Sherwood Number Calculator
Compute the Sherwood number to quantify convective mass transfer relative to molecular diffusion. Use it when designing absorbers, membranes, or any system where species transport rates matter.
About this calculator
The Sherwood number (Sh) is a dimensionless quantity in mass transfer analogous to the Nusselt number in heat transfer. It compares the rate of convective mass transfer to diffusive mass transport across a characteristic length. The formula is Sh = (k × L) / D, where k is the mass transfer coefficient (m/s), L is the characteristic length (m), and D is the molecular diffusivity (m²/s). A Sh of 1 indicates pure diffusion dominates; larger values signal strong convective enhancement. Engineers use Sh alongside correlations involving the Reynolds and Schmidt numbers to design contactors, reactors, and membrane modules. Accurate Sh estimates help size equipment and predict separation efficiency.
How to use
Suppose you are analyzing a tubular absorber where the mass transfer coefficient k = 0.005 m/s, the tube diameter (characteristic length) L = 0.05 m, and the molecular diffusivity of the solute D = 1.0 × 10⁻⁹ m²/s. Apply the formula: Sh = (k × L) / D = (0.005 × 0.05) / 1.0×10⁻⁹ = 2.5×10⁻⁴ / 1.0×10⁻⁹ = 250,000. This high Sh confirms that convection dominates diffusion by a factor of 250,000, which is typical for turbulent liquid-phase mass transfer in industrial absorbers.
Frequently asked questions
What does a high Sherwood number mean for a mass transfer system?
A high Sherwood number indicates that convective mass transfer far exceeds molecular diffusion across the characteristic length. This typically occurs under turbulent flow conditions or with highly effective mixing. In practical terms, it means your equipment is efficiently transporting species, reducing the required contact area or residence time. Engineers aim for higher Sh values to minimize equipment size and capital cost.
How is the Sherwood number related to the Reynolds and Schmidt numbers?
In most engineering correlations, the Sherwood number is expressed as a function of the Reynolds number (Re) and the Schmidt number (Sc): Sh = a × Re^b × Sc^c, where a, b, and c are empirical constants that depend on geometry and flow regime. The Reynolds number captures the flow intensity, while the Schmidt number (Sc = ν/D) reflects the ratio of momentum to mass diffusivity. This relationship allows engineers to predict Sh from easily measured flow and fluid properties without direct measurement of the mass transfer coefficient.
What units does the Sherwood number have and why is it dimensionless?
The Sherwood number is dimensionless because the units in the numerator (m/s × m = m²/s) cancel exactly with the diffusivity in the denominator (m²/s). Dimensionless numbers are powerful because they allow results from one scale or fluid system to be generalized to another through similitude. This means Sh correlations developed in laboratory-scale experiments can be applied directly to industrial-scale equipment, provided the relevant dimensionless groups match.