velocity of air just under ceiling fan...

Replies

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  Voltaire

  Starting with a simple square wooden paddle turned at angle q and rotating around an axis in the horizontal plane. The paddle will present a frontal area (in the horizontal plane) which is a simple geometric function of the area of the paddle and the angle q.
  
  It is obvious then that the paddle will displace this volume every revolution. But remember: the velocity of the air is a function of radius (tangential velocity) and hence it will change at different points on the length of the blade. I would have put some formulas here but I do not know how to do that 😕
• 

  vvishwaskumar

  Voltaire

  Starting with a simple square wooden paddle turned at angle q and rotating around an axis in the horizontal plane. The paddle will present a frontal area (in the horizontal plane) which is a simple geometric function of the area of the paddle and the angle q.
  
  It is obvious then that the paddle will displace this volume every revolution. But remember: the velocity of the air is a function of radius (tangential velocity) and hence it will change at different points on the length of the blade. I would have put some formulas here but I do not know how to do that 😕

  thanks Voltaire
  would u elaborate this clearly using some formulas...or through some derivation..!
• 

  Voltaire

  Ok. I don't know how to (if) formulas can be posted and even to post the letter p takes time and some knowledge.
  Consider a perfectly frictionless paddle with dimensions 0.1m x 0.1m moving at velocity v in a straight line and angled at angle q with the vertical. The frontal or effective area of the paddle is then A[sub]e[/sub] = l x b = 0.1m x 0.1m x cos(q). We can say that the volume of air displaced per second is the effective area multiplied by its velocity i.e. A[sub]e[/sub] x v = Q.
  
  In a rotating paddle the angular velocity is also dependent on the radius i.e. how far from the centre so that the velocity depends on where you measure it. If you measure near the tip then the air velocity would be higher that near the centre since v[sub]c[/sub] = r x w. To calculate the total air flow you should end up with an integral with respect to dr.
• 

  Voltaire

  Right; so I did some searching and found out that there is no real life calculation. Eddies and floor effects affect internal recirculation and even precise CFD simulations came up with the wrong answers (see Modeling of Ceiling Fan Based on Velocity Measurement for CFD Simulation of Airflow in Large Room, Y. Momoi, K. Sagara, T. Yamanaka and H. Kotani). There are some correlations though between power spectrum density and frequency/volume curve. Although these are interesting it does not provide a definite and conclusive answer; merely a relationship between a probability and a ratio - if my understanding is correct.
  
  It is nevertheless a good question 2 stars
• 

  gohm

  And also a good discussion and answer session as well!