What is the difference between volumetric and mass flow rate?

Volumetric flow rate measures the volume of fluid per unit time (liters/second), while mass flow rate measures the mass per unit time (kg/second). For compressible fluids like gases, mass flow rate is more meaningful because volume changes with pressure and temperature.

What is laminar versus turbulent flow?

Laminar flow is smooth and orderly, with fluid moving in parallel layers. Turbulent flow is chaotic with eddies and mixing. The transition occurs at a Reynolds number of about 2300 for pipe flow. Most practical systems operate in turbulent flow.

How does pipe diameter affect flow rate?

Flow rate is proportional to the square of the diameter (since area = pi × r^2). Doubling the pipe diameter quadruples the cross-sectional area and thus the flow rate at the same velocity.

Flow Rate Calculator

Calculate volumetric flow rate (Q = A x v)

Flow Rate

Enter cross-sectional area and velocity

Area (m2)

Velocity (m/s)

Formula

Q = A x v

What Is Flow Rate?

Flow rate (or volumetric flow rate) measures how much volume of fluid passes through a cross-section per unit of time. It is fundamental to fluid mechanics and appears in plumbing, HVAC, hydraulics, chemical engineering, and medicine. The SI unit for flow rate is cubic meters per second (m³/s), though liters per minute (L/min) and gallons per minute (GPM) are widely used in practice.

The relationship between flow rate, cross-sectional area, and fluid velocity is expressed by the continuity equation Q = A × v. This tells us that for a given flow rate, a narrower pipe means faster velocity, and a wider pipe means slower velocity. This principle explains why water speeds up at a nozzle and why rivers flow faster through narrow gorges.

How to Use This Calculator

Select the quantity to solve for: Flow Rate (Q), Cross-Sectional Area (A), or Velocity (v).
Enter the two known values with appropriate units (m³/s, m², or m/s).
Click Calculate to instantly see the result.
Use Reset to clear the inputs and start over.

Formula & Explanation

Q = A × v
A = Q / v
v = Q / A

For circular pipes: A = π × (d/2)²

Q = Volumetric flow rate (m³/s), A = Cross-sectional area (m²), v = Average fluid velocity (m/s), d = pipe diameter (m). For a circular pipe, the area is π × r². Multiply m³/s by 1000 to get L/s, or by 15,850 to get US GPM.

Worked Examples

Example 1 — Water Pipe Flow

A pipe with diameter 0.1 m (100 mm) carries water at 2 m/s. A = π × (0.05)² = 0.00785 m². Q = 0.00785 × 2 = 0.0157 m³/s = 15.7 L/s = 248 GPM.

Example 2 — HVAC Duct

A rectangular duct (0.4 m × 0.3 m) has air flowing at 3 m/s. A = 0.4 × 0.3 = 0.12 m². Q = 0.12 × 3 = 0.36 m³/s = 763 CFM.

Example 3 — Find Velocity

A 50 mm diameter pipe must deliver 500 L/min = 0.00833 m³/s. A = π × (0.025)² = 0.00196 m². v = Q/A = 0.00833/0.00196 = 4.25 m/s.

Frequently Asked Questions

What is the difference between flow rate and flow velocity?▾

Flow velocity (v) is how fast the fluid is moving (m/s). Flow rate (Q) is the total volume passing a point per second (m³/s). A river can have high velocity but low flow rate (narrow, fast stream), or low velocity but high flow rate (wide, slow river).

What is the continuity equation?▾

The continuity equation states that for an incompressible fluid in a steady flow, A₁v₁ = A₂v₂. If a pipe narrows (A₂ < A₁), the velocity must increase (v₂ > v₁) to maintain the same flow rate. This is the Venturi effect in action.

What is Reynolds number and why does it matter?▾

Reynolds number (Re = ρvD/μ) predicts whether flow is laminar (smooth, Re < 2,300) or turbulent (chaotic, Re > 4,000). Laminar flow is efficient and predictable; turbulent flow causes more pressure drop and energy loss. Pipe sizing calculations use Reynolds number to account for friction losses.

How do I convert between flow rate units?▾

1 m³/s = 1,000 L/s = 60,000 L/min = 35.3 ft³/s = 264.2 US GPM. For gas flows, volumetric flow depends on temperature and pressure — standard conditions (0°C, 1 atm) are often specified for comparison.

What is mass flow rate vs volumetric flow rate?▾

Volumetric flow rate (Q) measures volume per time (m³/s). Mass flow rate (ṁ) measures mass per time (kg/s). They relate by ṁ = ρ × Q, where ρ is fluid density. For compressible fluids like gas, mass flow rate is more useful because density changes with pressure and temperature.