Bernoulli's Principle Lab

Fluid Flow, Velocity Distribution & Pressure Variations in Venturi Tubes

Venturi Tube Apparatus

LIVE SIMULATION
Section A (Inlet) Section B (Throat) Section C (Outlet)
SECTION A (INLET) P₁ / V₁
Pressure (P₁) 100.00 kPa
Velocity (V₁) 1.27 m/s
Dynamic (q₁) 0.81 kPa
Area: 19.63 cm²
SECTION B (THROAT) P₂ / V₂
Pressure (P₂) 87.27 kPa
Velocity (V₂) 5.09 m/s
Dynamic (q₂) 12.95 kPa
Area: 4.91 cm²
SECTION C (OUTLET) P₃ / V₃
Pressure (P₃) 100.00 kPa
Velocity (V₃) 1.27 m/s
Dynamic (q₃) 0.81 kPa
Area: 19.63 cm²
U-TUBE MANOMETER ΔP / Δh
Diff P (ΔP) 12.73 kPa
Head (Δh) 129.8 cm H₂O
Fluid Head 9.57 cm Hg
Fluid: Mercury

Pressure vs Velocity Tradeoff

Dynamic Contrast
Inlet (Sec A)
V: 1.27 m/s
P: 100 kPa
Throat (Sec B)
V: 5.09 m/s
P: 87.27 kPa
Outlet (Sec C)
V: 1.27 m/s
P: 100 kPa

Bernoulli Head / Energy Balance

P + ½ρv² = Constant
Inlet Head
Static P₁
Dynamic ½ρv₁²
100.81 kPa
Throat Head
Static P₂
Dynamic ½ρv₂²
100.81 kPa
Outlet Head
Static P₃
Dynamic ½ρv₃²
100.81 kPa
✓

BERNOULLI RELATIONSHIP VERIFIED

Conservation of Mechanical Energy: P₁ + ½ρv₁² = P₂ + ½ρv₂² = P₃ + ½ρv₃²

Continuous Pressure & Velocity Profiles Along Tube

Pressure P(x) Velocity v(x) Hover graph to inspect values at x

Flow Continuity Verification

Q = A₁V₁ = A₂V₂ = A₃V₃
Inlet Flow Rate (Q₁) 2.50 L/s
Throat Flow Rate (Q₂) 2.50 L/s
Outlet Flow Rate (Q₃) 2.50 L/s
✓ INCOMPRESSIBLE STEADY FLOW CONFIRMED

Experimental Observation Log

# Section Diameter (mm) Area (cm²) Flow Q (L/s) Velocity (m/s) Pressure (kPa) Density (kg/m³)
No logged readings yet. Adjust controls and click "Add Current Reading".

Guided Laboratory Procedure

  1. Select a fluid preset (Water, Oil, Air, or Custom).
  2. Set the Inlet Diameter (D₁) to 50 mm.
  3. Set the Throat Diameter (D₂) to 25 mm.
  4. Set the Volumetric Flow Rate (Q) to 2.5 L/s.
  5. Observe the baseline inlet velocity (V₁) and static pressure (P₁).
  6. Watch animated flow particles speed up as they enter Section B (Throat).
  7. Note the sharp drop in throat pressure (P₂) on gauge P2 and piezometer column.
  8. Observe pressure recovery after Section B as fluid decelerates into Section C.
  9. Vary throat diameter (D₂) down to 15 mm and note further pressure drop.
  10. Toggle U-Tube Manometer to visually observe the fluid height difference (Δh).
  11. Click Add Current Reading to log experimental observations.

Physics Principles & Equations

1. Bernoulli's Principle

For an ideal, incompressible, steady fluid flow along a horizontal streamline:

P + ½ρv² = Constant

Where P is static pressure, ρ is fluid density, and v is fluid flow velocity.

2. Venturi Effect

When fluid flows through a constricted throat (A₂ < A₁), continuity requires velocity to increase (v₂ > v₁), causing static pressure to drop (P₂ < P₁):

P₁ - P₂ = ½ρ (v₂² - v₁²) = ½ρ Q² ( 1/A₂² - 1/A₁² )

3. Continuity Equation

Q = A₁v₁ = A₂v₂ = Constant