# Fluid Mechanics Simulator - Bernoulli, Venturi, Torricelli, Buoyancy, Reynolds

> Interactive fluid mechanics: drag a pipe to see Bernoulli at work, Venturi meter, Torricelli tank draining, buoyancy, Pascal press and Reynolds number.

- URL: https://qilingtools.com/en/math/fluid
- Category: Physics Tools (https://qilingtools.com/en/physics)
- Tags: [Physics](https://qilingtools.com/en/tags/physics), [Education](https://qilingtools.com/en/tags/education)
- Last updated: 2026-10-26
- Price: Free, no sign-up
- Privacy: Runs locally in the browser; files are never uploaded

Classic fluid mechanics, from school to first-year engineering, as hands-on simulations. In Bernoulli / Venturi you drag the pipe wall to change the diameter anywhere: particles visibly speed up in the throat, the piezometer columns above drop, and a chart shows static, dynamic and total pressure along the pipe, with warnings for suction and cavitation — plus a Venturi flow-meter calculator. Torricelli draining handles cylindrical, funnel, conical and spherical tanks, integrates the water level h(t) with RK4, draws the jet from a side hole and the drain time, and can compare the ranges of holes at three heights. Buoyancy lets you drop wood, ice, metal or a custom solid into water, sea water, oil or mercury and watch it bob, settle at its equilibrium draft or sink, including Archimedes’ crown problem. There are also layered hydrostatic pressure, Pascal’s hydraulic press, and Reynolds number, flow regime, friction factor and a Moody chart.

## How to use

1. Pick a scene: Bernoulli, Torricelli, buoyancy, hydrostatic pressure, Pascal press or Reynolds
2. Drag the pipe’s control points or the pressure probe, or set flow rate, sizes and densities with sliders and presets
3. Press play to watch particles, the water jet or the floating body; scrub the time slider to any moment
4. Read velocities, pressures, drain time, buoyant force or Reynolds number from the results and the formulas below

## Features

- Draggable Bernoulli pipe with flowing particles, piezometer columns and static/dynamic/total pressure chart
- Venturi meter calculator (U-tube manometer or piezometers) with suction and cavitation warnings
- Torricelli draining of four tank shapes via RK4, jet trajectory and best hole height
- Buoyancy animation: float, sink or rest on the bottom, with draft, apparent weight and bobbing period
- Archimedes’ crown: density and gold content by weighing
- Layered hydrostatics with wall force and centre of pressure, Pascal press, Reynolds number with Colebrook friction factor and Moody chart

## FAQ

### Why is the pressure lower where the pipe is narrower?

For an incompressible fluid the flow rate Q = Av is the same everywhere, so a narrower section forces a higher speed. Bernoulli’s equation p + ½ρv² + ρgz = constant then says that, at the same height, the gain in dynamic pressure ½ρv² must come out of the static pressure p. The fluid needs a pressure difference behind it to accelerate into the throat. If the throat pressure drops below atmospheric an open piezometer sucks in air, and below the vapour pressure the liquid cavitates.

### Why is Torricelli’s speed √(2gh) the same as free fall?

Follow a streamline from the free surface, where the speed is almost zero and the pressure is atmospheric, to the hole, where the pressure is also atmospheric. Bernoulli’s equation reduces to ½v² = gh — exactly the speed of a body dropped from height h. The real discharge is multiplied by a coefficient C_d (about 0.61 for a sharp-edged hole, 0.98 for a rounded nozzle) because the jet contracts and loses a little energy. As the level falls the outflow slows, so drain time scales with √h, not h.

### How much of a floating object is under water?

A floating body displaces its own weight: ρ_liquid·g·V_sub = ρ_object·g·V, so V_sub/V = ρ_object/ρ_liquid. Ice (917 kg/m³) in sea water (1025 kg/m³) floats about 89% submerged; pine (about 500 kg/m³) sits roughly half under water. For a cube or upright cylinder the draft is simply that fraction of the height; for a sphere the submerged volume is a spherical cap, so the tool solves the cap equation by bisection.

### What does the Reynolds number tell you?

Re = ρvD/μ compares inertial to viscous forces. In a round pipe, below about 2300 the flow is laminar: smooth layers, a parabolic velocity profile, the Hagen–Poiseuille pressure drop and a friction factor f = 64/Re. Above about 4000 it is turbulent: strong mixing, a flatter profile and a friction factor that also depends on the wall’s relative roughness, found from the Colebrook equation or the Moody chart. In between the flow switches back and forth, so friction there is only approximate.

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