WoPhO 2012, Теория — Задача 3.4. Shall you open or close the windows?
Theoretical 3: Tornado
Внимание: Бележка към темата
The official solutions (Ver. 1.1, June 2012) label their sub-parts differently from the problem sheet: under [Q.2], (a) answers question 2(c), (b) answers 2(b), (c) answers 2(d) and (d) answers 2(e); under [Q.3], (a) answers question 2(a), and (b)–(e) answer 3(a)–3(d). The solutions are reproduced with their printed labels.
Условие
The differential pressure near a tornado is thought to cause poorly ventilated houses to “explode” even though the tornado is only passing at a distance. Therefore some people suggest that the windows have to be opened to vent or let the pressure in the house equilibrates with outside quickly. However, opening the windows will risk more damage due to debris and projectiles getting into the house.
Consider a house with all windows and openings closed with a flat roof of dimension (width x length x thickness) 15 m x 15 m x 0.1 m and mass density . The tornado is coming fast and passing at a distance away from the house.
(a) What is the ratio of the lift force on the roof compared to its weight? [0,8 т.]
(b) Shall you open or close the windows? [0,2 т.]
Отговори
(a) 3.6
Official solution [Q.4] (a), Eq. (27): .
(b) Close all the windows.
Official solution [Q.4] (b).
Решение
(a) We assume that the house is tightly enclosed maintaining the initial pressure at . When the tornado approaches at a distance from the house, the differential pressure will be (Eq. 19):
The lift force on the roof (relative to weight)
(b) The lift force is not much larger than the weight of the roof – and certainly most roof are mounted firmly to withstand forces multiple of its weight. So chances are the tornado pressure differential would not cause the house to explode so soon (unless the roof is very poorly mounted, or you are inside the tornado in which case this question becomes irrelevant).
Furthermore some residual opening in the house like ventilation and chimney will alleviate the pressure differential. However at a very close distance of . it is more likely the house get smashed with flying debris. Thus you would just close all the windows.
REFERENCES
[1] W.H. Hoecker, “Wind speed and air flow patterns in the Dallas tornado of April 2, 1957”, Mon. Wea. Rev. 88, 167-180.
Оригинал в Архива: WoPhO_2012_Q13.pdf · официални решения: WoPhO_2012_S13.pdf