Bernoulli Pressure Estimator
Total pressure head (Pa)
37500
How it works
Bernoulli's principle states that for an incompressible, inviscid fluid in steady flow, total mechanical energy per unit volume is conserved along a streamline: P + ½ρv² + ρgh = constant (static pressure + dynamic pressure + hydrostatic pressure = total pressure).
**Speed-pressure trade-off** Where flow velocity increases, pressure decreases. This is the basis for: aircraft lift (faster flow over curved upper wing surface → lower pressure → lift), venturi meters (flow measurement by pressure drop at throat), carburetor and atomizer operation, and Pitot tube airspeed measurement.
**Assumptions and limitations** Bernoulli applies along a streamline in steady, incompressible, inviscid flow with no energy addition or removal. Real flows deviate due to: viscosity (boundary layer effects), turbulence, compressibility (above ~Mach 0.3), and energy additions (pumps, fans). In pipes with significant length, friction losses must be added (Darcy-Weisbach equation).
**Stagnation pressure** At a stagnation point (where flow velocity = 0), all dynamic pressure converts to static pressure: P_stag = P_static + ½ρv². This is the principle of the Pitot tube — stagnation pressure minus static pressure equals dynamic pressure, from which airspeed is calculated.
**Venturi effect applications** A venturi constriction in a pipe accelerates flow and drops pressure. If pressure drops below atmospheric, a venturi can draw in a secondary fluid (venturi pump, jet pump). Venturi scrubbers, paint sprayers, and aspiration systems all use this effect. The throat area ratio determines the velocity increase and corresponding pressure drop.
Frequently Asked Questions
- The simple 'equal transit time' explanation (air over the curved top must travel farther and faster) is partially wrong. The real explanation: the wing's angle of attack and camber deflect airflow downward (Newton's 3rd law — air pushed down, wing pushed up). This downward deflection requires lower pressure above the wing (Bernoulli: higher velocity = lower pressure). The pressure difference integrated over the wing area produces lift. Modern computational fluid dynamics shows the pressure distribution; Bernoulli describes the energy conservation that determines what that pressure must be given the velocity field.
- A venturi meter has a converging section, throat, and diverging section. By measuring pressure at the inlet and throat, flow rate is calculated: Q = A_throat × √(2ΔP / (ρ(1 - (A_throat/A_inlet)²))). This is derived from continuity (A₁v₁ = A₂v₂) and Bernoulli (P₁ + ½ρv₁² = P₂ + ½ρv₂²). Venturi meters have low permanent pressure loss (80–90% pressure recovery) making them efficient for large flows. Orifice plates are cheaper but less efficient. Venturi meters are used for water, gas, and steam flow measurement in industrial piping.
- Dynamic pressure q = ½ρv². It represents the kinetic energy per unit volume of the moving fluid. At a stagnation point, all kinetic energy converts to pressure: P_stagnation = P_static + q. Aerodynamic forces scale with dynamic pressure: Lift = CL × q × S; Drag = CD × q × S, where S is wing area and CL, CD are dimensionless coefficients. At sea level (ρ = 1.225 kg/m³), 100 m/s (360 km/h): q = ½ × 1.225 × 100² = 6,125 Pa. At altitude where air is thinner, the same speed produces less dynamic pressure — aircraft must fly faster to generate the same lift.
- Bernoulli fails when: viscous losses are significant (turbulent pipe flow — use Darcy-Weisbach equation instead), energy is added by a pump or fan (modified Bernoulli: add pump head), flow is unsteady (transient events like water hammer), flow is compressible (above Mach 0.3 — use compressible flow equations), or streamlines are not followed (Bernoulli applies along a streamline only, not between different streamlines in general). For most low-speed liquid and gas flows in smooth pipes and open channels, Bernoulli with a head loss term (hL) gives accurate results.