Physics Lab

Bernoulli Effect

Interactive simulation of Bernoulli's Principle and fluid dynamics. Explore pipe flow, airfoils, Torricelli's theorem, and Magnus effect.

Pipe Flow & Venturi Effect

Observe how flow speed increases in narrower sections while pressure decreases (Bernoulli's equation & continuity).

Bernoulli: P + ½ρv² + ρgh = constant
Continuity: A₁v₁ = A₂v₂

Inlet Diameter (mm) 60

Outlet Diameter (mm) 30

Inlet Velocity (m/s) 2.0

Fluid Density (kg/m³) 1000

v₁ (wide section)

2.0 m/s

v₂ (narrow section)

8.0 m/s

P₁ (wide section)

100.0 kPa

P₂ (narrow section)

98.0 kPa

✓ Continuity check: 2832 = 2832 (A₁v₁ = A₂v₂)

Slow flow (blue)

Fast flow (red)

Pressure gauge

Airfoil Lift Generation

Curved upper surface creates faster flow and lower pressure above, generating net upward lift force.

Lift = ½ρv²S·CL
Bernoulli shows: P_lower > P_upper → net upward force

Angle of Attack (°) 5

Airspeed (m/s) 30

Wing Area (m²) 30

Flow Type

Lift Coefficient (CL)

0.82

Lift Force (N)

14,850 N

ΔP (Upper-Lower)

-990 Pa

Flow Status

Attached

Low pressure (fast)

High pressure (slow)

Lift force

Torricelli's Theorem

Water efflux velocity from a hole depends on the height of water column above it: v = √(2gh)

Torricelli: v = √(2gh)
where g = 9.81 m/s², h = water height above hole

Water Height (m) 1.0

Hole Position (m from bottom) 0.3

Hole Diameter (mm) 15

Animation Speed 1.0x

Efflux Velocity (v)

4.43 m/s

Jet Range

1.86 m

Flow Rate (Q)

0.79 L/s

Time to Empty

2.5 min

Water

Jet stream

Magnus Effect

Spinning objects deflect fluid flow, creating pressure asymmetry and curved motion (curveball effect).

Magnus Force: FM = ½ρv²S·CL(spin)
Faster flow on one side → lower pressure → curved trajectory

Forward Velocity (m/s) 30

Spin Rate (rpm) 2000

Ball Radius (cm) 3.7

Spin Direction

Spin Rate (ω)

209.4 rad/s

Magnus Force

18.2 N

Deflection Distance

0.85 m

Flight Time

1.33 s

Slower flow side

Faster flow side

Curved trajectory