Last Updated: October 20, 2025
Calculate volumetric flow rate from cross-sectional area and velocity instantly using the fundamental fluid mechanics equation with our advanced 2025 hydraulic engineering calculator for pipe sizing, pump selection, and fluid system design applications.
Enter the cross-sectional area and average velocity to calculate volumetric flow rate. The calculator will automatically convert between units and display results in multiple flow rate units. Results update instantly as you type.
Enter values to see results
The Volumetric Flow Rate Calculator is a fundamental fluid mechanics tool that calculates the volume of fluid passing through a cross-sectional area per unit time. This calculator is essential for hydraulic engineering, pipe sizing, pump selection, and fluid system design.
For more information about volumetric flow rate and fluid mechanics, visit Wikipedia: Volumetric Flow Rate and Wikipedia: Fluid Mechanics.
In fluid mechanics and hydraulic engineering, volumetric flow rate is crucial for designing water distribution systems, HVAC systems, industrial piping, and pump systems. This calculator helps engineers and technicians determine flow rates for system sizing, pressure drop calculations, and pump performance analysis. It's also essential for understanding fluid behavior in pipes, channels, and conduits.
Volumetric flow rate is the foundation of fluid mechanics - it determines how much fluid moves through a system per unit time.
Whether you're designing water supply systems, sizing pumps, calculating pipe flow, or analyzing fluid dynamics, this calculator provides accurate, instant results with comprehensive unit conversions for all your hydraulic engineering calculations. For related calculations, explore our pipe flow calculator, velocity calculator, displacement calculator, power factor calculator, and horsepower to amps calculator.
Q = A × v
Where Q = volumetric flow rate, A = cross-sectional area, v = average velocity
The volumetric flow rate equation Q = A × v is derived from the principle of continuity in fluid mechanics. This equation states that the volume of fluid flowing through a cross-section per unit time equals the product of the cross-sectional area and the average velocity of the fluid.
Cross-sectional area (A) is the area perpendicular to the direction of flow. For circular pipes, A = πr² = πd²/4, where r is radius and d is diameter. For rectangular channels, A = width × height. The area must be measured in square units consistent with the velocity units.
Area: 1 m² = 10,000 cm² = 10.764 ft² = 1,550 in²
Velocity: 1 m/s = 3.281 ft/s = 2.237 mph = 3.6 km/h
Flow Rate: 1 m³/s = 1,000 L/s = 15,850 gpm = 2,119 cfm
Flow Rate: 1 L/s = 0.001 m³/s = 15.85 gpm = 2.119 cfm
Average velocity (v) is the mean velocity across the entire cross-section. In real pipes, velocity varies from zero at the walls to maximum at the center due to viscosity. The average velocity is typically 0.8-0.9 times the maximum velocity for turbulent flow in smooth pipes.
| Field/Application | Typical Flow Rate Range | Importance |
|---|---|---|
| Water Distribution | 10-1000 L/min | Critical for municipal water supply systems |
| HVAC Systems | 100-5000 m³/h | Essential for air conditioning and ventilation |
| Industrial Processing | 50-50000 L/min | Critical for manufacturing and production |
| Oil & Gas | 100-1000000 L/min | Essential for pipeline and refinery operations |
| Chemical Processing | 10-10000 L/min | Important for reactor and mixing systems |
| Agricultural Irrigation | 100-5000 L/min | Critical for crop irrigation systems |
| Wastewater Treatment | 1000-100000 L/min | Essential for treatment plant operations |
| Power Generation | 5000-500000 L/min | Critical for cooling and steam systems |
Given:
Step 1: Calculate cross-sectional area
A = πd²/4 = π × (0.1 m)² / 4
A = π × 0.01 m² / 4 = 0.00785 m²
Step 2: Apply flow rate equation
Q = A × v
Q = 0.00785 m² × 2.5 m/s
Q = 0.0196 m³/s
Step 3: Convert to common units
Q = 0.0196 m³/s × 1,000 L/m³ = 19.6 L/s
Q = 19.6 L/s × 15.85 gpm/L/s = 311 gpm
Final Answer
19.6 L/s
or 311 gpm
Given:
Step 1: Calculate cross-sectional area
A = width × height = 12 in × 8 in = 96 in²
A = 96 in² × (1 ft/12 in)² = 0.667 ft²
Step 2: Convert velocity to ft/s
v = 1,200 ft/min × (1 min/60 s) = 20 ft/s
Step 3: Apply flow rate equation
Q = A × v = 0.667 ft² × 20 ft/s = 13.33 ft³/s
Q = 13.33 ft³/s × 60 s/min = 800 cfm
Final Answer
800 cfm
Air flow rate in HVAC duct
💡 Did you know? The continuity equation Q = A × v is fundamental to fluid mechanics and is used in everything from designing water supply systems to calculating blood flow in medical applications!
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