# Replacement of Pump Motor | Energy Saving Purpose | GD² | Pump Motor Replacement | Moment of Inertia | Moment of Inertia Formula | Pump head Calculation

Replacing a pump motor with an energy-efficient one is a great way to save energy, reduce operating costs, and increase equipment reliability. However, it requires careful consideration and expertise to ensure that the new motor is the right fit for the pump, operates efficiently, and does not pose any risks to the system. In this article, we will discuss the steps for replacing a pump motor from an energy-saving point of view.

## Steps for replacement of pump motor, from energy saving point of view

### Check GD² of the New Motor

The GD² (Moment of Inertia of the rotor of any rotating equipment) of the new motor should be higher than that of the pump. GD² is a measure of the resistance of the rotor to changes in speed. If the GD² of the motor is less than that of the pump, it may not be able to maintain the required speed during operation, resulting in reduced efficiency and increased energy consumption.

**What is GD²**

GD² unit kg.m2

G= Weight of rotating mass in kg (=W)

D= 2 R (R= Radius of gyration in meters)

GD² =4WR^2/g

### Check Starting Torque and Current Carrying Capacity

Positive displacement pumps, such as oil circulation pumps, are typically started with an open discharge condition. Hence, the starting torque and current carrying capacity of the new motor should be checked to ensure that it can handle the load during startup.

### Check Maximum Oil Pressure and Power Consumption

If the pump is a positive displacement pump, the maximum oil pressure that may be developed in the system should be checked. If there is scope for an increase in pressure, power consumption will increase, and the power required at maximum pressure should be calculated. During cold start, the oil viscosity will be high, and accordingly, the oil pressure will also increase, resulting in maximum power consumption. The motor should be selected to suit the maximum power requirement.

### Select the Motor for Full Load Efficiency

Motors are designed to take the maximum load demand of the pump, and safety margins are not provided. If motors are underutilized, their efficiency becomes poor. Motor selection should aim for motors to run at full load with maximum efficiency and not at partial load. Nowadays, motors are also manufactured to have the same efficiency at various loads. If you can locate such a motor, you can save energy with the new motor, even at partial load, but the investment is more leading to a more extended payback period. The motor supplier should assure safe running of the motor at full load.

### Consider Motor Overload and Ambient Temperature

Several other factors need to be considered during motor selection. For instance, the chances of overload can be high because of high viscosity during cold start or partial clogging of oil pipes. If the ambient temperature is greater than 40°C, the motors cannot be used up to their rated capacity and must be derated. If there is additional heat generating equipment nearby or restricted airflow, this may be partly accounted for in the rise in ambient. Cost of equipment failure should also be considered, as failure of this motor may lead to a very high loss

Normally motors are designed to take maximum load demand of the pump and safety margins are not provided. There is a general observation that when motors are under utilized their efficiency becomes poor. Motor selection should aim at motors to run at full load with maximum efficiency and not at partial load. Now a days, motors are also manufactured to have same efficiency at various load, if you can locate on such motor, you can save the energy with new motor, even at partial load, but investment is more leading to more payback period.

One must take motor suppliers' assurance on safe running of motor at full load.

**Other important aspects to consider:**

Apart from the above-mentioned steps, there are other important aspects to consider before the replacement of pump motor from an energy-saving point of view. These include:

**Ambient temperature:** If the ambient temperature is greater than 40 degrees Celsius, the motors cannot be used up to their rated capacity and must be derated. Additional heat generating equipment nearby or restricted airflow: This may be partly accounted for in the rise in ambient temperature.

**Cost of failure of equipment: **If the failure of this motor leads to a very high loss, chances are that everyone will want to play it safe.

**Maintenance practices:** Maintenance practices like cleaning of motor surface for heat dissipation, periodic change of bearings, etc., should be considered.

Precise selection of the motor keeping in view all the above, requires considerable expertise. Idea of saving energy is commendable, but equally it is fraught with a risk, which cannot be neglected.

**Evaluate the motor's efficiency:** Once you have found a motor that meets the requirements outlined above, evaluate its efficiency rating. Choose a motor with a high efficiency rating as this will consume less energy and therefore save costs in the long run.

**Install the new motor:**Once you have selected the right motor, it's time to install it. Make sure that the installation is done properly and all safety protocols are followed. If you are unsure about the installation process, it is recommended that you seek the help of a professional.

**Monitor the energy usage:** After the new motor has been installed, it's important to monitor its energy usage. Keep track of the amount of energy consumed by the pump system before and after the replacement. This will help you determine the energy savings achieved by replacing the old motor with the new, more efficient one.

