Fluid pressure is the force a fluid exerts on each unit of area it touches. It matters in swimming, diving, plumbing, dams, weather, and the design of submarines and storage tanks. Unlike a solid block pushing in one direction, a fluid at rest presses on surfaces in every direction.
The basic definition is P = F / A, with pressure measured in pascals, where 1 Pa = 1 N/m².
In a liquid of constant density, pressure increases with depth because deeper points support the weight of more fluid above them. This increase is described by P = P0 + ρgh, where P0 is the pressure at the surface, ρ is density, g is gravitational field strength, and h is depth. The pressure difference between two depths is ΔP = ρgΔh, which explains why dams are thicker at the bottom and why divers feel greater pressure as they descend.
At the same depth in the same connected fluid, the pressure is the same no matter the container shape.
Understanding Physics: Pressure in Fluids
A useful way to picture liquid pressure is to imagine a tiny cube of water floating deep in a pool. Water above it has weight, so the water just above pushes down on the cube. If the cube did not push back upward with equal pressure, it would be squeezed downward.
Water beside the cube presses inward too. At rest, these pushes balance in every direction.
This balance explains why pressure depends on vertical depth rather than on the amount of water held by the whole container. A tall narrow tube can produce the same bottom pressure as a wide tank when the liquid height is the same.
Density changes the effect strongly. Salt water creates more pressure at a given depth than fresh water because the same volume contains more mass. Mercury produces far more pressure than water over the same height.
Gravity matters for the same reason. On a planet with weaker gravity, each layer of liquid weighs less, so pressure rises more slowly as depth increases. Students should keep depth separate from distance travelled through water.
Swimming sideways for ten metres at one level does not change the pressure. Moving down by one metre does.
The pressure at a liquid surface is often not zero. An open pool has air above it, and the atmosphere presses on the water. A diver experiences atmospheric pressure plus the extra pressure due to the water overhead.
This is why divers must equalise the pressure in their ears while descending. Air spaces in the body can become uncomfortable when their internal pressure does not match the surrounding water pressure.
In a sealed tank, a pump can raise the surface pressure. That added pressure reaches every point in the liquid, on top of the pressure caused by depth.
Engineers use these ideas whenever a liquid is stored or moved. A dam wall needs greater strength near its base because the pressure difference across the wall is largest there. Water towers work because raising water creates pressure in pipes below, allowing taps in nearby buildings to run without a pump at each tap.
Hydraulic brakes use a confined liquid to pass a pressure change through the system. A small force on one piston can help create a larger force on a larger piston because the larger piston has more area.
When solving problems, first identify whether the pressure needed is the extra pressure from the liquid or the total pressure including air. Then use the vertical height difference, the correct density, and gravitational field strength in consistent units.
Key Facts
- Fluid pressure is force per unit area: P = F / A.
- The SI unit of pressure is the pascal: 1 Pa = 1 N/m².
- Pressure in a fluid at rest acts in all directions, not just downward.
- Gauge pressure in a liquid is caused by depth: Pgauge = ρgh.
- Absolute pressure includes surface pressure: P = P0 + ρgh.
- At the same depth in the same static fluid, pressure is equal: ΔP = ρgΔh depends only on vertical height difference.
Vocabulary
- Pressure
- Pressure is the force applied perpendicular to a surface divided by the area of that surface.
- Fluid
- A fluid is a substance, such as a liquid or gas, that can flow and take the shape of its container.
- Pascal
- A pascal is the SI unit of pressure and equals one newton per square meter.
- Gauge pressure
- Gauge pressure is the pressure above the surrounding atmospheric or surface pressure.
- Absolute pressure
- Absolute pressure is the total pressure measured relative to a perfect vacuum.
Common Mistakes to Avoid
- Using volume instead of area in P = F / A is wrong because pressure depends on how force is spread over surface area, not how much space the object occupies.
- Forgetting atmospheric pressure in absolute pressure problems is wrong because P = P0 + ρgh includes the pressure already acting at the fluid surface.
- Thinking pressure only pushes downward is wrong because a fluid at rest exerts pressure perpendicular to every surface in all directions.
- Assuming container shape changes pressure at a given depth is wrong because in a connected static fluid, pressure depends on depth, density, and gravity, not the shape of the container.
Practice Questions
- 1 A force of 120 N is applied evenly over an area of 0.30 m². What pressure is produced in pascals?
- 2 A diver is 8.0 m below the surface of freshwater with density 1000 kg/m³. Using g = 9.8 m/s², find the gauge pressure at that depth.
- 3 Two holes are made in the side of a water tank, one near the top and one near the bottom. Explain which water stream travels farther and why.