure from depth with $P_h = ho g h$

The fluid column contributes

P_{h} = ρ g h = 9.8 kPa

at depth

1 m

3. Add the two parts to get the probe reading

So the probe reads

P_{probe} = P_{s} + P_{h} = 14.6 kPa

, with the hydrostatic contribution currently larger.

Predicted probe pressure

P_{s} = 4.8 kPa, P_{h} = 9.8 kPa, P_{probe} = 14.6 kPa

The fluid column is doing most of the work here, so moving deeper or changing density would matter more than changing the same already-moderate surface load.

Quick test

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Accessibility

Open the text-first descriptions when you need the simulation and graph translated into words.

The simulation shows a piston pressing on a fluid surface and a pressure probe at an adjustable depth. The piston width represents area, the downward arrow represents surface force, the depth marker shows how far the probe is below the surface, and equal arrows around the probe show pressure acting equally in all directions at that point.

The readout card separates surface pressure, hydrostatic pressure, and total probe pressure. Compare mode overlays a second setup on the same tank so you can compare different ways of producing similar total pressures.

Each graph changes one variable at a time in a static fluid: depth, density, force, or piston area. The other variables stay fixed so the cause of each pressure change is easier to read.

Graph summary

The pressure-depth graph is the main hydrostatic graph. The surface-pressure line stays flat, while the hydrostatic and total pressures rise linearly with depth.

The other graphs isolate the remaining causes. Density changes only the hydrostatic part, force changes only the surface-pressure part, and area changes surface pressure by spreading the same force over more or less area.

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Fluid and Pressure

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