How Do You Calculate the Energy Conversion Efficiency of a Blower-Nozzle System?

[mgibson]

Homework Statement

The problem asks to find the energy conversion efficiency of a blower-nozzle combination that produces a velocity of 30m/s for air with a density of 1.1kg/mcubed. The nozzle has a diameter of .15m

input power is 1 hp

Homework Equations

given the flow rate = (density)(Area)(velocity)

The Attempt at a Solution

I know how to find the efficiency but do not know how to convert flow rate in (kg/s) to Power units in order to use (power out/power in) formula

Thanks for your help!

 

[Redbelly98]

Can you figure out the volume of air that exits the nozzle in 1 second?

And from that, can you use the velocity, and mass of that volume, to get it's kinetic energy?

 

[Mene]

I would suggest using the following equation to convert flow rate in kg/s to power units:

Power = (flow rate) x (density) x (velocity) x (cross-sectional area)

This equation takes into account the mass flow rate, density, and velocity of the air, as well as the cross-sectional area of the nozzle. By plugging in the given values, you can find the power output of the blower-nozzle combination.

Once you have the power output, you can use the formula for energy conversion efficiency (power output/power input) to find the efficiency of the blower-nozzle combination. Keep in mind that the power input in this case is 1 hp, which you may need to convert to units of watts before using in the efficiency formula.

I hope this helps you solve the problem. Don't hesitate to reach out if you have any further questions.

 

[Mene]

To convert the flow rate from kg/s to power units, you can use the equation P = m dot * V, where P is power, m dot is mass flow rate, and V is velocity. First, you need to calculate the mass flow rate by multiplying the density (1.1 kg/m^3) by the area (πr^2, where r is the radius of the nozzle, which is 0.075m). This will give you a mass flow rate of approximately 0.0012 kg/s. Then, using the given velocity of 30m/s, you can calculate the power by multiplying the mass flow rate by the velocity, which gives you 0.036 watts. Finally, you can convert this to horsepower by dividing by 746, which gives you an input power of approximately 0.00005 hp.

Now, you can use the efficiency formula (power out/power in) to find the energy conversion efficiency of the blower-nozzle combination. The power output is given in the problem as 1 hp, so the efficiency can be calculated as 1/0.00005 = 200,000%. This means that the blower-nozzle combination is very efficient in converting input power to output power.