Power Consumption Homework: Find Equations

In summary, the equations and information needed to solve the question are the density of air, the area of the air duct, and the average speed of the air passing through the duct. Using these values, the volume flow rate, mass flow rate, and kinetic energy of the air can be calculated. The average power can then be determined by dividing the kinetic energy by the time of one second. However, this is a minimum value as it assumes perfect efficiency in energy transfer.
  • #1
TyErd
299
0

Homework Statement


Okay, all I want to know is, what are the equations/information I need to solve this question. I'm not too sure.


Homework Equations



Not sure

The Attempt at a Solution

 

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  • #2
Average power is given by the energy or work per unit time. The sort of energy we could make a calculation for, using the available information about the air flow, is the kinetic energy of the air. We know the area of the cross-section of the air duct and the average speed at which the air passes through the duct. What volume of air passes by the fan every second?

We are given the density of air, so what is the mass of air passing the fan in one second?

We now have a mass of air and its speed. What is the kinetic energy of that mass of air? This energy flows by in one second, so what power does that represent?
 
  • #3
density = mass / volume

Work done by fan = KE of air = 1/2 mv2

power = workdone / time, where your time is 1s if you use the values given in the question
 
  • #4
so the volume flow rate is simply the avg velocity times the cross sectional area. so volume flow rate is 1 x 7 = 7m^3 / second right?? which then allows us to calculate mass flow rate as you said which is density times the volume flow rate which is 1.2 x 7 = 8.4 kg/second. So the kinetic energy in one second becomes 0.5 x 8.4 x 7^2 = 205.8 Watts. ? that right?
 
  • #5
A more precise way to say it is that the kinetic energy in one second is 206 Joules, so the estimate for the average power is 206 Watts. I agree with your value.

It is a minimum because we are assuming for the problem that 100% of the electrical power consumption goes into the mechanical work of moving the air at that flow rate. The actual value would be larger because the efficiency of energy transfer will not be perfect.
 
  • #6
okay thankyou very much for your help
 

FAQ: Power Consumption Homework: Find Equations

What is power consumption and why is it important?

Power consumption refers to the amount of energy used by an electronic device or system. It is important because it impacts our environment and our wallets. The more energy a device consumes, the more it contributes to air pollution and climate change. Additionally, higher power consumption means higher electricity bills for consumers.

What are the factors that affect power consumption?

There are several factors that can affect power consumption, including the type of device, its components, and its usage. Devices with larger and more powerful components tend to consume more energy. Additionally, the way a device is used, such as the brightness settings on a computer screen or the number of applications running, can also impact power consumption.

How is power consumption calculated?

Power consumption is typically calculated using the equation P = VI, where P is power in watts, V is voltage in volts, and I is current in amps. This equation is known as Ohm's law and can be used to calculate power for both DC and AC circuits.

How can power consumption be reduced?

There are several ways to reduce power consumption, including using energy-efficient devices, turning off or unplugging devices when not in use, and adjusting settings to reduce energy usage. Another way to reduce power consumption is to switch to renewable energy sources, such as solar or wind power.

Are there any regulations or standards for power consumption?

Yes, there are regulations and standards in place to control power consumption and promote energy efficiency. In the United States, the Energy Policy Act of 2005 sets minimum efficiency standards for certain electronic devices. Additionally, organizations such as ENERGY STAR provide energy efficiency ratings for products to help consumers make more informed purchasing decisions.

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