Calculating mass of air from Speed and Density?

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Homework Help Overview

The discussion revolves around calculating the mass of air moved by a hovering helicopter based on the speed of air displacement and its density. Participants are exploring how to derive the mass per second of air and the rate of change in momentum associated with this air movement.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the need for the area of the helicopter blades to calculate the mass of air displaced. Some suggest calculating the volume of air based on the area and speed, while others question the specifics of the momentum change being referenced.

Discussion Status

The conversation is ongoing, with participants providing various interpretations and calculations related to the area of the blades and the volume of air displaced. There is no explicit consensus on the approach to take, but several lines of reasoning are being explored.

Contextual Notes

Some participants mention specific dimensions and areas related to the helicopter blades, while others express uncertainty about the details of the momentum change being asked. The density of air is provided as a constant factor in the calculations.

ntk_k
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For the hovering helicopter, it is assumed that all the air beneath the blades is pushed vertically downwards with the same speed of 4.0m/s. No other air is disturbed.

The density of air is 1.2kg m^-3

How can you calculate, for the air moved downwards by the rotating blades,

i) the mass per second
ii) the rate of change in momentum ??
 
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You can't unless you know the area of the blades. Do you?
 
The length of each blade of the helicopter is 0.70m. The area that the blades sweep out as they rotate is 1.5 m^2.
 
could you not just calculate the area of the cylinder? which would be an area of 6m^3. then find out the mass of the air in the 6m^3. I believe that would be the mass per second.

As for the change in momentum, I am unclear as to what the question is asking. Are you asking for the change in momentum of the helicopter? Or the change in momentum of the air?
 
in case of any ambiguity, the 6m^3 arises from 1.5m^2(area of the blades), multiplied by the metres of air displaced in one second.(4m)
 
ntk_k said:
For the hovering helicopter, it is assumed that all the air beneath the blades is pushed vertically downwards with the same speed of 4.0m/s. No other air is disturbed.

The density of air is 1.2kg m^-3

How can you calculate, for the air moved downwards by the rotating blades,

i) the mass per second
ii) the rate of change in momentum ??[i don't know]
 
ideasrule said:
You can't unless you know the area of the blades. Do you? the area = 85.9645m^2
 
kabwe said:
ideasrule said:
You can't unless you know the area of the blades. Do you? [yes area = 85.9645m^2]
 
the area = 85.9645m^2
 

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