## Pump head Calculation

Pump head calculation is an important aspect of pump design and selection. The pump head is the pressure required to move fluid from the inlet of the pump to the outlet of the pump. It is a combination of the static head (the height difference between the inlet and outlet of the pump) and the dynamic head (the pressure required to overcome frictional losses in the system).

To calculate the pump head, you will need to know the following information:

Flow rate: The volume of fluid that the pump needs to move per unit time (usually measured in liters per minute or gallons per minute).

Static head: The height difference between the inlet and outlet of the pump (usually measured in meters or feet).

Friction loss: The pressure drop due to frictional losses in the piping system (usually measured in meters or feet of head).

The formula for calculating the pump head is:

Pump head (H) = Static head (Hs) + Friction loss (Hf)

where Hs = height difference between the inlet and outlet of the pump, and Hf = pressure drop due to frictional losses in the piping system.

For example, let's say you have a pump that needs to move 100 liters per minute of water from a tank located 10 meters above the pump to a tank located 20 meters above the pump. The friction loss in the piping system is 5 meters of head. The pump head would be:

H = Hs + Hf

H = 20 - 10 + 5

H = 15 meters

So, the pump would need to be able to generate a pressure of 15 meters of head to move the required flow rate of water.

Calculation Examples

GD2 is a parameter that describes the rotating inertia of a machine, and it's given by the formula:

GD2 = (J x N^2) / (1000^2)

where J is the moment of inertia of the machine in kg.m^2, and N is the speed of rotation in rpm.

Let's assume we have a machine with a moment of inertia J = 5 kg.m^2 and a speed of rotation N = 1500 rpm. To calculate the GD2 of this machine, we can use the above formula as follows:

GD2 = (J x N^2) / (1000^2)

GD2 = (5 x 1500^2) / (1000^2)

GD2 = 11.25 kg.m^2

Therefore, the GD2 of this machine is 11.25 kg.m^2.

It's worth noting that GD2 is an important parameter in designing mechanical systems and selecting motors and other rotating equipment. A high GD2 value indicates that a machine has a large rotating mass, which can impact its starting and stopping times and affect the required torque and power of the driving motor.

To calculate the power (kW) of a motor with respect to the above GD2 data, we need to know the acceleration time of the machine. The power required to accelerate a machine is given by:

Power (kW) = (GD2 x 2 x π x N) / (t x 60 x 1000)

where t is the time in seconds required to accelerate the machine from rest to its maximum speed N.

Let's assume the machine takes 5 seconds to accelerate from rest to its maximum speed of 1500 rpm. Plugging in the values, we get:

Power (kW) = (GD2 x 2 x π x N) / (t x 60 x 1000)

Power (kW) = (11.25 x 2 x 3.14 x 1500) / (5 x 60 x 1000)

Power (kW) = 7.4 kW (approx.)

Therefore, the power required to accelerate this machine is approximately 7.4 kW.

Please note that this calculation assumes ideal conditions and doesn't take into account losses due to friction and other factors. Also, the power required to operate the machine at its steady-state speed will depend on the load and other factors, and may be different from the power required for acceleration.

To calculate the pump head for the above example, we need to know the flow rate of the fluid being pumped, the density of the fluid, and the efficiency of the pump.

Let's assume that the pump is operating at a flow rate of 10 cubic meters per hour (10 m^3/h), and the fluid being pumped has a density of 1000 kg/m^3. Let's also assume that the pump has an efficiency of 80%.

The pump head can be calculated using the following formula:

Pump Head (m) = (Pressure Rise (Pa) / (Density (kg/m^3) x Gravity (m/s^2)))

where the pressure rise can be calculated using the following formula:

Pressure Rise (Pa) = (Flow Rate (m^3/s) x Pump Head (m) x Density (kg/m^3) x Gravity (m/s^2)) / Efficiency

Let's assume a value of 40 meters for the pump head. Using the above formulas, we can calculate the pressure rise as follows:

Pressure Rise (Pa) = (10 / 3600 x 40 x 1000 x 9.81) / 0.8

Pressure Rise (Pa) = 32584.5 Pa (approx.)

Now we can calculate the pump head:

Pump Head (m) = 32584.5 / (1000 x 9.81)

Pump Head (m) = 3.32 meters (approx.)

Therefore, the pump head for the above example is approximately 3.32 meters.

## Example 1:

A pump is required to pump water from a storage tank to an overhead tank located 10 meters above the storage tank. The flow rate required is 2 cubic meters per hour, and the efficiency of the pump is 75%. Calculate the pump head required.

