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ERIC Number: EJ892013
Record Type: Journal
Publication Date: 2007-Sep
Pages: 2
Abstractor: As Provided
Reference Count: 0
ISBN: N/A
ISSN: ISSN-0031-921X
Caught in the Draft
Edge, Ron
Physics Teacher, v45 n6 p338-339 Sep 2007
We've all seen (in movies, newscasts, or perhaps in person) the violent effect of the downwash that occurs when a helicopter hovers over the ground. Leaves, grass, and debris are dramatically blown about. We've also sat in front of circulating room fans and felt a large draft, whereas there seems to be very little air movement behind the fan. The cause of this is a delightful manifestation of Bernoulli's principle. The fan blades, or helicopter rotor blades, produce a pressure differential as air passes through them--let us say p[subscript 1] before and p[subscript 2] after, as shown in Fig. 1, with p[subscript 2] greater than p[subscript 1]. If p[subscript 0] is the ambient pressure, Bernoulli's equation gives p[subscript 0]=p[subscript 1]+(1/2)[rho]v[subscript 1][superscript 2] where v[subscript 1] is the velocity of the air entering the fan. Continuity requires that v[subscript 2] leaving the fan must equal v[subscript 1] entering the fan for an incompressible fluid, approximately true here (Av[subscript 1] = Av[subscript 2], where A is the area swept out by the blades, the "rotor disk area"). However, some distance below the rotor (or in front of the fan) the velocity is v[subscript d] (v[subscript downdraft] in the figure) and the pressure again p[subscript 0], so Bernoulli gives us p[subscript 2]+(1/2)[rho]v[[subscript 2][superscript 2]=(p[subscript 1]+[delta]p)+(1/2)[rho]v[[subscript 1][superscript 2]=[p[subscript 1]+(p[subscript 2]-p[subscript 1])]+(1/2)[rho]v[[subscript 1][superscript 2]=p[subscript 2]+(1/2)[rho]v[[subscript 1][superscript 2]=p[subscript 0]+(1/2)[rho]v[[subscript d][superscript 2].
American Association of Physics Teachers. One Physics Ellipse, College Park, MD 20740. Tel: 301-209-3300; Fax: 301-209-0845; e-mail: pubs@aapt.org; Web site: http://scitation.aip.org/tpt
Publication Type: Journal Articles; Reports - Descriptive
Education Level: N/A
Audience: N/A
Language: English