Fluid Flow Formulas
Calculate flow rate, velocity, and pressure drop in pipes.
Covers continuity equation and Poiseuille's law.
The Formulas
Flow Rate: Q = A × v
Continuity Equation: A₁ × v₁ = A₂ × v₂
Poiseuille's Law: Q = (π × r⁴ × ΔP) / (8 × μ × L)
Continuity Equation: A₁ × v₁ = A₂ × v₂
Poiseuille's Law: Q = (π × r⁴ × ΔP) / (8 × μ × L)
Fluid flow formulas describe how liquids and gases move through pipes and channels. The continuity equation ensures mass is conserved. Poiseuille's law gives flow rate in long, straight pipes.
Variables
| Symbol | Meaning | Unit |
|---|---|---|
| Q | Volumetric flow rate | m³/s |
| A | Cross-sectional area of pipe | m² |
| v | Flow velocity | m/s |
| r | Pipe radius | m |
| ΔP | Pressure difference | Pa (Pascals) |
| μ | Dynamic viscosity of the fluid | Pa·s |
| L | Length of the pipe | m |
Example 1
Water flows at 2 m/s through a pipe with radius 0.05 m. Find the flow rate.
A = π × r² = π × 0.05² = 0.00785 m²
Q = A × v = 0.00785 × 2
= 0.0157 m³/s ≈ 15.7 liters/s
Example 2
A pipe narrows from 10 cm to 5 cm diameter. If v₁ = 1 m/s, find v₂.
A₁ × v₁ = A₂ × v₂
A₁ = π(0.05)² = 0.00785 m², A₂ = π(0.025)² = 0.00196 m²
v₂ = (A₁ × v₁) / A₂ = (0.00785 × 1) / 0.00196
= 4 m/s (velocity quadruples when diameter halves)
When to Use Them
Use fluid flow formulas when:
- Designing plumbing, irrigation, or hydraulic systems
- Sizing pumps and calculating required flow rates
- Analyzing blood flow in medical applications
- Calculating pressure drops in piping networks