An engineering diffuser is a component that decelerates a flowing fluid, converting kinetic energy back into pressure energy, thereby increasing the static pressure. Diffusers are used in compressors, wind tunnels, aircraft intakes, and HVAC systems to recover pressure with minimal losses. The performance of a diffuser is characterised by the pressure recovery coefficient, which compares actual pressure rise to the ideal isentropic value.
C_p = (P2 - P1) / (0.5 × ρ × V1²)
LaTeX: C_p = \frac{P_2 - P_1}{\frac{1}{2} \rho V_1^2}
| Symbol | Meaning | Unit |
|---|---|---|
| C_p | Pressure recovery coefficient | dimensionless |
| P_1 | Inlet static pressure | Pa |
| P_2 | Outlet static pressure | Pa |
| \rho | Fluid density | kg/m³ |
| V_1 | Inlet velocity | m/s |
Problem
Air enters a diffuser at 80 m/s with a static pressure of 100 kPa and density 1.2 kg/m³. The outlet static pressure is 103.84 kPa. Calculate the pressure recovery coefficient.
Solution
Step 1: ΔP = P2 − P1 = 103,840 − 100,000 = 3,840 Pa. Step 2: Dynamic pressure = 0.5 × 1.2 × 80² = 0.5 × 1.2 × 6400 = 3,840 Pa. Step 3: C_p = 3,840 / 3,840 = 1.0 (ideal diffuser in this case).
Answer
C_p = 1.0 (ideal recovery; real diffusers achieve 0.6–0.9)
| Type | Geometry | Typical C_p | Application |
|---|---|---|---|
| Straight-walled | Linear diverging | 0.6–0.75 | Wind tunnels |
| Curved | Curved diverging walls | 0.7–0.85 | Compressor stages |
| Annular | Radial expanding | 0.75–0.90 | Centrifugal compressors |
| Vaned | With guide vanes | 0.80–0.88 | Turbomachinery |
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