Minimum Power Needed to Accelerate Air from Rest to 15 m/s

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Homework Help Overview

The problem involves determining the minimum power required to accelerate a volume of air from rest to a specified velocity. The context is within fluid dynamics, specifically focusing on the mechanics of airflow and power calculations related to a fan system.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between force, momentum, and power, with some suggesting the use of density to convert volume to mass. There are inquiries about the necessity of acceleration in the calculations and the correct formulation of power in relation to force and velocity.

Discussion Status

The discussion is ongoing, with participants exploring various aspects of the problem. Some have provided hints regarding momentum and force, while others express confusion about the need for acceleration and how to calculate it. There is no explicit consensus yet, but guidance has been offered regarding the use of momentum.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may limit the information they can access or the methods they can use. There is a focus on understanding the underlying principles rather than arriving at a final answer.

arpsachin2
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Homework Statement



A fan accelerates 2 m^3/min of air from rest to a velocity of 15 m/s. If the density of air is 1.25 kg/m^3, determine the minimum power that must be supplied to the fan?

Homework Equations





The Attempt at a Solution



Need some hints or something.
 
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welcome to pf!

hi arpsachin2! welcome to pf! :smile:

(try using the X2 icon just above the Reply box :wink:)

hint: momentum :wink:
 
Thank you.

Okay a bit more I guess. :(
 
You can convert the volume of air to mass using density.
 
(just got up :zzz: …)

force = rate of change of momentum

power = force times … ? :wink:
 
Power = force * velocity

Am I heading the right way?Fan accelerates at 2m^3/60 secs to 15 m/s

And density is 1.25kg/m^3.

So is it Power = 1.25kg/m^3 * Acceleration?

How do I get the acceleration?
 
hi arpsachin2! :smile:
arpsachin2 said:
Power = force * velocity

Am I heading the right way?

yes :smile:
Fan accelerates at 2m^3/60 secs to 15 m/s

And density is 1.25kg/m^3.

So is it Power = 1.25kg/m^3 * Acceleration?

and now you've totally lost me! :confused:

you don't need the acceleration!

you only need the force, and you can get that from the change in momentum :smile:
 
if possible could you show me an example or something?

Thanks
 
tiny-tim said:
hi arpsachin2! :smile:


yes :smile:


and now you've totally lost me! :confused:

you don't need the acceleration!

you only need the force, and you can get that from the change in momentum :smile:

Hey,

would it be possible to chat on Gmail or yahoo or something?
Please
 
  • #10
tiny-tim said:
hi arpsachin2! :smile:


yes :smile:


and now you've totally lost me! :confused:

you don't need the acceleration!

you only need the force, and you can get that from the change in momentum :smile:

So change in momentum is

Final momentum - Initial Momentum right

So, would it be 15 m/s - xxxx?
 
  • #11
hi arpsachin2! :smile:

(just got up :zzz: …)
arpsachin2 said:
So change in momentum is

Final momentum - Initial Momentum right

So, would it be 15 m/s - xxxx?

15 m/s is a speed, you need a momentum (= mass times speed), in kg m/s,

and then you need a rate of change of momentum, in kg m/s2
 

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