Project ForgeFor the laminar flow of water over a sphere, the drag coefficient CF is defined as CF=F/(ρU²D²), where F is the drag force, ρ is the fluid density, U is the fluid velocity and D is the diameter of the sphere. The density of water is 1000 kg/m³. When the diameter of the sphere is 100 mm and the fluid velocity is 2 m/s, the drag coefficient is 0.5. If water now flows over another sphere of diameter 200 mm under dynamically similar conditions, the drag force (in N) on this sphere is __________.
Explanation
Dynamic similarity requires equal Reynolds number: U1D1 = U2D2 → U2 = U1×D1/D2 = 2×100/200 = 1 m/s. Since CF depends only on Re, it stays 0.5. F2 = CF·ρ·U2²·D2² = 0.5×1000×1²×0.2² = 20 N.
Source: GATE ME 2017 Session 2 (ME-2) (2017)
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