Question

The compressed-air requirements of a plant are being met by a 90 -hp screw compressor. The facility stops production for one hour every day, including weekends, for lunch break, but the compressor is kept operating. The compressor consumes 35 percent of the rated power when idling, and the unit cost of electricity is \(\$ 0.11 / \mathrm{kWh}\). Determine the amount of energy and money saved per year as a result of turning the compressor off during lunch break. Take the efficiency of the motor at part load to be 84 percent.

Short answer

Answer: To find the amount of energy and money saved per year by turning off the compressor during lunch break, follow these steps: 1. Convert the rated power of the compressor from horsepower to kilowatt. 2. Calculate the power consumed by the compressor when idling. 3. Calculate the energy consumption when the compressor is idling and when it's turned off. 4. Calculate the energy saved per day. 5. Calculate the energy saved per year. 6. Calculate the money saved per year by multiplying the energy saved with the unit cost of electricity.

Step-by-step solution

Convert horsepower to kilowatt

The rated power of the compressor is given in horsepower. We need to convert it to kilowatt before proceeding further. We know that 1 hp = 0.7355 kW. So, we can use the following equation to convert: \[P_{kW} = P_{hp} \times 0.7355\]

Calculate power consumed when idling

The compressor consumes 35% of the rated power when idling. We can find the power consumed when idling by using the following equation: \[P_{idle} = P_{kW} \times 0.35\]

Calculate energy consumption when idling and turned off

We have to find the energy consumed when the compressor is idling and when it is turned off. Energy consumption can be calculated using the formula: \[E = P \times t \times \eta\] where E is the energy consumption, P is power, t is the time, and η is the efficiency. In our case, t=1 hour and η=0.84 when idling.

Calculate energy saved per day

Now we have the energy consumption when idling and when turned off. We can find the energy saved per day by subtracting the two values: \[E_{saved\_day} = E_{idle} - E_{off}\] Since E_off = 0 kWh, the energy saved per day is just the energy consumed when idling.

Calculate energy saved per year

We have found the energy saved per day. To find the energy saved per year, we can simply multiply the energy saved per day by the number of days in a year: \[E_{saved\_year} = E_{saved\_day} \times 365\]

Calculate money saved per year

We have the energy saved per year, and we know the unit cost of electricity. We can easily find the money saved per year by multiplying the energy saved by the unit cost of electricity: \[Money\_saved = E_{saved\_year} \times cost\_per\_kWh\] By performing these calculations, we can find the amount of energy and money saved per year by turning the compressor off during lunch break.

Key concepts

Understanding Energy Efficiency

Energy efficiency refers to the practice of using less energy to perform the same task or produce the same output. Typically, increased energy efficiency results in lower energy bills, reduced energy consumption, and less strain on natural resources. It is an essential aspect in industries, homes, and businesses to save costs and protect the environment.

In the given problem, the focus is on how to increase energy efficiency by reducing unnecessary power consumption. The compressor in the scenario is using 35% of its rated power even during idle time. By turning the compressor off during lunch breaks, the energy efficiency of the plant would improve significantly, as energy that would have otherwise been wasted is saved. Remember, effective energy management is not only about using energy-saving appliances but also involves the optimal operation of equipment, such as turning off machines when they are not in use.

Power Conversion from Horsepower to Kilowatt

When working with machines like the compressor in the exercise, it's common to encounter power ratings in horsepower (hp). However, for energy calculations, particularly those related to electrical energy, we often need to convert this power into kilowatts (kW), which is a unit of power within the International System of Units.

The formula used for this conversion is straightforward: \[P_{kW} = P_{hp} \times 0.7355\] It's important not only to perform this conversion accurately but also to understand that this step is critical for subsequent calculations, like determining energy consumption or savings, since these are typically measured in kilowatt-hours (kWh).

Energy Consumption Calculation

The energy consumption of a device or system is the amount of energy used by it over time. Calculating this value is fundamental for understanding the energy efficiency of any operation. The formula is: \[E = P \times t \times \eta\] where

• (E) is the energy consumption,
• (P) represents power usage,
• (t) is the time for which the system operates,
• (\eta) stands for efficiency, a dimensionless factor accounting for losses in the system.

For the compressor, you'd calculate the energy used both while idling and while turned off (which is zero). Once you have the energy consumption for a single day, you can easily scale this to annual energy consumption by multiplying by the number of days in a year. This forms a basis for calculating potential savings, both in energy and monetary terms, highlighting how critical these calculations are for efficient energy management.