Hydrostatic Pressure Calculator
Free calculate pressure at depth in fluids using density, depth, and gravity. solve for pressure or depth.
Input Parameters
Water: 1000 kg/m³, Seawater: ~1025 kg/m³
Earth: 9.81 m/s²
Results
Enter values to calculate
What is Hydrostatic Pressure?
Hydrostatic pressure is the pressure exerted by a fluid at rest due to the weight of the fluid above a given point. It increases linearly with depth and depends on the fluid's density and the acceleration due to gravity.
This principle is fundamental in fluid mechanics and explains why pressure increases with depth in oceans, lakes, and any container of fluid. The pressure at any depth is independent of the container's shape and depends only on the depth and fluid density.
Hydrostatic pressure is crucial in engineering applications such as dam design, submarine operations, scuba diving, and hydraulic systems. It's also the principle behind barometers and manometers.
Hydrostatic Pressure Formula
Where:
- • P = Hydrostatic pressure (Pa)
- • ρ = Fluid density (kg/m³)
- • g = Gravitational acceleration (9.81 m/s² on Earth)
- • h = Depth below surface (m)
To find depth: h = P / (ρ × g)
How to Calculate Hydrostatic Pressure
-
1
Identify the fluid and its density
Determine the density of the fluid (water = 1000 kg/m³, seawater ≈ 1025 kg/m³).
-
2
Measure or specify the depth
Determine the depth below the fluid surface where you want to calculate pressure.
-
3
Apply the formula
Multiply density, gravitational acceleration, and depth: P = ρ × g × h
-
4
Convert units if needed
Convert the result to your preferred pressure units (bar, PSI, etc.).
Practical Examples
Example 1: Swimming Pool
Calculate the pressure at the bottom of a 3-meter deep swimming pool filled with water.
Solution:
P = ρ × g × h
P = 1000 kg/m³ × 9.81 m/s² × 3 m
P = 29,430 Pa = 29.43 kPa ≈ 0.29 bar
Example 2: Ocean Depth
Calculate the pressure at 100 meters depth in seawater (density = 1025 kg/m³).
Solution:
P = 1025 kg/m³ × 9.81 m/s² × 100 m
P = 1,005,525 Pa = 1.01 MPa ≈ 10.1 bar
This is approximately 10× atmospheric pressure!
Example 3: Finding Depth from Pressure
A pressure gauge reads 50 PSI in water. At what depth is this measurement taken?
Solution:
Convert: 50 PSI = 344,738 Pa
h = P / (ρ × g) = 344,738 Pa / (1000 kg/m³ × 9.81 m/s²)
h = 35.1 m (115 ft)
Applications
Scuba Diving
Understanding pressure at depth is critical for dive planning, decompression schedules, and gas consumption calculations.
Dam Engineering
Hydrostatic pressure determines the forces acting on dam walls and is crucial for structural design and safety.
Submarine Design
Hull strength must withstand increasing hydrostatic pressure with depth to prevent implosion.
Water Distribution
Water towers and elevated tanks use hydrostatic pressure to deliver water to lower elevations.
Frequently Asked Questions
Does hydrostatic pressure depend on container shape?
No! Hydrostatic pressure depends only on depth, fluid density, and gravity. The shape of the container doesn't affect the pressure at a given depth.
What is the pressure at 10 meters depth in water?
At 10 m depth: P = 1000 kg/m³ × 9.81 m/s² × 10 m = 98,100 Pa ≈ 1 bar. This is approximately double atmospheric pressure.
How does saltwater differ from freshwater?
Seawater has higher density (~1025 kg/m³ vs 1000 kg/m³), so pressure increases about 2.5% faster with depth compared to freshwater.
Is atmospheric pressure included?
This calculator gives gauge pressure (pressure above atmospheric). Absolute pressure = gauge pressure + atmospheric pressure (101.325 kPa at sea level).
Why does pressure increase with depth?
Pressure increases because the weight of the fluid above pushes down. Each meter of depth adds the weight of that fluid column, creating linear pressure increase.