Drag the red probe (or tap the tank) to read the pressure at that depth.

Hydrostatic Pressure Lab - 2D cross-section

Drag the red probe up and down the tank, open or close the jets, pump the press and read the U-tube. p = p0 + rho g d.

-probe depth

-absolute pressure at the probe

-gauge pressure (above p0)

-movable jet: speed / range

-manometer level difference

-press: force on the big piston

Independent checks

Each row compares a closed form with a separate calculation (trapezoid integral, Runge-Kutta flight, stepped drain).

The science

Hydrostatic pressure. In a liquid at rest dp/dz = -rho g, so p(d) = p0 + rho g d. It depends on depth, density and gravity only, not on the width or shape of the vessel. The arrows on the left wall are proportional to the gauge pressure rho g d.

Torricelli's law. A small hole at depth d gives a jet speed v = Cv sqrt(2 g d); leaving horizontally at height y0 = H - d it lands at R = v sqrt(2 y0 / g) = 2 Cv sqrt(d (H - d)). The range is largest for d = H/2 and does not depend on g or on the liquid.

Pascal's principle. p = F1/A1 is transmitted undiminished, so F2 = F1 A2/A1. The fluid volume is conserved (d2 = d1 A1/A2), so work in = work out: force is traded for distance.

Manometer. The U-tube liquid rises until rho_m g Dh = p_gauge. 101 325 Pa supports 760 mm of mercury.

Simplifications. Incompressible liquid with constant density, uniform gravity, tank area much larger than the holes, no viscosity, no surface tension, no air drag on the jets.