240 The UMAP Journal 23.3(2002) The largest particle of water that we want to contain is the size of average drop of water 0.05 mL. The column of water breaks into smaller particles at the peak of its ascent, and they descend individually. We estimate that particles smaller than that size would be acceptable to bystanders hit by them. Any larger particle would have more mass, hence a lower mass-to- surface-area ratio, so the pressure could not push it as far. Water drop behaves as a rigid body. Since a drop is small, internal currents have very little effect. Additionally, the pressure acts over the entire surface area of the drop and should accelerate it as a single body Model Design Effects of Buildings on wind velocit Because buildings surround the fountain the wind velocity at the anemome- ter on top of a building is different from that at fountain level. Buildings disrupt wind currents, slow the wind, and change its direction [Liu 1991, 62]. Buildings create areas of increased turbulence, as well as a wake--an area of decreased pressure--behind the building. Thus, the behavior of wind after it passes a building is so complex as to be almost impossible to model. Hence, we assume that the fountain is located outside of the wakes of the buildings Wind speed reduction The wind inside a group of buildings is less than that outside of the group the interaction between the wind and the buildings causes a decrease in speed The drag between the building and the wind decreases the kinetic energy of the wind and hence its speed Since the fountain is squirting water into the air in a symmetrical shape, the wind affects where the water lands in the same way regardless of the winds direction; so there is no need to find the wind direction after it hits the building rag Nevertheless, wind direction before the wind hits the building is an impor- tant factor. The angle at which the wind hits the building changes the surface area that the wind interacts with and drag changes with area. The drag force Fd Is given Fd where p is the density of air, Ubh is the speed of wind at height h, Cd is the drag coefficient, and A is the surface area interacting with the wind. Therefore, we
240 The UMAP Journal 23.3 (2002) • The largest particle of water that we want to contain is the size of average drop of water 0.05 mL. The column of water breaks into smaller particles at the peak of its ascent, and they descend individually. We estimate that particles smaller than that size would be acceptable to bystanders hit by them. Any larger particle would have more mass, hence a lower mass-tosurface-area ratio, so the pressure could not push it as far. • Water drop behaves as a rigid body. Since a drop is small, internal currents have very little effect. Additionally, the pressure acts over the entire surface area of the drop and should accelerate it as a single body. Model Design Effects of Buildings on Wind Velocity Because buildings surround the fountain, the wind velocity at the anemometer on top of a building is different from that at fountain level. Buildings disrupt wind currents, slow the wind, and change its direction [Liu 1991, 62]. Buildings create areas of increased turbulence, as well as a wake—an area of decreased pressure—behind the building. Thus, the behavior of wind after it passes a building is so complex as to be almost impossible to model. Hence, we assume that the fountain is located outside of the wakes of the buildings. Wind Speed Reduction The wind inside a group of buildings is less than that outside of the group; the interaction between the wind and the buildings causes a decrease in speed. The drag between the building and the wind decreases the kinetic energy of the wind and hence its speed. Since the fountain is squirting water into the air in a symmetrical shape, the wind affects where the water lands in the same way regardless of the wind’s direction; so there is no need to find the wind direction after it hits the building. Drag Nevertheless, wind direction before the wind hits the building is an important factor. The angle at which the wind hits the building changes the surface area that the wind interacts with, and drag changes with area. The drag force Fd is given by Fd = 1 2 ρv2 bhCdA, where ρ is the density of air, vbh is the speed of wind at height h, Cd is the drag coefficient, and A is the surface area interacting with the wind. Therefore, we
Wind and Waterspray 241 must know from which angle the wind approaches the building and how this affects the surface area perpendicular to the direction of the wind For a rectangular building with the narrow face to the wind, Cd MAcdonald 1975, 80] Figure 2 diagrams the plaza and fountain. No matter which way the wind blows, it interacts with a narrow edge of a building Wind from due east or west create a problem for this model, because of discontinuity in the the drag coefficient. Instead, we assume that the coefficient remains constant Figure 2. The plaza. Wind Speed at Differing Heights The speed of wind changes with the height from the ground because there is an additional force on the wind due to surface friction(dependent on the surface characteristics of the ground). The effect of this friction decreases the wind speed is measured from a greater distance to the ground creating faster speeds at greater heights Wind speed also varies because the temperature varies with heigh location. However, if we assume that temperature and ground roughness are constant, a mean speed at a certain height can be modeled by bh=Uz2 MAcdonald 1975, 47, where Ubh is the speed of the wind before it hits the building, Uz is the wind measure ed by the anemometer at the height z of the building, h is the
Wind and Waterspray 241 must know from which angle the wind approaches the building and how this affects the surface area perpendicular to the direction of the wind. For a rectangular building with the narrow face to the wind, Cd = 1.4 [Macdonald 1975, 80]. Figure 2 diagrams the plaza and fountain. No matter which way the wind blows, it interacts with a narrow edge of a building. Wind from due east or west create a problem for this model, because of discontinuity in the the drag coefficient. Instead, we assume that the coefficient remains constant. Figure 2. The plaza. Wind Speed at Differing Heights The speed of wind changes with the height from the ground because there is an additional force on the wind due to surface friction (dependent on the surface characteristics of the ground). The effect of this friction decreases as the wind speed is measured from a greater distance to the ground, creating faster speeds at greater heights. Wind speed also varies because the temperature varies with height and location. However, if we assume that temperature and ground roughness are constant, a mean speed at a certain height can be modeled by vbh = vz h z α [Macdonald 1975, 47], (1) where vbh is the speed of the wind before it hits the building, vz is the wind speed measured by the anemometer at the height z of the building, h is the