Pressure rise in a diffuser (expanding section) — ideal Bernoulli recovery vs actual recovery with losses. Borda-Carnot for sudden expansions.
Fluid Mechanics IILoss coefficient K (referenced to inlet dynamic pressure ½ρV₁²)
Bernoulli — ideal pressure recovery:
Actual pressure recovery with losses:
K is referenced to inlet dynamic pressure q₁ = ½ρV₁². K = 0 is the ideal case.
Borda-Carnot (sudden expansion):
Borda-Carnot is the upper bound on losses for abrupt expansion. A well-designed gradual diffuser achieves much lower K.
Continuity:
Typical diffuser efficiencies:
| Diffuser type | K (approx.) | η (approx.) |
|---|---|---|
| Ideal (frictionless) | 0 | 100 % |
| Well-designed conical (7°) | 0.05 | 90–95 % |
| Typical conical diffuser | 0.15 | 75–85 % |
| Sudden expansion (Borda) | auto | 50–70 % |
| Poorly designed / separated | 0.4+ | < 50 % |
Where: