Engineers are worried about the wind forces on a sculpture in Queen Mary campus. The sculpture has a height Ha = 5 m and a diameter, Da = 2 m, as shown in Figure Q3. The engineers decide to investigate by making a smaller scale model testing in a water tunnel. They need to match the Reynolds number and the aspect ratio, AR = H/D. The characteristic length scale in the Reynolds number can be the diameter. Water has a density and viscosity of pw = 1000 kg/m3 and μw = 1 mPa. s, while air has a density and viscosity of pa = 1.2 kg/m3 and ua = 18 x 10-6 Pa. s. The average wind speed by the sculpture is Ua = 6 m/s. 1. The maximum height of the model that the engineers can place in the water tunnel is 1.5 m. Find the diameter of the model needed.

Engineers are worried about the wind forces on a sculpture in Queen Mary campus. The sculpture has a height Ha = 5 m and a diameter, Da = 2 m, as shown in Figure Q3. The engineers decide to investigate by making a smaller scale model testing in a water tunnel. They need to match the Reynolds number and the aspect ratio, AR = H/D. The characteristic length scale in the Reynolds number can be the diameter. Water has a density and viscosity of pw = 1000 kg/m3 and μw = 1 mPa. s, while air has a density and viscosity of pa = 1.2 kg/m3 and ua = 18 x 10-6 Pa. s. The average wind speed by the sculpture is Ua = 6 m/s. 1. The maximum height of the model that the engineers can place in the water tunnel is 1.5 m. Find the diameter of the model needed.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

Engineers are worried about the wind forces on a sculpture in Queen Mary campus. The sculpture has
a height Ha = 5 m and a diameter, Da = 2 m, as shown in Figure Q3.
The engineers decide to investigate making a smaller scale model testing in a water tunnel. They
need to match the Reynolds number and the aspect ratio, AR = H/D. The characteristic length scale in
the Reynolds number can be the diameter.
Water has a density and viscosity of pw = 1000 kg/m3 and μw = 1 mPa. s, while air has a density and
viscosity of pa = 1.2 kg/m3 and μa = 18 x 10-6 Pa. s. The average wind speed by the sculpture is Ua = 6
m/s.
1. The maximum height of the model that the engineers can place in the water tunnel is 1.5 m. Find
the diameter of the model needed.
2. Find the average speed of water needed for the experiments to match the average wind speed past
the sculpture.
3. It is known that at a wind speed of Ua = 4 m/s, the flow past the sculpture becomes turbulent. To
visualise the flow in the experiments, engineers place fluorescent beads in the water and use high
speed cameras to track their motion. When the water speed is Uw = 0.5 m/s, what do these
measurements reveal (e.g. (i) streamlines, (ii) pathlines, (iii) streaklines, (iv) all three)? Justify your
answer.
4. When the water speed is Uw = 1.3 m/s, what do these measurements reveal (e.g. (i) streamlines, (ii)
pathlines, (iii) streaklines, (iv) all three)? Justify your answer.
Da
H₂
a

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