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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 μa = 18 x 10-6 Pa.s. The average wind speed by the sculpture is Ua = 6 m/s. Ha D₂ a) 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. b) Find the average speed of water needed for the experiments to match the average wind speed past the sculpture. c) It is known that at a wind speed of U₁ = 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. d) 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.

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 μa = 18 x 10-6 Pa.s. The average wind speed by the sculpture is Ua = 6 m/s. Ha D₂ a) 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. b) Find the average speed of water needed for the experiments to match the average wind speed past the sculpture. c) It is known that at a wind speed of U₁ = 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. d) 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.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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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 μa 18 x 10-6 Pa. s. The average wind speed by the sculpture is U₁ = 6 m/s. = H₂ a Da a) 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. b) Find the average speed of water needed for the experiments to match the average wind speed past the sculpture. c) It is known that at a wind speed of U₁ = 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. = d) 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.
Transcribed Image Text: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 μa 18 x 10-6 Pa. s. The average wind speed by the sculpture is U₁ = 6 m/s. = H₂ a Da a) 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. b) Find the average speed of water needed for the experiments to match the average wind speed past the sculpture. c) It is known that at a wind speed of U₁ = 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. = d) 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.
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