Effect of Impeller Diameter on Flow, Head & Power
In pumps and turbomachinery, the impeller diameter is one of the most important factors affecting performance. The Affinity Laws explain how Flow, Head, and Power change when the impeller diameter changes, while speed remains constant.
Affinity Laws (Constant Speed, Varying Diameter):
1. Flow (Q): Q₁/Q₂ = (D₁/D₂)³
2. Head (H): H₁/H₂ = (D₁/D₂)²
3. Power (P): P₁/P₂ = (D₁/D₂)⁵
Explanation:
– Larger impellers increase flow capacity.
– Head increases with square of diameter due to velocity rise.
– Power rises sharply with fifth power of diameter.
– Impeller trimming (reducing diameter) is used to match pump duty but limited to ~10–15%.
Numerical Example with Step-by-Step Calculation:
Let’s consider a pump with:
• Original diameter D₁ = 200 mm
• Flow Q₁ = 100 m³/h
• Head H₁ = 40 m
• Power P₁ = 15 kW
Now trimmed to D₂ = 180 mm:
- Flow (Q₂):
- Q₂ = Q₁ × (D₂/D₁)³
- Q₂ = 100 × (180/200)³
- Q₂ = 100 × (0.9)³ = 100 × 0.729 = 72.9 ≈ 73 m³/h
- Head (H₂):
- H₂ = H₁ × (D₂/D₁)²
- H₂ = 40 × (180/200)²
- H₂ = 40 × (0.9)² = 40 × 0.81 = 32.4 m
- Power (P₂):
- P₂ = P₁ × (D₂/D₁)⁵
- P₂ = 15 × (180/200)⁵
- P₂ = 15 × (0.9)⁵ = 15 × 0.59049 = 8.86 ≈ 8.9 kW
Comparison Table:
| Parameter | Before (D₁ = 200 mm) | After (D₂ = 180 mm) |
| Flow (Q) | 100 m³/h | ≈ 73 m³/h |
| Head (H) | 40 m | ≈ 32.4 m |
| Power (P) | 15 kW | ≈ 8.9 kW |
Graphs:
The following graphs illustrate how Flow, Head, and Power vary with impeller diameter.
Conclusion:
The Affinity Laws clearly show that a small change in impeller diameter results in a large impact on pump performance.
– Flow reduces with the cube of diameter.
– Head reduces with the square of diameter.
– Power reduces with the fifth power of diameter.
Thus, selecting or trimming impeller diameter is a key tool for optimizing pump energy efficiency and performance.
- Effect of Impeller Diameter on Flow, Head & Power
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