Analyze pipe or channel velocity behavior with inputs. Generate tables, charts, and downloadable reports instantly. Turn profile assumptions into dependable flow estimates for projects.
| Case | Geometry | Profile | Density (kg/m³) | Reference Velocity (m/s) | Main Dimensions (m) | Average Velocity (m/s) | Volumetric Flow (m³/s) | Mass Flow (kg/s) |
|---|---|---|---|---|---|---|---|---|
| Example 1 | Circular Pipe | Parabolic | 998 | 3.2 max | D = 0.40 | 1.60 | 0.201 | 200.7 |
| Example 2 | Rectangular Channel | Linear | 1000 | 1.8 max | B = 1.20, H = 0.80 | 0.90 | 0.864 | 864.0 |
| Example 3 | Circular Pipe | Power Law | 1.20 | 14 average | D = 0.25, n = 7 | 14.00 | 0.687 | 0.824 |
Flow area
For a circular pipe: A = πD² / 4
For a rectangular channel: A = B × H
Velocity profile models
Uniform: v = vmax
Linear: v = vmax(1 - η)
Parabolic: v = vmax(1 - η²)
Power Law: v = vmax(1 - η)1/n
For channels, η = |y| / (H/2). For pipes, η = r / R.
Volumetric flow rate
Circular pipe: Q = ∫ v(r) 2πr dr
Rectangular channel: Q = B ∫ v(y) dy
Average velocity
Vavg = Q / A
Mass flow rate
ṁ = ρQ
Momentum correction factor
β = (∫ v² dA) / (A Vavg²)
Energy correction factor
α = (∫ v³ dA) / (A Vavg³)
Velocity distribution and mass flow rate sit at the center of fluid engineering. A section can carry the same peak velocity and still produce different total flow because the profile shape changes the area average. That is why a clear diagram matters during design, checking, and troubleshooting.
This calculator helps you study how velocity varies across a circular pipe or a rectangular channel. You can choose a uniform, linear, parabolic, or power-law profile. You can also enter either a maximum velocity or an average velocity as the reference value. The tool then reconstructs the section behavior, estimates discharge, and converts discharge into mass flow rate with density.
The plotted diagram makes the profile easy to inspect. A flat curve suggests nearly uniform transport. A curved profile suggests stronger gradients near the wall. That difference affects bulk flow, momentum transfer, and energy transfer. For many engineering tasks, those changes matter more than the peak reading alone.
The calculator also reports momentum and energy correction factors. These values are useful when the velocity field is not uniform. They help when you apply control volume equations, compare test sections, or build simplified hydraulic models. Including these outputs creates a more complete engineering picture.
Engineers can use this page for preliminary pipe sizing, channel studies, pump system reviews, and teaching examples. It is also helpful when you need a quick comparison between alternative assumptions. A uniform profile may be acceptable for a rough estimate. A parabolic or power-law profile may be better when the flow field is clearly developed.
The numerical integration approach adds flexibility. It supports different section sizes and different profile shapes without forcing one closed-form shortcut. That makes the calculator useful when you want transparent assumptions and repeatable results. Increasing the segment count usually improves smoothness in the plotted diagram and reduces numerical error in the integrated outputs.
Because the page provides a table, graph, CSV export, and PDF export, it can fit design notes and review workflows. The example data table shows how different shapes change results. The formula section explains the relationships behind the calculations. The usage steps make setup quick for repeated checks. Together, these features support faster and better flow analysis.
It estimates velocity distribution, average velocity, volumetric flow, mass flow rate, and correction factors for a pipe or channel section using the profile model and dimensions you enter.
Real flow is rarely uniform. A profile changes average velocity, total discharge, momentum transport, and energy transport. Using a realistic shape improves engineering checks, sizing work, and comparison studies.
Use it for idealized laminar behavior or when you want a smooth profile that peaks at the center and falls to zero at the boundary.
It changes profile bluntness. Higher exponents create flatter cores and steeper edge gradients. Lower exponents make the profile more curved and reduce the average-to-maximum velocity ratio.
Volumetric flow measures space filled each second. Mass flow rate adds density, so it shows how much actual material passes through the section each second.
Yes. Enter the correct density and geometry. The calculator works for either fluid when the chosen profile is a reasonable engineering representation of the section.
They help when profile nonuniformity matters. Beta supports momentum equations. Alpha supports energy equations. Both become important in accurate hydraulic, process, and piping calculations.
Use more segments for smoother plots and tighter numerical integration. Values from 80 to 200 are usually a good balance for routine engineering work.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.