An aluminum sphere (specific gravity 2.7) falling through water reaches a terminal speed of 3.1 cm/sWhat is the terminal speed of an air bubble of the same radius rising through water? Assume viscous drag in both cases and ignore the possibility of changes in size or shape of the air bubble; the temperature is 20°C where air density is 1.20 kg/m3 and water density is 1001.80 kg/m3.
It has a high strength-to-weight ratioIt's the most abundant metal on Earth, so it's cheapIt's malleable so you can shape it however you want.
strong, light, conductivity, cheap, corrosion resistant but manly titanium is used
Weight of aluminium sphere(volume V) is: WA V x 2.7x1001.80 x 9.81 26534.6766V Weight of air bubble, WB (volume V) is: WB V x 1.20 x 9.81 11.772V Upthrust (buoyancy force) on both sphere and bubble: U weight of water displaced U V x 1001.80 x 9.81 9827.658V From Stoke' law, viscous drag D is proportional to speed, other factors being the same: For sphere with speed vA, drag force is DA kvA 0.031k For bubble with speed vB, drag force is DB kvB At terminal velocity the resultant force 0For the sphere falling: weight upthrust + drag force 26534.6766V 9827.658V + 0.031k k 16707.0186V/0.031 538936.0839V For the bubble rising : weight + drag force upthrust 11.772V + kvB 9827.658V Substituting for k 11.772V + 538936.0839VvB 9827.658V 11.772 + 538936.0839vB 9827.658 vB 9815.866/538936.0839 0.0178 m/s 1,8cm/s (Arithmetic not guaranteed!)