### Solution:

We can use the formula:

Pump Head (m) = (Pressure Rise (Pa) / (Density (kg/m^3) x Gravity (m/s^2)))

The pressure rise can be calculated as follows:

Pressure Rise (Pa) = (Flow Rate (m^3/s) x Pump Head (m) x Density (kg/m^3) x Gravity (m/s^2)) / Efficiency

Let's assume a density of 1000 kg/m^3 for water. Plugging in the values, we get:

Pressure Rise (Pa) = (2 / 3600 x Pump Head (m) x 1000 x 9.81) / 0.75

Pressure Rise (Pa) = 865.5 x Pump Head (m)

To pump water to a height of 10 meters, we need a pressure rise of 98100 Pa. Therefore:

98100 = 865.5 x Pump Head (m)

Pump Head (m) = 113 meters (approx.)

Therefore, the pump head required is approximately 113 meters.

## Example 2:

A centrifugal pump is used to pump a fluid with a density of 800 kg/m^3. The pump is located 3 meters below the surface of a tank, and the fluid level inside the tank is 2 meters above the pump suction. The pump is required to deliver a flow rate of 8 cubic meters per hour, and its efficiency is 85%. Calculate the pump head required.

### Solution:

The pump head required is the sum of the suction head and the discharge head. The suction head is the vertical distance from the pump centerline to the fluid level in the tank, and the discharge head is the vertical distance from the pump centerline to the discharge point. We can use the following formula to calculate the pump head:

Pump Head (m) = Discharge Head (m) + Suction Head (m)

The suction head is:

Suction Head (m) = 2 - 3 = -1 meter

The negative sign indicates that the pump is located below the fluid level in the tank.

The discharge head is:

Discharge Head (m) = Pressure Rise (Pa) / (Density (kg/m^3) x Gravity (m/s^2))

Pressure Rise (Pa) = (Flow Rate (m^3/s) x Pump Head (m) x Density (kg/m^3) x Gravity (m/s^2)) / Efficiency

Let's assume a pump head of 20 meters. Plugging in the values, we get:

Pressure Rise (Pa) = (8 / 3600 x 20 x 800 x 9.81) / 0.85

Pressure Rise (Pa) = 39535 Pa (approx.)

Therefore, the discharge head is:

Discharge Head (m) = 39535 / (800 x 9.81)

Discharge Head (m) = 5.08 meters (approx.)

Therefore, the pump head required is:

Pump Head (m) = Discharge Head (m) + Suction Head (m)

Pump Head (m) = 5.08 - 1 = 4.08 meters (approx.)

Therefore, the pump head required is approximately 4.08 meters.

We need to calculate the GD2 value of the pump motor to ensure that the motor can safely handle the load and provide smooth operation. The formula to calculate GD2 is:

GD2 = (J x D^4) / 32

Where J is the polar moment of inertia of the pump impeller, and D is the diameter of the impeller.

Assuming the impeller diameter to be 250 mm, we need to determine the polar moment of inertia of the impeller (J). This value is typically provided by the pump manufacturer or can be calculated using a CAD model. Let's assume a polar moment of inertia of 0.001 kg-m^2 for this example.

Plugging in the values, we get:

GD2 = (0.001 x (0.25)^4) / 32

GD2 = 0.00012207031 kg-m^2

Now, we need to select an appropriate GD2 value for the motor. This value should be greater than or equal to the calculated GD2 value to ensure safe operation. A general rule of thumb is to select a GD2 value that is 1.5 to 2 times the calculated value. In this case, we can select a GD2 value of 0.0002 kg-m^2.

Therefore, the appropriate GD2 value for the motor in this example is 0.0002 kg-m^2.

## FAQs

### How much energy can be saved by replacing the pump motor with an energy-efficient one?

The amount of energy that can be saved by replacing the pump motor with an energy-efficient one depends on various factors such as the size of the pump, the efficiency of the old motor, and the efficiency of the new motor. However, on average, it is estimated that energy savings can range from 20% to 50%.

#### How long does it take to recover the investment in an energy-efficient motor?

The payback period for the investment in an energy-efficient motor depends on the cost of the motor, the energy savings achieved, and the electricity rates in the area. On average, the payback period can range from 1 to 3 years.

#### Can any motor be used to replace the old motor of a pump?

No, not all motors can be used to replace the old motor of a pump. It's important to select a motor that meets the requirements of the pump such as the GD² of the motor, starting torque, and starting current carrying capacity.

#### Can an energy-efficient motor be used for all types of pumps?

Yes, energy-efficient motors can be used for all types of pumps. However, it's important to select a motor that meets the requirements of the pump to ensure that it works efficiently.

#### How can I find the GD² of a motor?

The GD² of a motor can be found in the manufacturer's specifications. If the information is not available, it can be calculated using the formula GD² = 4WR²/g, where W is the weight of the rotating mass in kg, R is the radius of gyration in meters, and g is the acceleration due to gravity in m/s²

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