What are the affinity laws?

The affinity laws (also called fan laws or pump laws) are a set of three relationships that describe how flow, head/pressure, and power change with rotational speed or impeller diameter for centrifugal pumps, fans, and turbines. Flow varies linearly, head varies as the square, and power varies as the cube of the speed ratio.

When do affinity laws apply?

Affinity laws apply to centrifugal pumps, fans, and blowers operating on a fixed system curve. They assume geometrically similar conditions and incompressible flow. They work best for speed changes up to about ±30% from the design point.

What are the limitations of affinity laws?

Affinity laws are approximations. They do not account for efficiency changes at off-design conditions, system curve shifts, cavitation, or compressibility effects. For large speed or diameter changes (>30%), actual performance may deviate significantly from predictions.

How does VFD speed control save energy?

Because power varies as the cube of speed, even a small speed reduction yields large energy savings. Reducing speed by 20% reduces power consumption by approximately 49% (0.8³ = 0.512). This is why Variable Frequency Drives (VFDs) are highly cost-effective for flow control compared to throttling valves.

What is the relationship between flow and pressure?

Per the affinity laws, if speed changes by a ratio r, flow changes by r and pressure/head changes by r². So if you double the speed, flow doubles but pressure quadruples. If you halve the speed, flow halves but pressure drops to one quarter.

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相似定律計算器

當泵或風機轉速（或葉輪直徑）發生變化時，計算新的流量、揚程/壓力以及功率。基於離心泵相似定律。

泵與風機轉速與直徑 VFD 節能

結果

新流量 Q₂

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新揚程 / 壓力 H₂

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新功率 P₂

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轉速比 (n₂/n₁)

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流量比 (Q₂/Q₁)

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揚程比 (H₂/H₁)

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功率比 (P₂/P₁)

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三大相似定律

相似定律描述了離心泵、風機和鼓風機的流量、揚程（壓力）以及功率與轉速或葉輪直徑變化之間的關係：

其中比值可以是 n₂/n₁（轉速變化）或 D₂/D₁（直徑變化）。

轉速變化與直徑變化

轉速變化和葉輪直徑變化均適用相同的數學關係：

參數	轉速變化	直徑變化
流量 Q	Q₂ = Q₁ × (n₂/n₁)	Q₂ = Q₁ × (D₂/D₁)
揚程 H	H₂ = H₁ × (n₂/n₁)²	H₂ = H₁ × (D₂/D₁)²
功率 P	P₂ = P₁ × (n₂/n₁)³	P₂ = P₁ × (D₂/D₁)³

VFD 節能效益

關鍵洞察： 功率隨轉速的 三次方 變化。轉速降低 20% 可節省約 49% 的功率 (0.8³ = 0.512)。這就是為什麼變頻器 (VFDs) 是泵和風機最具成本效益的節能措施之一。

轉速降低	流量降低	揚程降低	功率節省
10%	10%	19%	27%
20%	20%	36%	49%
30%	30%	51%	66%
40%	40%	64%	78%
50%	50%	75%	88%

實務範例

範例 — 離心泵轉速增加

已知： n₁ = 1450 RPM, n₂ = 1750 RPM, Q₁ = 100 m³/h, H₁ = 25 m, P₁ = 7.5 kW

轉速比 r = 1750 / 1450 = 1.2069

Q₂ = 100 × 1.2069 = 120.7 m³/h

H₂ = 25 × 1.2069² = 36.4 m

P₂ = 7.5 × 1.2069³ = 13.2 kW

⚠️ 限制： 相似定律假設效率恆定、幾何相似條件以及不可壓縮流體。對於超過 ±30% 的轉速變化，實際性能可能會顯著偏差。葉輪車削定律不如轉速變化定律準確 — 請務必使用製造商曲線進行驗證。