Flow Rate Velocity Calculator
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Understanding Flow Rate and Velocity
In fluid dynamics, understanding the relationship between flow rate and velocity is fundamental. These two concepts help us quantify how a fluid is moving through a system.
Flow Rate
Flow rate, often denoted by 'Q', represents the volume of fluid that passes through a given surface per unit of time. It's a measure of how much fluid is moving. Common units for flow rate include cubic meters per second (m³/s), liters per minute (L/min), or gallons per minute (GPM).
Velocity
Velocity, often denoted by 'v', is the speed and direction of fluid movement at a specific point. In many practical applications, we are interested in the average velocity across a cross-section of a pipe or channel. Units for velocity include meters per second (m/s) or feet per second (ft/s).
The Relationship: The Continuity Equation
The core principle that connects flow rate and velocity is the continuity equation. For an incompressible fluid flowing through a pipe or channel, the flow rate (Q) is equal to the product of the cross-sectional area (A) of the flow and the average velocity (v) of the fluid:
Q = A * v
This equation tells us that if the flow rate is constant, a smaller cross-sectional area will result in a higher fluid velocity, and a larger cross-sectional area will result in a lower fluid velocity. This is why water speeds up when you put your thumb over the end of a garden hose – you're reducing the cross-sectional area.
How to Use This Calculator
This calculator helps you determine the average velocity of a fluid when you know its flow rate and the cross-sectional area through which it is flowing. Simply input the values for flow rate and cross-sectional area in their respective units, and the calculator will provide the resulting velocity.
Example Calculation
Let's say you have a pipe where water is flowing at a rate of 0.5 cubic meters per second (m³/s). The internal cross-sectional area of the pipe is 0.1 square meters (m²). To find the average velocity of the water:
Flow Rate (Q) = 0.5 m³/s
Cross-Sectional Area (A) = 0.1 m²
Velocity (v) = Q / A
Velocity (v) = 0.5 m³/s / 0.1 m² = 5 m/s
Therefore, the average velocity of the water in the pipe is 5 meters per second.