Fluid Pressure Calculator
Calculate fluid pressure at depth using density, gravity, and height for hydrostatics problems
Hydrostatic Pressure
Depth (h)
Fluid Density (ρ)
Gravity (g)
Absolute Pressure
Pressure in atm
Pressure in psi
Calculation Details
Understanding Fluid Pressure
Fluid pressure is the force per unit area exerted by a fluid at rest. In a static fluid, pressure increases linearly with depth due to the weight of the fluid above. This principle, described by Pascal's law, is fundamental to hydraulics, underwater engineering, atmospheric science, and many other fields. The hydrostatic pressure equation P = ρgh relates pressure to fluid density, gravitational acceleration, and depth below the surface.
Key Formulas
- P = ρgh — Hydrostatic pressure (gauge pressure due to the fluid column)
- P_abs = P₀ + ρgh — Absolute pressure (atmospheric pressure plus hydrostatic pressure)
- P_gauge = P_abs − P₀ — Gauge pressure (pressure relative to atmospheric)
Variables
- P — Pressure (Pa, Pascals)
- ρ — Fluid density (kg/m³)
- g — Gravitational acceleration (m/s²)
- h — Depth below the surface (m)
- P₀ — Atmospheric pressure (101,325 Pa at sea level)
Common Fluid Densities
| Fluid | Density (kg/m³) | Pressure at 10 m depth (Pa) |
|---|---|---|
| Fresh Water | 997 | 97,776 |
| Seawater | 1,025 | 100,522 |
| Mercury | 13,534 | 1,327,560 |
| Ethanol | 789 | 77,387 |
| Crude Oil | ≈870 | 85,321 |
| Glycerin | 1,260 | 123,568 |
| Air (sea level) | 1.225 | 12.02 |
Types of Pressure
Absolute Pressure
- • Total pressure relative to a perfect vacuum
- • P_abs = P₀ + P_gauge
- • Always a positive value
- • Used in thermodynamic calculations
Gauge Pressure
- • Pressure relative to atmospheric pressure
- • P_gauge = P_abs − P₀
- • Can be positive or negative (vacuum)
- • Measured by most pressure gauges
Hydrostatic Pressure
- • Pressure exerted by a fluid at rest
- • P = ρgh
- • Increases linearly with depth
- • Independent of container shape
Real-World Applications
Fluid pressure principles are applied across many fields of engineering and science:
- A scuba diver at 10 m depth in seawater experiences roughly 2 atm of absolute pressure (1 atm atmospheric + 1 atm from the water column)
- Hydraulic brakes in cars use Pascal's law to multiply force through an incompressible fluid
- Dam design must account for increasing pressure with depth — the base of Hoover Dam withstands over 2 million Pa from the water behind it
- Blood pressure in humans varies with body position due to hydrostatic effects of the blood column
- Deep-sea submersibles like the Trieste reached the Mariana Trench at 10,916 m, enduring pressures exceeding 110 MPa
Pascal's Law
Pascal's law (also known as Pascal's principle) states that a pressure change applied to an enclosed, incompressible fluid is transmitted undiminished throughout the fluid and to the walls of its container. Formulated by Blaise Pascal in 1653, this principle is the basis of hydraulic systems.
Key Consequences:
- Pressure at a given depth is the same in all directions
- Pressure depends only on depth, not on the shape of the container (hydrostatic paradox)
- A small force applied over a small area can generate a large force over a large area (hydraulic advantage)
- Hydraulic presses, lifts, and brakes all exploit this principle
References
The formulas and physical constants used in this calculator are based on established fluid mechanics principles and verified sources:
Related Calculators
Note: This calculator assumes an ideal, incompressible, static fluid at uniform temperature. It does not account for fluid compressibility, temperature gradients, dissolved gases, or dynamic flow effects. Results are based on classical hydrostatics and may differ from real-world conditions.
Recommended Calculator
Casio FX-991ES Plus
The professional-grade scientific calculator with 417 functions, natural display, and solar power. Perfect for students and professionals.
View on Amazon