Analyze fluid flow in pipes and open channels. Calculate pressure drop, flow rates, and Reynolds numbers.
Fluid flow analysis is essential for designing and optimizing piping systems, channels, and hydraulic structures. It involves calculating key parameters like flow velocity, pressure drop, and energy losses.
Key Insight: The Reynolds number (Re) determines whether flow is laminar (Re < 2000) or turbulent (Re > 4000). Transitional flow occurs between these values.
Continuity Equation: Describes mass conservation in fluid flow:
Q = A · v
Where Q is the volumetric flow rate, A is the cross-sectional area, and v is the flow velocity.
Bernoulli Equation: Describes energy conservation in fluid flow:
P/ρg + v²/2g + z = constant
Where P is pressure, ρ is density, g is gravity, v is velocity, and z is elevation.
Darcy-Weisbach Equation: Calculates head loss in pipes:
hf = f · (L/D) · (v²/2g)
Where hf is the head loss, f is the friction factor, L is pipe length, and D is pipe diameter.
| Fluid | Density (kg/m³) | Viscosity (cP) | Specific Heat (J/kg·K) | Applications |
|---|---|---|---|---|
| Water (20°C) | 998 | 1.0 | 4186 | Domestic, industrial, cooling |
| Air (20°C) | 1.2 | 0.018 | 1005 | Ventilation, combustion, HVAC |
| Oil (SAE 30) | 900 | 200 | 1900 | Lubrication, hydraulic systems |
| Ethanol | 789 | 1.2 | 2440 | Fuel, solvents, pharmaceuticals |
Pressure drop in pipes is typically calculated using the Darcy-Weisbach equation:
ΔP = f × (L/D) × (ρv²/2)
Where:
The friction factor (f) depends on the Reynolds number and the relative roughness of the pipe. For laminar flow, f = 64/Re. For turbulent flow, the Moody chart or Colebrook equation is used.
Engineering Application: Proper fluid flow analysis is critical in designing efficient piping systems. Undersized pipes can lead to excessive pressure drops and energy losses, while oversized pipes increase material costs unnecessarily.