Hedstrom number, abbreviated as \(He\), a dimensionless number, is used in fluid dynamics to characterize the relative importance of viscous forces to inertial forces in a fluid flow. The Hedström number helps determine whether viscous effects or inertial effects dominate in a fluid flow. Its interpretation is similar to the Reynolds number, which is another dimensionless parameter used in fluid dynamics. The key differences between the Hedström number and the Reynolds number are the choice of characteristic velocity and the absence of density in the Hedström number.
Hedstrom Number formula |
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| \( He \;=\; \dfrac{ \left(\rho \cdot d^2\right) \cdot \tau }{ \mu^2 } \) | ||
| Symbol | English | Metric |
| \( He \) = Hedstrom Number | \(dimensionless\) | \(dimensionless\) |
| \( \rho \) (Greek symbol rho) = Fluid Mass Density | \(lbm\;/\;ft^3\) | \(kg\;/\;m^3\) |
| \( d \) = Pipe Inside Diameter | \(in^2\) | \(mm^2\) |
| \( \tau \) (Greek symbol tau) = Pipe Yield Point | \(in\) | \(mm\) |
| \( \mu \) (Greek symbol mu) = Fluid Dynamic Viscosity | \(lbf-sec\;/\;ft^2\) | \( Pa-s \) |
Hedstrom Number Interpretation
He represents the ratio of yield stress forces to viscous forces (in squared form, analogous to how Reynolds number represents inertial-to-viscous force ratios).
He = 0 - No yield stress. Fluid behaves as pure Newtonian. The Bingham model reduces to Newtonian flow.
Small He - Yield stress effects are minor relative to viscous effects; the unsheared "plug" core in pipe flow is thin relative to the pipe radius.
Large He - Yield stress dominates; a large central plug region moves as a solid-like core, with shearing confined to a thin annulus near the wall. The fluid requires significant force just to initiate flow.
He is essentially a measure of the relative size of the unsheared plug zone in Bingham plastic pipe flow, and it governs how strongly the yield stress distorts the velocity profile away from the parabolic Newtonian shape.
He = 0 - No yield stress. Fluid behaves as pure Newtonian. The Bingham model reduces to Newtonian flow.
Small He - Yield stress effects are minor relative to viscous effects; the unsheared "plug" core in pipe flow is thin relative to the pipe radius.
Large He - Yield stress dominates; a large central plug region moves as a solid-like core, with shearing confined to a thin annulus near the wall. The fluid requires significant force just to initiate flow.
He is essentially a measure of the relative size of the unsheared plug zone in Bingham plastic pipe flow, and it governs how strongly the yield stress distorts the velocity profile away from the parabolic Newtonian shape.
