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Selling more gas

The owner of a gas station near a highway uses a colourful, smooth sphere with diameter 5 m and mounted on a high post, as a means of advertising.
a) Compute the drag force on the sphere when the wind blows at i) 10 km/h and ii) 100 km/h. Use an air density of 1.2 kg/m3 and a kinematic viscosity of 15×10-6 m2/s.
b) After some time, the sphere surface becomes rough due to the accumulation of bird droppings. Would the drag increase or decrease for the above wind speeds?
c) A new owner of the gas station replaces the sphere by a cube of the same approximate size. Would roughness increase or decrease the drag on the cube at the above wind speeds?
d) For an extra effect, a third owner puts back the sphere in question (a) but, this time, attached to a motor so that it rotates horizontally at an angular velocity of 60 rpm. Find the total wind force on the sphere at a wind speed of 50 km/h.


Contributed by Stavros Tavoularis, Department of Mechanical Engineering, University of Ottawa, Ottawa, Canada.

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