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Microchannel Hydraulic Diameter & Friction Calculator

Microfluidic lab-on-a-chip channels are predominantly fabricated with rectangular cross-sections via lithography and PDMS molding.

Width of rectangular microchannel.

Height / depth of rectangular microchannel.

Calculated Result
133.33 µm

Hydraulic Diameter (Dh)

Aspect Ratio (α)

0.500

Laminar Poiseuille Friction (f·Re)

62.2

Cross-Section Area

20000 µm²

Calculation Breakdown

  1. Step 1: Hydraulic Diameter FormulaDh = 4·A / P = (4 · w·h) / [2·(w + h)] = (2 · 200 · 100) / (200 + 100) = 133.33 µm
  2. Step 2: Shah-London Poiseuille Constantf·Re = 62.2 for rectangular duct with aspect ratio α = 0.500

What Is the Microchannel Hydraulic Diameter & Friction Calculator?

Hydraulic diameter is a commonly used term when handling flow in non-circular tubes and channels, converting a 2D cross-section into an equivalent circular tube.

How Does the Microchannel Hydraulic Diameter & Friction Calculator Work?

Calculates cross-sectional area A = w · h and wetted perimeter P = 2(w + h).

Computes Dh = 4A / P.

Evaluates the Shah-London polynomial for laminar Poiseuille number f·Re as a function of aspect ratio.

Microchannel Hydraulic Diameter & Friction Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

Dh = (4 · A) / P = (2 · w · h) / (w + h), α = h / w

Hydraulic diameter definition and Shah-London polynomial for laminar friction factor.

How to Use the Microchannel Hydraulic Diameter & Friction Calculator

  1. Enter channel width and height in microns.

Step-by-Step Example Calculation

Rectangular Lab-on-a-Chip Channel

Input Values:

width:200
height:100
Worked Steps: 200 µm × 100 µm rectangular microchannel with Dh = 133.3 µm.

Understanding Your Result

Primary output reports hydraulic diameter in microns.

Summary displays laminar friction constant f·Re (ranges from 56.9 for parallel plates to 96 for high aspect ratio).

Factors That Affect the Result

  • Channel aspect ratio α.

When Should You Use This Calculator?

  • Microfluidic lab-on-a-chip pressure drop calculations, microchannel heat sinks, and capillary design.

Assumptions & Limitations

  • Assumes straight rectangular duct with fully developed laminar flow.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Shah and London analytical duct flow correlation.

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