Understanding Affinity Laws: Electricity's Complex Relationship

The Affinity Laws, also known as the Fan Laws or Pump Laws, are a set of formulas that can be used to predict the performance characteristics of pumps, fans, and hydraulic turbines. They are derived using the Buckingham π theorem and are based on principles of fluid dynamics. The Affinity Laws are useful because they allow for the prediction of the head discharge characteristic of a pump or fan from a known characteristic measured at a different speed or impeller diameter. They can also be used to predict how pump performance will change when the impeller diameter changes. In terms of electricity, the Affinity Laws can be applied to pumps that are driven by Variable Frequency Drives (VFDs) or are supplied by mains electricity.

Flow is proportional to shaft speed or impeller diameter

The Affinity Laws, also known as the "Fan Laws" or "Pump Laws", are a set of formulas that predict the impact of a change in rotational speed or impeller diameter on the head and flow produced by a pump and the power demanded by a pump. They are derived using the Buckingham π theorem and are useful for predicting the head discharge characteristic of a pump or fan from a known characteristic measured at a different speed or impeller diameter.

The Affinity Laws are as follows:

Law 1: Flow is Proportional to Shaft Speed or Impeller Diameter

This law means that as shaft speed or impeller diameter changes, flow changes by the same proportional amount. In other words, if the shaft speed increases by 10%, then the flow at the same head will also increase by 10%. This law is expressed with the following formula:

> Q1/Q2 = (N1/N2) or (D1/D2)

Where:

• Q is equal to flow
• N is equal to shaft speed
• D is equal to impeller diameter

Law 2: Pressure is Proportional to the Square of Shaft Speed or Impeller Diameter

As per this law, as shaft speed or impeller diameter changes, pressure changes in proportion to the square of the change in shaft speed or impeller diameter. So, if shaft speed increases by 10%, then pressure at the same flow will increase by 21% (1.10^2). This law is expressed as:

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Pressure is proportional to the square of shaft speed or impeller diameter

The Affinity Laws (also known as the "Fan Laws" or "Pump Laws") are a set of formulas that predict the impact of changes in rotational speed or impeller diameter on the head, flow, and power of a pump or fan. They are derived using the Buckingham π theorem and are useful for predicting the performance characteristics of pumps and fans at different speeds or impeller diameters.

One of the Affinity Laws states that pressure is proportional to the square of shaft speed or impeller diameter. In other words, if the shaft speed or impeller diameter increases by 10%, the pressure at the same flow will increase by 21% (1.10^2). This relationship is expressed by the formula:

> H1/H2 = (N1/N2)^2 or (D1/D2)^2

Where:

• H is equal to head or pressure
• N is equal to shaft speed
• D is equal to impeller diameter

This law is particularly relevant in the context of energy savings. By installing variable speed drives (VSDs) to reduce motor running speeds, businesses can achieve significant cost savings. For example, installing a VSD to reduce speed by 25% can cut electricity consumption by about 50%.

The Affinity Laws are widely used in hydraulics, hydronics, and HVAC systems to express the relationship between variables involved in pump or fan performance, such as head, volumetric flow rate, shaft speed, and power. They are applicable to both centrifugal and axial flows and are essential for

Power is proportional to the cube of shaft speed or impeller diameter

The Affinity Laws, also known as the "Fan Laws" or "Pump Laws", are a set of formulas that predict the impact of changes in rotational speed or impeller diameter on the head, flow, and power of a pump or fan. They are derived using the Buckingham π theorem and are useful for predicting the performance characteristics of a pump or fan when the impeller speed or diameter is changed while maintaining dynamic similarity and efficiency.

One of the Affinity Laws states that power is proportional to the cube of shaft speed or impeller diameter. This means that as the shaft speed or impeller diameter increases or decreases, the power required changes in proportion to the cube of that change. For example, if the shaft speed increases by 10%, the power required will increase by 33.1% (1.10^3). Similarly, if the shaft speed is reduced by 25%, the power required will be reduced by approximately 50%. This relationship is represented by the formula:

> P1/P2 = (N1/N2)^3 or (D1/D2)^3

Where P is power, N is shaft speed, and D is impeller diameter.

This law has important implications for energy savings. By installing variable speed drives (VSDs) to reduce the speed of motors, significant reductions in electricity consumption can be achieved. For example, in the case of a mid-sized fan or pump motor rated at 37 kW, installing a VSD to reduce the speed by 25% would cut electricity consumption by about 50%. This would result in substantial cost savings over the lifetime of the motor.

It is important to note that the Affinity Laws assume constant pump or fan efficiency, which may not always be the case in practice. Therefore, while the laws can provide highly accurate predictions for changes in shaft speed, they may be less accurate for changes in impeller diameter due to the impact of diameter changes on efficiency.

Affinity laws and variable frequency drives (VFDs)

Variable Frequency Drives (VFDs), also known as variable speed drives or adjustable frequency drives, are electronic devices that control the speed and torque of electric motors. They achieve this by varying the frequency and voltage of the power supplied to the motor. VFDs are used in a wide range of industries, including HVAC, water and wastewater treatment, manufacturing, and mining.

