Flow Rate Calculator Fluid Mechanics

Volumetric Flow Rate · Mass Flow Rate · Pipe Area · Fluid Velocity

📖 Flow Rate Calculator

Flow rate measures how much fluid passes through a given cross-section per unit time. In fluid mechanics, engineers calculate two main types:

This calculator supports four modes: Volumetric Flow, Mass Flow, Velocity from Flow, and Pipe Area.

🧮 Key Flow Rate Formulas

Volumetric Flow Rate: Q = A × v
Mass Flow Rate: ṁ = ρ × Q = ρ × A × v
Pipe Area (circular): A = π × D² / 4
Fluid Velocity: v = Q / A

Where:
Q = Volumetric flow rate (m³/s)
ṁ = Mass flow rate (kg/s)
ρ = Fluid density (kg/m³)
A = Cross-sectional area (m²)
v = Fluid velocity (m/s)
D = Pipe diameter (m)

📊 Common Units for Flow Rate

UnitDescriptionConversion
m³/sCubic meter per second (SI)1 m³/s = 1000 L/s
L/sLiter per second1 L/s = 0.001 m³/s
L/minLiter per minute1 L/min = 0.0000167 m³/s
GPMGallons per minute (US)1 GPM = 0.0000631 m³/s
CFMCubic feet per minute1 CFM = 0.000472 m³/s
kg/sKilogram per second (mass)1 kg/s = 1000 g/s

📝 Worked Example

Example: Water Flow Through a 50 mm Pipe at 2 m/s
Given: D = 50 mm = 0.05 m | v = 2 m/s | ρ(water) = 1000 kg/m³

Step 1: Cross-sectional Area
A = π × (0.05)² / 4 = π × 0.0025 / 4 = 0.001963 m²

Step 2: Volumetric Flow Rate
Q = A × v = 0.001963 × 2 = 0.003927 m³/s = 3.927 L/s

Step 3: Mass Flow Rate
ṁ = ρ × Q = 1000 × 0.003927 = 3.927 kg/s

Step 4: In GPM
Q = 0.003927 ÷ 0.0000631 ≈ 62.2 GPM

💡 Practical Applications

⚠️ Limitations & Assumptions

📌 Important Notes
  • Assumes steady, incompressible flow — not suitable for compressible gases at high velocity.
  • Assumes fully developed pipe flow — entrance effects are ignored.
  • Pipe area formula assumes a circular pipe.
  • Does not include friction losses, pressure drops, or minor losses.
  • Fluid density is assumed constant with temperature and pressure.
  • For accurate engineering design, consult ASME, ISO, or relevant standards.

📚 References & Sources

❓ Frequently Asked Questions

What is the difference between volumetric and mass flow rate? ▼
Volumetric flow rate (Q) measures volume per unit time (m³/s). Mass flow rate (ṁ) measures mass per unit time (kg/s). They are related by density: ṁ = ρ × Q.
What is a normal water flow rate for a household? ▼
A typical household faucet delivers 6–12 L/min. A shower uses about 8–15 L/min. A garden hose can deliver 15–30 L/min.
How do I convert m³/s to GPM? ▼
Multiply m³/s by 15,850.3 to get GPM. Example: 0.001 m³/s × 15,850.3 = 15.85 GPM.
Does flow rate change with pipe diameter? ▼
For the same velocity, a larger diameter pipe carries more flow. For the same flow rate, a smaller diameter pipe has higher velocity. This is why pipe sizing is critical in engineering.
What is a typical velocity for water in pipes? ▼
Recommended water velocity is typically 1–3 m/s in building services and 0.6–1.5 m/s in long-distance transmission pipelines to reduce friction losses and noise.

🔗 Related Calculators

Pipe Flow Calculator Flow, velocity, Reynolds number Reynolds Number Laminar vs turbulent flow Pump Horsepower HP required for flow Pressure Calculator Force / area calculations Density Calculator Mass / volume Unit Converter Convert any unit
⚠️ Disclaimer
This Flow Rate Calculator is provided for informational and educational purposes only. All calculations are based on ideal assumptions (steady, incompressible flow) and do not account for friction losses, pressure drops, temperature effects, or other real-world factors. For critical engineering design, please consult a licensed professional engineer and refer to applicable standards (ASME, ISO, etc.). Online Calculator Zone is not responsible for any decisions made based on these calculations.