Bernoulli's Principle Calculator

Bernoulli's Equation

Bernoulli's Equation:

P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂
Where: P = pressure, ρ = fluid density, v = velocity, g = gravity, h = height
For horizontal flow (h₁ = h₂): P₁ + ½ρv₁² = P₂ + ½ρv₂²

Point 1

Pressure 1 (P₁) - Pa:

Velocity 1 (v₁) - m/s:

Height 1 (h₁) - m:

Point 2

Pressure 2 (P₂) - Pa:

Velocity 2 (v₂) - m/s:

Height 2 (h₂) - m:

Fluid Density (ρ) - kg/m³:

Pipe Flow & Continuity Equation

Continuity Equation:

A₁v₁ = A₂v₂ (conservation of mass)
Q = Av (flow rate = area × velocity)
For circular pipes: A = πr² = π(d/2)²

Pipe Diameter 1 (d₁) - cm:

Velocity 1 (v₁) - m/s:

Flow Rate (Q) - L/s:

Pipe Diameter 2 (d₂) - cm:

Velocity 2 (v₂) - m/s:

Typical Flow Velocities:
Water mains: 0.5-2 m/s
House pipes: 0.3-1.5 m/s
Industrial: 1-5 m/s
High pressure: 5-15 m/s

Venturi Meter & Flow Measurement

Venturi Meter Formula:

v = √[2(P₁ - P₂)/(ρ(A₁²/A₂² - 1))]
Q = A₂v = A₂√[2(P₁ - P₂)/(ρ(A₁²/A₂² - 1))]
Used for measuring flow rate by pressure difference

Inlet Pressure (P₁) - kPa:

Throat Pressure (P₂) - kPa:

Inlet Diameter (D₁) - cm:

Throat Diameter (D₂) - cm:

Fluid Density (ρ) - kg/m³:

Venturi Meter Advantages:
• High accuracy (±1%)
• Low permanent pressure loss
• Self-cleaning design
• Wide flow range

Applications:
• Water treatment plants
• Process industries
• HVAC systems

Pitot Tube Velocity Measurement

Pitot Tube Formula:

v = √[2(P₀ - P)/(ρ)]
Where: P₀ = stagnation pressure, P = static pressure, ρ = fluid density
Used for measuring fluid velocity, especially in aircraft

Stagnation Pressure (P₀) - Pa:

Static Pressure (P) - Pa:

Fluid Density (ρ) - kg/m³:

Velocity (v) - m/s:

Fluid Densities (kg/m³):
Air (sea level): 1.225
Air (10,000 ft): 0.905
Water: 1000
Gasoline: 750

Applications:
• Aircraft airspeed indicators
• Wind tunnel testing
• Industrial flow measurement