The Affinity Laws, also known as the "Fan Laws" or "Pump Laws", are a set of mathematical relationships that describe how changes in the speed, flow rate, or head of a centrifugal pump or fan impact its performance. These laws are particularly useful for engineers and technicians working with centrifugal loads, as they can help predict how changes in operating conditions will affect performance and efficiency.

The Affinity Laws state that flow is directly proportional to the speed of the device. This means that if the speed of a pump or fan is reduced by 25%, the flow will also decrease by 25%. Similarly, if the speed is doubled, the flow will double as well.

The Affinity Laws also dictate that pressure is proportional to the square of the device's speed. So, if the speed is reduced by half, the pressure will decrease by a factor of four (2^2). Conversely, if the speed is increased by 50%, the pressure will go up by a factor of 2.25 (1.5^2).

Furthermore, according to the Affinity Laws, the power required to operate a centrifugal pump or fan is proportional to the cube of the device's speed. Therefore, a 20% reduction in speed would result in a power requirement reduction of 80% (0.2^3). On the other hand, a 10% increase in speed would lead to a 33.1% increase in power (1.1^3).

The Affinity Laws are especially relevant when considering the use of VFDs. By understanding these laws, engineers can optimise the efficiency of VFDs and achieve significant energy savings. For instance, in many applications, VFDs are used to control the speed of pumps and fans, resulting in substantial energy savings. The Affinity Laws can help determine the optimal speed for these devices, ensuring that they operate at the most efficient level while still meeting the required performance.

In conclusion, the Affinity Laws provide a valuable framework for understanding the relationship between speed, flow, pressure, and power in centrifugal pumps and fans. When applied to VFDs, these laws enable engineers to make informed decisions about speed adjustments, ultimately leading to improved energy efficiency and cost savings.

Affinity laws and energy savings

With the world facing an energy crisis, it is imperative to explore cost-effective ways to save electricity. The Affinity Laws offer a great opportunity to achieve this, with the potential for massive savings in electricity usage, especially in the context of electric motor applications.

Understanding Affinity Laws

The Affinity Laws, also known as the "Fan Laws" or "Pump Laws", are a set of formulas that govern the relationship between variables in pump or fan performance, such as head, volumetric flow rate, shaft speed, and power. They are derived using the Buckingham π theorem and are applicable to pumps, fans, and hydraulic turbines, including both centrifugal and axial flows.

The Affinity Laws consist of three main laws:

• Flow is Proportional to Shaft Speed or Impeller Diameter: This law states that as the shaft speed or impeller diameter changes, the flow changes by the same proportional amount. For example, if the shaft speed increases by 10%, the flow at the same head will also increase by 10%.
• Pressure is Proportional to the Square of Shaft Speed or Impeller Diameter: According to this law, when the shaft speed or impeller diameter changes, the pressure changes in proportion to the square of that change. So, a 10% increase in shaft speed results in a 21% increase in pressure at the same flow rate.
• Power is Proportional to the Cube of Shaft Speed or Impeller Diameter: This law explains that as the shaft speed or impeller diameter changes, the horsepower or power demanded changes in proportion to the cube of that change. Therefore, a 10% increase in shaft speed leads to a 33.1% increase in power at the same flow rate.

Application to Electricity Savings

The Affinity Laws have significant implications for energy savings, especially when applied to electric motor applications. Mid-sized motors, commonly used in industrial and commercial settings, can cost tens of thousands of pounds a year to run. However, by installing variable speed drives (VSDs) and utilising the Affinity Laws, organisations can achieve substantial electricity cost reductions.

For example, consider a typical mid-sized fan or pump motor rated at 37kW with 90% efficiency. Assuming it runs for 40 hours a week for 48 weeks a year, its annual electricity consumption can be calculated as:

> 40 x 48 x 41 = 78720 kWh of electricity a year

At 17p per kWh, this results in an annual cost of £13,382, or approximately £200,000 over its lifetime.

Now, let's apply the Affinity Laws with a VSD to reduce the motor speed by 25%. According to the laws, this reduction in speed cuts electricity consumption by about 50%, resulting in an annual saving of over £6,600.

Optimising Energy Efficiency

It is important to note that the Affinity Laws assume constant pump/fan efficiency, which may not always be the case. In reality, as the diameter of an impeller changes, its efficiency also changes. Therefore, while the Affinity Laws provide valuable predictions, they may not always yield highly accurate results, especially when calculating the impact of impeller diameter changes on pump performance.

To optimise energy efficiency, it is crucial to consider other factors such as motor efficiency, drive efficiency, and the use of additional equipment like harmonic filters. Additionally, proper sizing of fans/pumps is essential. Oversized fans/pumps may not operate at their best efficiency point, and while VSDs can help correct for this, they may not always be the most economical solution.

In conclusion, the Affinity Laws provide a powerful framework for understanding and optimising pump and fan performance, leading to significant energy savings. By applying these laws and considering the specific characteristics of their electric motor applications, organisations can make substantial strides towards reducing their electricity costs and environmental impact.

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