Calculated Results
Results appear below the header and above the form after submission.
Calculator Inputs
Pressure–Flow Plot
The graph shows total flow and Reynolds number versus pressure drop for the current geometry and fluid properties.
Example Data Table
| Case | Geometry | Length | Size | Viscosity | Pressure Drop | Channels | Total Flow | Re | Wall Shear |
|---|---|---|---|---|---|---|---|---|---|
| Example A | Rectangular | 40 mm | 400 um × 100 um | 1.0 mPa·s | 20 kPa | 2 | 1,685.0000 uL/min | 56.1667 | 1.0531 Pa |
| Example B | Circular | 50 mm | 150 um diameter | 1.2 mPa·s | 35 kPa | 1 | 48.3210 uL/min | 4.5560 | 0.4952 Pa |
| Example C | Rectangular | 25 mm | 200 um × 50 um | 3.5 mPa·s | 60 kPa | 4 | 348.7850 uL/min | 8.0180 | 2.4420 Pa |
Formula Used
1) Circular channel flow
Q = πD⁴ΔP / (128μL)
2) Rectangular channel flow
Q ≈ [1 - 0.630(h/w)] · w·h³·ΔP / (12μL), using the smaller side as h and the larger side as w.
3) Average velocity
u = Q / A
4) Hydraulic diameter
D_h = 4A/P and for a rectangle D_h = 2wh / (w + h).
5) Reynolds number
Re = ρuD_h / μ
6) Hydraulic resistance
R_hyd = ΔP / Q
7) Residence time
t = V / Q, where V includes channel volume and any extra system volume you entered.
8) Wall shear
Circular: γ̇_w = 32Q / (πD³)
Rectangular approximation: γ̇_w ≈ 6Q / (w h²)
Then τ_w = μγ̇_w.
9) Péclet number
Pe = uD_h / D, where D is diffusion coefficient.
10) Capillary number
Ca = μu / σ, where σ is interfacial or surface tension.
How to Use This Calculator
Choose a solve mode first. Use pressure mode when you know the pressure drop and want the resulting flow. Use target-flow mode when you know the desired total flow and need the required pressure.
Select the channel geometry. Enter either width and height for a rectangular channel or diameter for a circular channel. The calculator automatically handles identical parallel channels.
Enter fluid properties carefully. Dynamic viscosity strongly affects pressure demand and flow. Density mainly affects Reynolds number. Surface tension and diffusion coefficient are optional transport indicators for advanced interpretation.
Add extra system volume when tubing, manifolds, reservoirs, or downstream chambers matter. This improves residence time estimates beyond the bare channel volume alone.
Click the submit button. The computed result block appears above the form. Review the flow rate, pressure, Reynolds number, wall shear, hydraulic resistance, residence time, and graph. Export the report as CSV or PDF when needed.
FAQs
1) What does this calculator solve?
It solves pressure-driven microchannel flow for circular and rectangular passages. It reports flow, required pressure, velocity, Reynolds number, wall shear, hydraulic resistance, residence time, and optional transport metrics.
2) When should I use rectangular versus circular mode?
Use rectangular mode for etched, molded, or milled lab-on-chip channels. Use circular mode for capillaries, tubing, needles, and round microbore passages.
3) Why is viscosity so important in microfluidics?
At microscale, viscous effects dominate strongly. A modest viscosity increase can noticeably raise the pressure needed for the same flow or reduce the delivered flow under fixed pressure.
4) What does Reynolds number tell me here?
It compares inertial and viscous effects. Most microfluidic devices operate in low-Reynolds laminar conditions, which makes pressure-flow behavior predictable and usually linear.
5) Is the rectangular-channel formula exact?
No. This page uses a standard engineering approximation with a side-wall correction. It is very good for many practical designs and especially useful for quick sizing and comparison work.
6) Why include extra system volume?
Channel residence time alone can be misleading when tubing, manifolds, junctions, or chambers add liquid hold-up. Extra volume gives a more realistic system transit time.
7) What does the capillary number mean?
It compares viscous forces with interfacial tension effects. It becomes especially useful in droplet generation, multiphase flow, emulsification, and wetting-sensitive microfluidic operations.
8) Can I use this for gases or non-Newtonian fluids?
Only with caution. This implementation assumes steady, incompressible, Newtonian behavior and no-slip walls. Gas slip, compressibility, and shear-dependent viscosity need more specialized models.