About the Rectangular Duct Shear Rate Calculator
Use this calculator to estimate apparent wall shear rate and related flow quantities for a Newtonian liquid moving through a rectangular duct. It is useful for fluid mechanics, process engineering, microfluidics, coating, and channel-flow checks where laminar flow is expected.
How to use this calculator
- Enter the volumetric flow rate and select its unit.
- Enter the duct width, height, and length, selecting the proper unit for each.
- Enter the dynamic viscosity and choose its unit.
- Enter the fluid density in kg/m³.
- Click Calculate shear rate to compute the results, or Reset to clear the form.
How it works
The calculator first converts the flow rate, duct dimensions, length, and viscosity to SI units. It treats the larger rectangular side as the broad side a and the smaller side as the gap b, then calculates the aspect ratio α = b/a, cross-sectional area, average velocity, and hydraulic diameter.
The corrected apparent wall shear rate is calculated from γ̇w ≈ 6Q / [a b² (1 − 0.630α + 0.053α⁵)]. This starts with the wide-slit shear-rate expression and adjusts it for a finite rectangular duct using the aspect-ratio correction factor.
Wall shear stress is estimated as τ = μγ̇w. Pressure drop is calculated with the matching laminar rectangular-duct correction, Reynolds number is found from Re = ρVDh/μ, and residence time is length divided by average velocity.
The method assumes laminar, fully developed, incompressible Newtonian flow in a smooth rectangular duct. Results are educational estimates; use validated engineering methods for design-critical work.
Example calculation
Suppose water-like fluid flows at 1 L/min through a duct that is 10 mm wide, 2 mm high, and 1 m long, with viscosity 1 cP and density 1000 kg/m³. The calculator converts Q to 1.667×10⁻⁵ m³/s, uses a = 0.010 m and b = 0.002 m, so α = 0.2 and the correction factor is about 0.874. The corrected apparent wall shear rate is about 1,430 s⁻¹, giving a wall shear stress of about 1.43 Pa for μ = 0.001 Pa·s.
Frequently asked questions
Why does the calculator use the smaller duct dimension as the gap?
The rectangular-channel correction is written in terms of a broad side and a smaller gap, so the calculator automatically assigns the smaller of width and height to b.
What does apparent wall shear rate mean in a rectangular duct?
It is an engineering estimate of the wall shear rate based on flow rate and duct geometry, corrected for rectangular rather than infinite-slit flow.
Can I use this for turbulent flow?
No, the shear-rate and pressure-drop formulas are intended for laminar, fully developed Newtonian flow. The Reynolds number result helps indicate whether that assumption is reasonable.
How is wall shear stress calculated?
For a Newtonian fluid, wall shear stress is dynamic viscosity multiplied by the corrected apparent wall shear rate: τ = μγ̇w.
Why is the hydraulic-diameter shear rate different from the corrected value?
The hydraulic-diameter result uses a pipe analogy, while the corrected value uses a rectangular-duct correction based on aspect ratio, so they are not expected to match exactly.