CE 2200 : Example For Buckingham Pi Theory
Document Summary
Example: drag force of sphere q problem: suppose there is a flow with velocity u passing around a sphere, shown below. F on the flow from the view of dimensional analysis. Fluid variables: n density : [ml 3] n dynamic viscosity : [ml 1t 1] n fluid velocity u: [lt 1] Sphere: n sphere size d: [l] n sphere drag f: [mlt 2] Gravitational effect can be neglected since the free surface effect is not important in this problem. The above list involves 5 variables and can be written as. Step-2: the 5 variables involves 3 basic dimensions, [m], [l] and. Thus, we have 5 3 = 2 independent dimensionless variables (or 2 s. Step-3: let us choose , u and d as repeating variables (note that the repeating variables must involve the 3 basic dimensions). Then according to the theorem, we have. 2 q !+ 1 = 0 q 3! T q !+ 1 = 0 q 3!
