Fluid Mechanics
Fluid Pressure Calculator
Calculate gauge and absolute pressure at any depth in a fluid. Includes fluid density presets and atmospheric pressure input.
Gauge Pressure
P = ρgh
Gauge Pressure
—
Pa
Absolute Pressure
—
Pa
Atmospheric Pressure
—
kPa
Step-by-Step Solution
What is Fluid Pressure?
Fluid pressure increases with depth because the weight of the fluid above presses down. The pressure at depth h depends on the fluid's density and local gravity. This relationship explains why submarines must withstand extreme pressures, why ears pop in aeroplanes, and how hydraulic systems work.
P_gauge = ρgh | P_absolute = P_atm + ρgh
ρ = fluid density (kg/m³) | g = 9.81 m/s² | h = depth (m) | P_atm = atmospheric pressure (Pa)
💡 Pressure in a fluid acts equally in all directions (Pascal's principle). This is why a submarine hull must withstand pressure from every direction, and why hydraulic jacks can lift cars with small input forces.
Real-World Applications
Scuba Diving
Pressure increases by ~1 atm every 10 m of water. Divers must breathe compressed air to equalise pressure.
Dam Design
Dams must withstand enormous water pressure — P = ρgh — which increases with the square of dam height.
Hydraulics
Hydraulic brakes and lifts use Pascal's principle to multiply force: same pressure, different areas.
Blood Pressure
Blood pressure is measured in mmHg (millimetres of mercury) — a direct application of P = ρgh.
Frequently Asked Questions
Why does pressure increase with depth?
At any depth h, the weight of the fluid column above presses down. This weight per unit area = ρgh. Deeper means more fluid above, hence more pressure.
What is gauge pressure vs absolute pressure?
Gauge pressure = pressure above atmospheric. Absolute pressure = gauge + atmospheric (101,325 Pa at sea level). Tyre pressure gauges read gauge pressure; absolute pressure is used in thermodynamics (PV = nRT).
What is Pascal's principle?
Pascal's principle: pressure applied to an enclosed fluid is transmitted equally in all directions. This enables hydraulics: a small force on a small piston creates the same pressure as a large force on a large piston — allowing force multiplication.