Calculate volumetric flow rate, area, velocity, volume, or time using Q = A × v or Q = V/t. Free online fluid mechanics calculator for physics and engineering with multiple unit support.
Calculate flow rate using Q = A × v or Q = V/t
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Flow rate is one of the most fundamental concepts in fluid mechanics and hydraulic engineering. It describes how much fluid passes through a given area per unit time. Whether you're studying physics, engineering, working on plumbing systems, or designing fluid transport systems, understanding flow rate is essential. Our Flow Rate Calculator makes it easy to calculate volumetric flow rate, area, velocity, volume, or time using two fundamental formulas: Q = A × v (flow rate equals area times velocity) or Q = V/t (flow rate equals volume divided by time).
Volumetric flow rate tells you the volume of fluid flowing through a system per unit time. This is crucial for understanding fluid dynamics, designing pipe systems, calculating pump requirements, and analyzing fluid transport in countless applications from household plumbing to industrial processes.
Our Flow Rate Calculator offers two calculation methods for maximum flexibility. Follow these steps:
Flow rate can be calculated using two equivalent formulas depending on what information you have:
Q = A × v
Where: Q = flow rate, A = cross-sectional area, v = velocity
This formula relates flow rate to the cross-sectional area through which the fluid flows and the velocity of the fluid. It's particularly useful when you know the pipe diameter or channel dimensions and the fluid speed.
Q = V/t
Where: Q = flow rate, V = volume, t = time
This formula relates flow rate to the volume of fluid that passes through a point and the time it takes. It's useful when measuring how much fluid has flowed over a known period.
Flow rate calculations are used in countless real-world scenarios across various fields:
It's crucial to use consistent units in your calculations. Our calculator supports multiple unit systems and automatically converts between them:
Note: 1 m³/s = 1000 L/s = 264.172 gal/min (US)
Tip: The calculator automatically handles unit conversions, so you can mix different unit systems. For example, you can input area in cm², velocity in m/s, and get flow rate in L/s.
Water flows through a pipe with a cross-sectional area of 0.0314 m² (diameter of 20 cm) at a velocity of 2 m/s. What is the flow rate?
Q = A × v = 0.0314 m² × 2 m/s = 0.0628 m³/s = 62.8 L/s
A pipe has a flow rate of 50 L/s and a cross-sectional area of 0.005 m². What is the velocity of the fluid?
v = Q / A = 50 L/s / 0.005 m² = 0.05 m³/s / 0.005 m² = 10 m/s
You need a flow rate of 100 L/min at a velocity of 1 m/s. What cross-sectional area is required?
A = Q / v = (100 L/min) / (1 m/s) = (1.667 L/s) / (1 m/s) = 0.001667 m³/s / 1 m/s = 0.001667 m² = 16.67 cm²
50 liters of water flow through a pipe in 30 seconds. What is the flow rate?
Q = V / t = 50 L / 30 s = 1.667 L/s
A pump delivers water at a rate of 10 gal/min. How much water is delivered in 2 hours?
V = Q × t = 10 gal/min × 120 min = 1,200 gallons
How long will it take to fill a 500-liter tank at a flow rate of 25 L/min?
t = V / Q = 500 L / 25 L/min = 20 minutes
Understanding the relationship between flow rate, area, and velocity is crucial for pipe system design:
This relationship is why water flows faster through narrow pipes and slower through wide pipes when the flow rate is constant.
It's important to distinguish between volumetric and mass flow rates:
For incompressible fluids like water, volumetric flow rate is commonly used. For compressible fluids like gases, mass flow rate is often more relevant because volume changes with pressure and temperature.
Understanding flow rate has practical applications in daily life:
Flow rate (Q) equals cross-sectional area (A) times velocity (v): Q = A × v. This means for a constant flow rate, smaller areas result in higher velocities, and larger areas result in lower velocities. Conversely, for a constant area, higher velocities produce higher flow rates.
Common units include m³/s (cubic meters per second) and L/s (liters per second) in the metric system, and gal/min (gallons per minute) and ft³/s (cubic feet per second) in the imperial system. The choice depends on the application and industry standards.
For a circular pipe, first calculate the cross-sectional area: A = π × (d/2)² = π × r², where d is diameter and r is radius. Then use Q = A × v. You can also combine these: Q = π × r² × v for a circular pipe.
Volumetric flow rate (Q) measures volume per time (m³/s, L/s), while mass flow rate (ṁ) measures mass per time (kg/s). They're related by density: ṁ = ρ × Q. Our calculator focuses on volumetric flow rate, which is most common for liquids.
For a constant velocity, larger pipe diameters allow higher flow rates because area increases with the square of the diameter. For a constant flow rate, smaller diameters result in higher velocities. Pipe diameter has a squared relationship with area: A = π × (d/2)².
For incompressible fluids in a closed system, volumetric flow rate is constant throughout (continuity principle). However, velocity changes with pipe diameter - smaller pipes have higher velocities. Pressure and head losses affect the driving force but don't change flow rate in steady flow.
Flow rate is one of the key parameters for pump selection. Engineers calculate the required flow rate based on system needs, then select pumps that can deliver that flow rate at the required pressure. Flow rate determines pump capacity, while head/pressure determines pump power requirements.
Water utilities often use L/s or m³/h. HVAC uses gal/min (GPM) or ft³/min (CFM). Chemical and process industries commonly use m³/h or L/min. Medical applications use mL/min or mL/h. The choice depends on industry standards and typical flow ranges.
Understanding flow rate and the relationships Q = A × v and Q = V/t is fundamental to fluid mechanics, hydraulic engineering, and many practical applications. Our Flow Rate Calculator simplifies these calculations, making it easy to solve problems involving fluid flow, pipe sizing, and system design.
Whether you're calculating flow rates for plumbing systems, designing fluid transport systems, or analyzing fluid dynamics, this calculator provides accurate results with support for multiple unit systems and two calculation methods. Ready to explore more physics concepts? Check out our other calculators like the Velocity Calculator for velocity calculations, or use our Volume Calculator calculator for volume calculations that complement flow rate analysis.
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