4. A factory chimney is a long cylinder of diameter 0.4m. When a steady wind blows...

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4. A factory chimney is a long cylinder of diameter 0.4m. When a steady wind blows past the cylinder it is known that vortices can develop on the downwind side and shed with a regular frequency (. Since this can cause harmful periodic forces on the chimney, it is important to determine the shedding frequency. To determine the shedding frequency for a wind speed of V = 50 km/h, a 20 mm model is tested in a water flow tank. The other important parameters are the density and viscosity which are: = 1.8x105 kgm s and p = 1.2 kgm for air and = 1.0x10 kgms and p = 1000 kgm for water. a) Using the Buckingham Pi approach, show that the two dimensionless parameters describing this problem are VD/p and >> D/V. [15 Marks] b) Find the speed of water required in the flow tank to ensure dynamic similarity [5 Marks] c) If the shedding frequency of the model is found to by 50 Hz, find the corresponding frequency for the chimney. [5 Marks] 4. A factory chimney is a long cylinder of diameter 0.4m. When a steady wind blows past the cylinder it is known that vortices can develop on the downwind side and shed with a regular frequency (. Since this can cause harmful periodic forces on the chimney, it is important to determine the shedding frequency. To determine the shedding frequency for a wind speed of V = 50 km/h, a 20 mm model is tested in a water flow tank. The other important parameters are the density and viscosity which are: = 1.8x105 kgm s and p = 1.2 kgm for air and = 1.0x10 kgms and p = 1000 kgm for water. a) Using the Buckingham Pi approach, show that the two dimensionless parameters describing this problem are VD/p and >> D/V. [15 Marks] b) Find the speed of water required in the flow tank to ensure dynamic similarity [5 Marks] c) If the shedding frequency of the model is found to by 50 Hz, find the corresponding frequency for the chimney. [5 Marks]

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This question deals with dimensional analysis using the Buckingham Pi theorem finding a dynamic similarity condition and scaling a frequency from a model to a prototype Lets tackle each part one at a ... View the full answer