Vertical Pipe Flow Rate Calculation

Calculate the volumetric flow rate of fluid passing through a vertical pipe based on diameter and velocity.

Millimeters (mm) Inches (in) Centimeters (cm)

Meters per second (m/s) Feet per second (ft/s)

*For gravity flow, velocity ≈ √(2 × gravity × height)

function calculateFlowRate() { // Get input values var diameterInput = document.getElementById('vp_diameter').value; var diameterUnit = document.getElementById('vp_diameter_unit').value; var velocityInput = document.getElementById('vp_velocity').value; var velocityUnit = document.getElementById('vp_velocity_unit').value; var resultsArea = document.getElementById('vp_results_area'); // Validation if (diameterInput === "" || velocityInput === "") { alert("Please enter both Pipe Diameter and Fluid Velocity."); resultsArea.style.display = "none"; return; } var D = parseFloat(diameterInput); var V = parseFloat(velocityInput); if (D <= 0 || V < 0) { alert("Please enter positive values for diameter and velocity."); return; } // 1. Normalize Diameter to Meters var diameterInMeters = 0; if (diameterUnit === 'mm') { diameterInMeters = D / 1000; } else if (diameterUnit === 'in') { diameterInMeters = D * 0.0254; } else if (diameterUnit === 'cm') { diameterInMeters = D / 100; } // 2. Normalize Velocity to Meters per Second (m/s) var velocityInMPS = 0; if (velocityUnit === 'mps') { velocityInMPS = V; } else if (velocityUnit === 'fps') { velocityInMPS = V * 0.3048; } // 3. Calculate Cross-Sectional Area (A = π * r²) // Radius = Diameter / 2 var radius = diameterInMeters / 2; var areaM2 = Math.PI * Math.pow(radius, 2); // 4. Calculate Volumetric Flow Rate (Q = A * v) in m³/s var flowMPS = areaM2 * velocityInMPS; // 5. Convert Flow Rate to target units var flowLPM = flowMPS * 60000; // m³/s to L/min var flowCMH = flowMPS * 3600; // m³/s to m³/h var flowGPM = flowMPS * 15850.3231; // m³/s to US GPM // 6. Display Results resultsArea.style.display = "block"; document.getElementById('res_area').innerHTML = areaM2.toFixed(6) + " m²"; document.getElementById('res_lpm').innerHTML = flowLPM.toFixed(2) + " L/min"; document.getElementById('res_cmh').innerHTML = flowCMH.toFixed(2) + " m³/h"; document.getElementById('res_gpm').innerHTML = flowGPM.toFixed(2) + " US GPM"; }

Understanding Vertical Pipe Flow Rate Calculations

Determining the flow rate in a vertical pipe is a fundamental task in fluid dynamics, plumbing engineering, and industrial process design. Whether you are designing a gravity-fed drainage system, sizing a pump for a cooling tower, or analyzing a chemical processing line, accurate flow rate calculations are essential for system efficiency and safety.

The Core Formula: Q = A × V

The flow rate of an incompressible fluid (like water) through a full pipe is governed by the continuity equation:

Q = A × V

• Q (Flow Rate): The volume of fluid moving per unit of time (e.g., m³/hr, GPM).
• A (Area): The cross-sectional area of the pipe's interior. For a round pipe, A = π × (Diameter/2)².
• V (Velocity): The speed at which the fluid is moving (e.g., m/s, ft/s).

Vertical Flow vs. Horizontal Flow

While the formula Q = A × V applies to pipes in any orientation, vertical pipes introduce the factor of gravity.

1. Pumped Systems (Upward Flow): In systems where fluid is pumped upwards, the pump must overcome the "static head" (the weight of the fluid column) plus friction losses. The velocity is determined by the pump's curve and the pipe resistance.
2. Gravity Systems (Downward Flow): In drainage systems, gravity accelerates the fluid. For a free-falling liquid in a full vertical pipe, the velocity can be estimated using Torricelli's Law (v = √2gh) initially, though terminal velocity is eventually reached due to friction.

Common Pipe Sizes and Typical Flow Rates

Below is a reference table for standard Schedule 40 steel pipes, assuming a typical design velocity of 2 m/s (approx 6.5 ft/s) for water.

Nominal Pipe Size (Inch)	Inner Diameter (mm)	Approx. Flow @ 2 m/s (L/min)	Approx. Flow @ 2 m/s (GPM)
1″	26.6 mm	66.9 L/min	17.7 GPM
2″	52.5 mm	259.7 L/min	68.6 GPM
4″	102.3 mm	985.8 L/min	260.4 GPM
6″	154.1 mm	2,238.5 L/min	591.3 GPM

Why Flow Velocity Matters

When using this calculator, it is crucial to input a realistic velocity.

• Too High (> 3 m/s): Can cause water hammer, pipe erosion, and excessive noise.
• Too Low (< 0.6 m/s): Can allow sediment to settle and clog the pipe.
• Optimal Range: For most water systems, a velocity between 1.5 m/s and 2.5 m/s is considered ideal.

How to Use This Calculator

1. Enter the Inner Diameter: Measure the inside width of your pipe. Select the unit (mm, cm, or inches).
2. Enter the Velocity: Input the speed of the fluid. If you have a flow meter, you can reverse calculate velocity. If relying on gravity, you may need to calculate velocity based on the drop height.
3. Click Calculate: The tool will instantly provide the volumetric flow rate in Liters per minute, Cubic meters per hour, and Gallons per minute.