Physic Labs

Fluid mechanics

Pressure in fluids and atmospheric pressure

Investigate how hydrostatic pressure depends on depth and density, verifying p=p0+ρghp = p_0 + \rho g h. Observe how pressure is transmitted undiminished through a confined liquid to amplify force on a piston, F2=F1 S2/S1F_2 = F_1\,S_2/S_1.

Middle school

Equipment

  • Virtual liquid tank with a pressure probe at adjustable depth
  • Sliders for depth h and density ρ
  • Two-piston hydraulic press with area and input-force sliders
  • Pressure and force readout panel

Procedure

  1. Measure pressure versus depth

    Drag the depth slider h through several values while keeping ρ fixed; read the pressure on the display. For each point, compute p−p0p - p_0 and compare it with ρgh\rho g h; check the linear relation p=p0+ρghp = p_0 + \rho g h.

  2. Change the liquid density

    Hold h fixed and increase ρ; watch the pressure grow proportionally. Note that points at the same depth share the same pressure whatever the vessel shape — pressure depends only on ρ\rho, gg, hh.

  3. Verify the hydraulic press

    In the piston section, set an input force F1F_1 and increase the large piston area S2S_2. Read the output force and compare it with F2=F1 S2/S1F_2 = F_1\,S_2/S_1: the same pressure increment reaches every point, so force scales with area. Try predicting F2F_2 before moving the slider.

Simulation

Experiment history

In 1643–1644 Evangelista Torricelli, a student of Galileo, built the mercury-tube experiment and concluded that a column of liquid about 76 cm high is held up by atmospheric pressure, refuting the idea that nature abhors a vacuum. Blaise Pascal repeated and extended the work: in 1648 he had a mercury tube carried up the Puy-de-Dôme, showing the column falls as altitude rises. Pascal also stated the principle of pressure transmission in confined fluids in his Traité de l'équilibre des liqueurs (published 1663 after his death), the basis of the hydraulic press — Joseph Bramah built a practical press in 1795. The SI unit of pressure, the pascal, honors this work.

Related physicists

Archimedes of Syracuse

Related library topics

Pressure in fluids and atmospheric pressure