Pressure vs Depth · SimulatorHydrostatic Pressure and Fluid Columns
A column of fluid with a movable depth gauge; pressure rises linearly with depth at rate ρg
Published: August 30, 2026
Objective
Verify that gauge pressure in a static fluid obeys P = ρ·g·h, where h is the vertical depth below the free surface and ρ is the fluid density. The sim shows that pressure depends only on depth and density, not on the horizontal extent or total volume of the fluid. Key idealizations: incompressible fluid, uniform density, negligible surface tension.
Setup
- Leave all sliders at their defaults: Gauge Depth = 4 m, Fluid Density = 1000 kg/m³, Column Height = 8 m. Observe the fluid column and the P-vs-depth graph before pressing Start.
- Record the predicted gauge pressure from the formula P = ρ·g·h = 1000 × 9.81 × 4 = 39.24 kPa. Note the readouts are at 0.00 kPa before the animation runs.
- Press Start. Watch the depth gauge descend from the surface to 4 m; the pressure arrows grow and the HUD updates every frame. When the gauge reaches 4 m the simulation stops.
- Read the Gauge pressure readout. Compare it to your prediction. Then set Fluid Density to 2000 kg/m³, press Reset, and Start again to observe the steeper pressure profile.
- Finally, increase Column Height to 12 m and set Gauge Depth to 8 m. Start the sim and check that the readout matches 1000 × 9.81 × 8 = 78.48 kPa, confirming that only depth (not column height above) matters.
Analytical Prediction
With Gauge Depth h = 4 m, Fluid Density ρ = 1000 kg/m³, and g = 9.81 m/s², the gauge pressure is:
Absolute pressure adds the standard atmosphere (101 325 Pa):
The P-vs-depth graph will show a straight line from 0 kPa at the surface to P = ρ·g·H_total at the bottom. Doubling the density to 2000 kg/m³ doubles the slope and the readout at the same depth (78.48 kPa). Changing Column Height from 8 m to 12 m while keeping Gauge Depth at 4 m leaves the readout unchanged at 39.24 kPa, illustrating that depth, not total column length, governs local pressure.
Results Analysis
After the animation completes, check the Gauge pressure (kPa) readout. At default settings it should read 39.24 kPa, matching the analytic value within ±0.01 kPa (the sim evaluates gaugePressure directly with no integrator error). The Abs. pressure (kPa) readout should show 140.6 kPa. Drag the Fluid Density slider to 500 kg/m³ and compare the P-vs-depth graph slope with the ghost profile left by the first run at 1000 kg/m³: the new slope is exactly half as steep, confirming the linear ρ dependence. At density 2000 kg/m³ the slope is exactly double. The Depth (m) readout should match the Gauge Depth slider value to within 0.01 m at stop.
Source of Error
The sim models an incompressible, uniform-density fluid with no flow or viscosity. Real fluids are weakly compressible (water density increases about 0.5% per 100 m of depth), so the linear P = ρgh formula slightly underestimates pressure at depths exceeding a few hundred metres. The sim also ignores temperature stratification, dissolved gases, and surface tension. The standard atmosphere value (101 325 Pa) is fixed, whereas actual atmospheric pressure varies by ±3% with weather. Because the sim evaluates the closed-form formula rather than integrating equations of motion, the residual between the prediction and the readout is purely numerical rounding (the last decimal place), not a physical effect.
Further Exploration
- Set Fluid Density to 1025 kg/m³ (salt water) and Gauge Depth to 6 m. How much larger is the pressure compared with fresh water at the same depth? Does the ratio match the density ratio exactly?
- Keep Gauge Depth fixed at 5 m and vary Column Height from 6 m to 15 m. Does the pressure readout change? What does this tell you about the role of total fluid volume in determining local pressure?
- Set Gauge Depth to its minimum (0.5 m) and maximum (10 m) and record both gauge pressures. Is the ratio of pressures exactly 20:1? Use the formula to check your answer.
- Compare runs at density 500 kg/m³ and 2000 kg/m³ with the same depth. The ghost profiles on the graph will show two linear slopes. What is the ratio of their gradients, and why does it equal the density ratio?