Question

The 1800 -rpm, 150 -hp motor of a compressor is burned out and is to be replaced by either a standard motor that has a full-load efficiency of 93.0 percent and costs \(\$ 9031\) or a high-efficiency motor that has an efficiency of 96.2 percent and costs \(\$ 10,942 .\) The compressor operates 4368 h/yr at full load, and its operation at part load is negligible. If the cost of electricity is \(\$ 0.125 / \mathrm{kWh}\), determine the amount of energy and money this facility will save by purchasing the high-efficiency motor instead of the standard motor. Also, determine if the savings from the high-efficiency motor justify the price differential if the expected life of the motor is 10 years. Ignore any possible rebates from the local power company.

Short answer

Answer: Yes, the high-efficiency motor justifies its higher price as the total cost savings over 10 years ($21,577.80) is greater than the price difference between the two motors ($1,911).

Step-by-step solution

Calculate the energy consumption of each motor per year

We know the power output required (150 hp) and motor efficiencies. First, we need to convert the power output into kilowatts (kW) and then calculate the input power for each motor. 1 horsepower (hp) = 0.7355 kW For the standard motor: 150 hp * 0.7355 kW/hp = 110.325 kW (output power) Input power = (Output power) / (efficiency) Input power = 110.325 kW / 0.93 = 118.63 kW For the high-efficiency motor: Output power is the same, so: Input power = 110.325 kW / 0.962 = 114.65 kW Next, we calculate the annual energy consumption of the two motors: Standard motor energy consumption per year: Energy_standard = Power input * Time Energy_standard = 118.63 kW * 4368 h = 517,862.44 kWh High-efficiency motor energy consumption per year: Energy_high_efficiency = Power input * Time Energy_high_efficiency = 114.65 kW * 4368 h = 500,600.20 kWh

Calculate the energy and cost savings with the high-efficiency motor

Now, we'll find the difference in energy consumption and calculate the cost savings by using the high-efficiency motor. Difference in energy consumption: Energy_savings = Energy_standard - Energy_high_efficiency Energy_savings = 517,862.44 kWh - 500,600.20 kWh = 17,262.24 kWh Cost savings per year: Cost_savings_per_year = Energy_savings * Cost of electricity Cost_savings_per_year = 17,262.24 kWh * \(0.125/kWh = \)2,157.78

Determine if the high-efficiency motor justifies the price difference over its life

We'll calculate the total cost savings over the motor's expected life of 10 years and compare it with the price difference of the two motors. Total cost savings: Total_cost_savings = Cost_savings_per_year * 10 years = \(2,157.78 * 10 = \)21,577.80 Price difference between the two motors: Price_difference = \(10,942 - \)9,031 = $1,911 Since the total cost savings over 10 years (\(21,577.80) is greater than the price difference between the two motors (\)1,911), the high-efficiency motor justifies its higher price.

Key concepts

Energy Consumption in Industrial Motors

Understanding energy consumption is crucial when it comes to industrial motors, as it directly affects operational costs. Let's take the example of a 150-hp motor for a compressor. By converting horsepower to kilowatts, we calculate the input power needed for both standard and high-efficiency motors, considering their respective efficiencies (93.0% and 96.2%). This allows us to estimate the annual energy consumed by each motor when operating at full load for 4368 hours a year.

For the standard motor, using the formula \( Energy = Power \times Time \), we find it consumes 517,862.44 kWh per year. The high-efficiency motor consumes less: 500,600.20 kWh per year. The difference in consumption illustrates the energy-saving potential of high-efficiency motors. Lower energy consumption not only translates to cost savings but also could imply a reduction in greenhouse gas emissions, contributing to more sustainable operations.

Cost Savings Analysis of High-Efficiency Motors

To perform a cost savings analysis, we first determine the energy cost for both the standard and high-efficiency motors. The annual cost is the product of energy consumption and electricity rate, \(\$0.125/kWh\). We find the high-efficiency motor saves 17,262.24 kWh per year, which amounts to \(\$2,157.78\) in annual cost savings.

Long-Term Savings

Over the expected 10-year lifespan of the motor, these annual savings add up, potentially exceeding the initial price difference between the motors. By comparing the total cost savings against the price difference, the high-efficiency motor offers a return on investment and can be justified not only in terms of environmental benefits but also financial gains. This analysis serves as a basis for making informed decisions concerning equipment upgrades and energy management.

When to Replace with an Industrial High-Efficiency Motor

In deciding whether to replace a burnt-out industrial motor with a standard or high-efficiency unit, several factors must be considered. First, the energy savings achieved by a high-efficiency motor can be substantial over time, meriting the initial higher investment. The problem demonstrates that the total savings on operational costs over a decade surpass the price difference, signifying the high-efficiency motor as the financially advantageous choice.

However, this is not the sole consideration. High-efficiency motors typically have a longer lifespan due to reduced electrical losses, leading to less operational heat and, as a result, wear on components. They also contribute to a company's sustainability goals by reducing energy consumption. When faced with motor replacement decisions, it's important to weigh the initial costs against long-term savings, environmental impact, and potential rebates from power companies or government incentives. These factors combined will guide the decision-making process for a cost-effective and energy-efficient motor replacement strategy.