Flow in rectangular, square, annular, and parallel-plate ducts using the hydraulic diameter Dh = 4A/P to apply Darcy-Weisbach and Reynolds number correlations.
Fluid Mechanics IIDuct cross-section:
Unit applies to all dimensions
Hydraulic diameter and radius:
Dh replaces D in Re = ρVDh/μ and Darcy-Weisbach hL = f(L/Dh)V²/2g. For a circular pipe, Dh = D exactly.
Shape formulas:
| Shape | Area A | Perimeter P | Dh |
|---|---|---|---|
| Rectangular a×b | ab | 2(a+b) | 2ab/(a+b) |
| Square a×a | a² | 4a | a |
| Circular D | πD²/4 | πD | D |
| Annular D₁,D₂ | π(D₁²−D₂²)/4 | π(D₁+D₂) | D₁−D₂ |
| Parallel plates H×W | HW | 2(H+W) | 2HW/(H+W) |
Laminar f×Re for common shapes:
| Shape | f × Re |
|---|---|
| Circular | 64.0 |
| Square | 56.9 |
| Rectangular a:b = 2 | 62.2 |
| Rectangular a:b = 4 | 73.0 |
| Rectangular a:b = 8 | 82.3 |
| Parallel plates (infinite) | 96.0 |
This calculator uses f = 64/Re (circular pipe approximation) for all laminar flows. For non-circular shapes use the exact f×Re value from the table above.
Darcy-Weisbach with Dh: