Calculate Linear Velocity from Flow Rate

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Linear Velocity Calculator

m³/s L/s m³/min L/min GPM (US) CFM (US)
m² cm² in² ft²
function calculateLinearVelocity() { var flowRateInput = document.getElementById("flowRate").value; var flowRateUnit = document.getElementById("flowRateUnit").value; var crossSectionalAreaInput = document.getElementById("crossSectionalArea").value; var areaUnit = document.getElementById("areaUnit").value; var flowRate = parseFloat(flowRateInput); var crossSectionalArea = parseFloat(crossSectionalAreaInput); if (isNaN(flowRate) || isNaN(crossSectionalArea) || flowRate <= 0 || crossSectionalArea <= 0) { document.getElementById("result").innerHTML = "Please enter valid positive numbers for flow rate and area."; return; } // — Flow Rate Conversion to m³/s — var flowRateInM3PerS; switch (flowRateUnit) { case "m3_per_s": flowRateInM3PerS = flowRate; break; case "L_per_s": flowRateInM3PerS = flowRate / 1000; break; case "m3_per_min": flowRateInM3PerS = flowRate / 60; break; case "L_per_min": flowRateInM3PerS = flowRate / 60000; break; case "gpm": // US Gallons per Minute flowRateInM3PerS = flowRate * 0.0000630902; break; case "cfm": // Cubic Feet per Minute flowRateInM3PerS = flowRate * 0.000471947; break; default: flowRateInM3PerS = 0; } // — Cross-Sectional Area Conversion to m² — var crossSectionalAreaInM2; switch (areaUnit) { case "m2": crossSectionalAreaInM2 = crossSectionalArea; break; case "cm2": crossSectionalAreaInM2 = crossSectionalArea / 10000; break; case "in2": crossSectionalAreaInM2 = crossSectionalArea * 0.00064516; break; case "ft2": crossSectionalAreaInM2 = crossSectionalArea * 0.092903; break; default: crossSectionalAreaInM2 = 0; } // — Calculate Linear Velocity — var linearVelocity = flowRateInM3PerS / crossSectionalAreaInM2; // — Display Result — var resultHTML = "

Result:

"; resultHTML += "Linear Velocity: " + linearVelocity.toFixed(4) + " m/s"; // — Optional: Convert to other units for display — resultHTML += "Linear Velocity: " + (linearVelocity * 3.28084).toFixed(4) + " ft/s"; resultHTML += "Linear Velocity: " + (linearVelocity * 3600).toFixed(4) + " m/hr"; document.getElementById("result").innerHTML = resultHTML; } .calculator-widget { font-family: sans-serif; border: 1px solid #ccc; padding: 20px; border-radius: 8px; max-width: 500px; margin: 20px auto; background-color: #f9f9f9; } .calculator-widget h2 { text-align: center; margin-bottom: 20px; color: #333; } .calculator-inputs .form-group { margin-bottom: 15px; display: flex; align-items: center; gap: 10px; } .calculator-inputs label { display: block; margin-bottom: 5px; font-weight: bold; flex-basis: 150px; /* Fixed width for labels */ } .calculator-inputs input[type="number"] { padding: 8px; border: 1px solid #ccc; border-radius: 4px; width: 120px; /* Adjust width as needed */ } .calculator-inputs select { padding: 8px; border: 1px solid #ccc; border-radius: 4px; } .calculator-widget button { display: block; width: 100%; padding: 10px 15px; background-color: #007bff; color: white; border: none; border-radius: 4px; cursor: pointer; font-size: 16px; margin-top: 20px; } .calculator-widget button:hover { background-color: #0056b3; } .calculator-result { margin-top: 25px; padding-top: 15px; border-top: 1px solid #eee; text-align: center; } .calculator-result h3 { margin-bottom: 10px; color: #555; } .calculator-result p { font-size: 1.1em; margin-bottom: 8px; } .calculator-result strong { color: #007bff; }

Understanding Linear Velocity from Flow Rate

Linear velocity, often denoted by 'v', is a fundamental concept in fluid dynamics. It represents the speed at which a fluid particle moves along a streamline. In simpler terms, it's how fast the fluid is moving in a specific direction within a conduit or open channel.

The flow rate (Q) of a fluid is the volume of fluid that passes through a given cross-sectional area per unit of time. It's typically measured in units like cubic meters per second (m³/s), liters per second (L/s), gallons per minute (GPM), or cubic feet per minute (CFM).

The cross-sectional area (A) is the area of the surface perpendicular to the direction of flow. For a pipe, this is usually the area of the circle inside the pipe. For an open channel, it's the area of the water's cross-section.

The Relationship: Q = A * v

The relationship between flow rate (Q), cross-sectional area (A), and linear velocity (v) is straightforward and is expressed by the continuity equation for incompressible fluids:

Q = A * v

This equation states that the volume of fluid passing through a cross-section per unit time is equal to the area of that cross-section multiplied by the average velocity of the fluid across that area.

To calculate the linear velocity (v) when you know the flow rate (Q) and the cross-sectional area (A), you can rearrange the formula:

v = Q / A

How to Use the Calculator

  1. Flow Rate: Enter the rate at which the fluid is flowing. Select the appropriate unit from the dropdown menu (e.g., m³/s, L/min, GPM).
  2. Cross-Sectional Area: Enter the area of the conduit or channel through which the fluid is flowing. Select the correct unit (e.g., m², cm², ft²).
  3. Calculate Velocity: Click the "Calculate Velocity" button.

The calculator will then display the calculated linear velocity, primarily in meters per second (m/s), and also in feet per second (ft/s) and meters per hour (m/hr) for convenience.

Example Calculation:

Imagine a pipe with a diameter of 0.2 meters (which gives a cross-sectional area of approximately 0.0314 m²). If the flow rate through this pipe is 50 liters per minute (which is 0.05 m³/min or 0.000833 m³/s).

  • Flow Rate (Q) = 50 L/min = 0.000833 m³/s
  • Cross-Sectional Area (A) = 0.0314 m²
  • Linear Velocity (v) = Q / A = 0.000833 m³/s / 0.0314 m² ≈ 0.0265 m/s

Using our calculator, if you input '0.05' for Flow Rate with 'L/min' selected, and '0.0314' for Cross-Sectional Area with 'm²' selected, you would get a result of approximately 0.0265 m/s.

This calculation is crucial in many engineering applications, from designing water distribution systems and pipelines to understanding blood flow in arteries and airflow in ventilation systems.

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