A 30-story office building (each story is \(12 \mathrm{ft}\) tall) is built in a suburban industrial park. Plot the dynamic pressure, \(ho u^{2} / 2\), as a function of elevation if the wind blows at hurricane strength \((75 \mathrm{mph})\) at the top of the building. Use the atmospheric boundary layer information of Problem 9.21.

Problem 9.21

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