An atmospheric boundary layer is formed when the wind blows over the Earth's surface. Typically, such velocity profiles can be written as a power law: \(u=a y^{n}\), where the constants \(a\) and \(n\) depend on the roughness of the terrain. As is indicated in Fig. P9.21, typical values are \(n=0.40\) for urban areas, \(n=0.28\) for woodland or suburban areas, and \(n=0.16\) for flat open country (Ref. 23).

(a) If the velocity is \(20 \mathrm{ft} / \mathrm{s}\) at the bottom of the sail on your boat \((y=4 \mathrm{ft}\) ), what is the velocity at the top of the mast \((y=\) \(30 \mathrm{ft}\) )?

(b) If the average velocity is \(10 \mathrm{mph}\) on the tenth floor of an urban building, what is the average velocity on the sixtieth floor?

Figure P9.21

Transcribed Image Text:

450 u - y0.40 - 1,0.28 E 300 150 0 u - y0.16