Flow Rate Calculator
Calculate volumetric flow rate, mass flow rate, fluid velocity, and pipe diameter using the continuity equation and Bernoulli's principle. Essential for engineers, students, and anyone working with fluid systems.
📊 Common Fluid Properties
| Fluid | Density (kg/m³) | Viscosity (Pa·s) | Typical Application |
|---|---|---|---|
| Water (20°C) | 998 | 0.001 | Hydraulic systems, plumbing |
| Air (20°C) | 1.204 | 1.81×10⁻⁵ | HVAC, aerodynamics |
| Engine Oil (SAE 30) | 875 | 0.29 | Lubrication systems |
| Gasoline | 750 | 0.0006 | Fuel systems |
| Mercury | 13,534 | 0.0016 | Manometers, barometers |
| Seawater | 1,025 | 0.0011 | Marine systems |
Understanding Flow Rate
Flow rate is the volume of fluid that passes through a cross-section per unit time. It is a fundamental concept in fluid dynamics with applications in engineering, plumbing, HVAC, and environmental science.
The continuity equation relates flow rate, velocity, and cross-sectional area: Q = A × v
Volumetric Flow Rate (Q):
Q = A × v = (π × d² / 4) × v (for circular pipes)
Mass Flow Rate (ṁ):
ṁ = ρ × Q = ρ × A × v
Reynolds Number (Re):
Re = ρ × v × d / μ
The Reynolds number determines the flow regime:
- Re < 2300: Laminar flow (smooth, orderly)
- 2300 < Re < 4000: Transitional flow
- Re > 4000: Turbulent flow (chaotic, mixing)
This calculator supports circular and rectangular pipe cross-sections and includes common fluid properties for accurate calculations.
How the Flow Rate Calculator Works
This calculator supports four calculation modes:
- Flow Rate: Calculate Q from velocity and pipe diameter.
- Velocity: Calculate v from flow rate and pipe diameter.
- Pipe Diameter: Calculate d from flow rate and velocity.
- Mass Flow Rate: Calculate ṁ from velocity, diameter, and fluid density.
For each mode, the calculator shows the formula, steps, and result. The Reynolds number is also calculated to indicate the flow regime.
❓ Flow Rate Calculator FAQ
What is volumetric flow rate?
Volumetric flow rate (Q) is the volume of fluid that passes through a cross-section per unit time. Common units are m³/s, L/min, or ft³/s.
What is the difference between volumetric and mass flow rate?
Volumetric flow rate (Q) measures volume per time. Mass flow rate (ṁ) measures mass per time. They are related by ṁ = ρ × Q, where ρ is the fluid density.
What is the continuity equation?
The continuity equation states that for an incompressible fluid, Q = A × v. It means the flow rate is constant along a pipe, so if the cross-sectional area decreases, the velocity must increase.
How do I calculate flow rate from velocity and pipe diameter?
Q = A × v, where A = π × d² / 4 for circular pipes. For example, d = 0.15 m, v = 2.5 m/s → Q = π × 0.15² / 4 × 2.5 = 0.0442 m³/s.
How do I calculate velocity from flow rate and pipe diameter?
v = Q / A = 4Q / (π × d²). For example, Q = 0.05 m³/s, d = 0.15 m → v = 4 × 0.05 / (π × 0.15²) = 2.83 m/s.
How do I calculate pipe diameter from flow rate and velocity?
d = √(4Q / (π × v)). For example, Q = 0.05 m³/s, v = 2.5 m/s → d = √(4 × 0.05 / (π × 2.5)) = 0.1596 m.
What is the Reynolds number?
The Reynolds number (Re) is a dimensionless quantity that indicates whether the flow is laminar or turbulent. Re = ρ × v × d / μ, where μ is the dynamic viscosity.
What is laminar flow?
Laminar flow is smooth, orderly flow where fluid layers slide past each other without mixing. It occurs at Re < 2300. It's characterized by low velocities and high viscosity.
What is turbulent flow?
Turbulent flow is chaotic, mixing flow with eddies and swirls. It occurs at Re > 4000. It's characterized by high velocities and low viscosity, and is typical in most industrial applications.
How does fluid density affect flow rate?
Density affects mass flow rate (ṁ = ρ × Q) but not volumetric flow rate. For the same volumetric flow, a denser fluid has a higher mass flow rate.
What is the difference between a circular and rectangular pipe?
For circular pipes, A = π × d² / 4. For rectangular pipes, A = width × height. This calculator supports both shapes.
How do I calculate the cross-sectional area of a pipe?
For circular pipes: A = π × d² / 4. For rectangular pipes: A = width × height. The calculator automatically computes the area based on your inputs.
What is the typical velocity in a water pipe?
Recommended water velocities: 0.6-1.5 m/s for residential plumbing, 1.5-3.0 m/s for industrial systems. Higher velocities cause noise and erosion.
What is the difference between flow rate and velocity?
Flow rate (Q) is the volume of fluid passing per unit time. Velocity (v) is the speed of the fluid. They are related by Q = A × v.
How do I convert between flow rate units?
1 m³/s = 1000 L/s = 60,000 L/min = 35.315 ft³/s = 15,850 gpm. This calculator uses SI units but can be adapted for other units.
What is Bernoulli's principle?
Bernoulli's principle states that an increase in fluid velocity results in a decrease in pressure. It's the basis for many flow measurement devices like Venturi meters and pitot tubes.
How does pipe diameter affect flow rate?
Flow rate is proportional to the square of the diameter (Q ∝ d²). Doubling the diameter increases the flow rate by a factor of 4 for the same velocity.
What is the hydraulic diameter for rectangular pipes?
The hydraulic diameter for rectangular pipes is D_h = 4A/P = 4 × (width × height) / (2 × (width + height)). It's used for non-circular cross-sections.
How accurate is this flow rate calculator?
This calculator provides accurate results based on the continuity equation and standard fluid properties. For precise engineering applications, consider factors like pipe roughness, fittings, and elevation changes.