Flow Rate Through Pipe Calculator

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This calculator helps you determine the volumetric flow rate of a fluid through a pipe. The calculation is based on the principle that flow rate (Q) is equal to the cross-sectional area of the pipe (A) multiplied by the average velocity of the fluid (v). The formula is Q = A * v. We also consider the relationship derived from the continuity equation and fluid dynamics principles.

Pipe Diameter (m):

Fluid Velocity (m/s):

function calculateFlowRate() { var diameter = parseFloat(document.getElementById("pipeDiameter").value); var velocity = parseFloat(document.getElementById("fluidVelocity").value); var resultDiv = document.getElementById("result"); resultDiv.innerHTML = ""; // Clear previous results if (isNaN(diameter) || isNaN(velocity) || diameter <= 0 || velocity < 0) { resultDiv.innerHTML = "Please enter valid positive numbers for diameter and velocity."; return; } // Calculate radius var radius = diameter / 2; // Calculate cross-sectional area (A = pi * r^2) var area = Math.PI * radius * radius; // Calculate flow rate (Q = A * v) var flowRate = area * velocity; resultDiv.innerHTML = "Flow Rate (Q): " + flowRate.toFixed(4) + " m³/s"; }

Understanding Flow Rate Through a Pipe

The flow rate through a pipe is a fundamental concept in fluid mechanics, describing the volume of fluid that passes through a given cross-sectional area per unit of time. It's crucial for designing and analyzing various systems, including water supply networks, industrial piping, and blood circulation.

Key Concepts:

Volumetric Flow Rate (Q): This is the primary output of our calculator. It represents the volume of fluid passing a point in the pipe per unit of time. Common units include cubic meters per second (m³/s), liters per minute (L/min), or gallons per minute (GPM).
Pipe Diameter (D): The internal diameter of the pipe is a critical factor as it directly influences the cross-sectional area available for the fluid to flow through.
Cross-Sectional Area (A): This is the area of the circle formed by the inner walls of the pipe. It's calculated using the formula for the area of a circle: A = π * r², where 'r' is the radius (half the diameter).
Fluid Velocity (v): This refers to the average speed at which the fluid is moving through the pipe. It's typically measured in meters per second (m/s) or feet per second (ft/s).

The Formula:

The relationship between these variables is straightforward and derived from the principle of continuity:

Q = A * v

Where:

Q is the volumetric flow rate
A is the cross-sectional area of the pipe
v is the average fluid velocity

How the Calculator Works:

Our calculator takes the internal pipe diameter and the average fluid velocity as inputs. It first calculates the cross-sectional area of the pipe using the provided diameter. Then, it multiplies this area by the fluid velocity to determine the volumetric flow rate. The result is displayed in cubic meters per second (m³/s).

Example Calculation:

Let's say you have a pipe with an internal diameter of 0.1 meters (10 cm) and the fluid is flowing through it at an average velocity of 2.5 meters per second.

Pipe Diameter = 0.1 m
Fluid Velocity = 2.5 m/s

First, we find the radius: Radius = Diameter / 2 = 0.1 m / 2 = 0.05 m.

Next, we calculate the cross-sectional area: Area = π * (0.05 m)² = π * 0.0025 m² ≈ 0.007854 m².

Finally, we calculate the flow rate: Flow Rate = Area * Velocity = 0.007854 m² * 2.5 m/s ≈ 0.019635 m³/s.

So, the volumetric flow rate through this pipe would be approximately 0.0196 m³/s.