Pipe Flow Calculator
Calculate volumetric flow rate through a round pipe as cross-sectional area times velocity, from the pipe diameter and flow speed.
Pipe Flow Calculator
Calculator
Adjust values & calculateEnter your values below. Every result is computed in your browser โ no data is sent to any server.
Formula: Q = A ร v = ฯ(d/2)ยฒ ร v
Worked example โ See calculated output above
Formula
Q = A ร v = ฯ(d/2)ยฒ ร v
Flow rate equals pipe cross-sectional area times flow velocity.
Worked Examples
Example 1: Basic Example
Problem:Enter sample values to see how Pipe Flow Calculator works.
Solution:Input your values into the fields and the result appears automatically.
Result:See calculated output above
Example 2: Practical Scenario
Problem:Use real-world values relevant to your physics scenario.
Solution:Adjust the inputs to match your specific needs and review the computed result.
Result:Result updates in real time
Frequently Asked Questions
How does the continuity equation relate flow in a wide pipe to flow in a narrow one?
For an incompressible fluid in a closed conduit, the volumetric flow rate is the same at every cross-section, so A1v1 = A2v2. Because area scales with the square of the diameter, halving the bore quadruples the mean velocity. That is why a reducer raises velocity sharply, and why velocity, not flow rate, is the quantity that changes through a taper.
What is the difference between volumetric flow rate and mass flow rate?
This tool returns volumetric flow rate Q in cubic metres per second. Mass flow rate is the product of density and volumetric flow, m_dot = rho x Q, in kilograms per second. For water at about 1000 kg/m3, a Q of 0.01 m3/s carries 10 kg/s. The distinction matters for gases, whose density changes with pressure and temperature, so Q alone does not fix the mass delivered.
Why does pipe diameter influence flow so strongly?
At a fixed velocity, cross-sectional area is pi x (d/2)^2, so Q rises with the square of the diameter. Under a fixed pressure gradient the sensitivity is far greater: for laminar flow the Hagen-Poiseuille result makes Q proportional to the fourth power of the bore, so a ten per cent reduction from scaling or corrosion cuts capacity by about a third.
How do I tell whether flow in the pipe is laminar or turbulent?
Compute the Reynolds number, Re = v x d / nu, where nu is kinematic viscosity. Water near 20 C has nu of roughly 1e-6 m2/s. Flow is generally laminar below about Re 2300, transitional to roughly 4000, and turbulent above that. The regime decides which friction correlation applies and how flat the velocity profile is, so check it before estimating pressure loss.
What is the difference between the mean velocity used here and the actual velocity profile?
Dividing Q by area gives the cross-sectional mean velocity, not the local speed. Fully developed laminar flow has a parabolic profile whose centreline speed is twice the mean. Turbulent flow is much flatter, with a centreline speed typically around 1.2 times the mean. Insertion probes read a local value, so a profile factor is needed before comparing them with this result.
Why does Pipe Flow Calculator not give pressure drop or head loss?
Continuity fixes flow rate from geometry and velocity alone and involves no friction. Pressure loss along a straight run comes from the Darcy-Weisbach relation, h_f = f x (L/D) x v^2 / (2g), which additionally needs pipe length, relative roughness and the friction factor. Fittings, valves and bends add further minor losses, so a separate hydraulic calculation is required.
How do I convert the result into litres per second, cubic metres per hour or gallons per minute?
One cubic metre per second equals 1000 litres per second and 3600 cubic metres per hour. Because a cubic metre is about 264.17 US gallons, one cubic metre per second is roughly 15850 US gallons per minute. Keep the input diameter in metres and velocity in metres per second so the raw output stays in SI before you convert.
What is hydraulic diameter and when should I use it instead of the pipe bore?
Hydraulic diameter is defined as four times the flow area divided by the wetted perimeter. For a round pipe running full it reduces exactly to the internal diameter. For rectangular ducts, annuli or part-full channels it is the length scale that goes into the Reynolds number and friction correlations, although the area used for Q must still be the true flow area.
What flow velocity is normally chosen when sizing a water pipe?
Designers usually aim for a moderate velocity, commonly a few metres per second for pumped water. Too slow and solids settle out or air pockets are not swept along; too fast and noise, erosion of the bore and surge pressures from sudden valve closure become problems, while friction loss climbs roughly with the square of velocity. Local codes and the fluid carried set the actual limits.
Should I enter the nominal pipe size or the measured internal diameter?
Always use the true internal bore. Nominal sizes are labels, and the actual inside diameter depends on wall thickness or schedule, on liners, and on scale or biofilm build-up in service. Since area varies with the square of the diameter, a five per cent error in the bore shifts the computed flow rate by about ten per cent.
References
Reviewed for accuracy by Manoj Kumar, Mathematics Educator ยท Editorial policy
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