When a viscous fluid flows parallel to a horizontal plate, it leads to the development of a thin boundary layer on the plate surface. The velocity within the boundary layer varies with the vertical direction as u(y) = Uwhere 8(x) = 3.5 / is the boundary layer thickness that increases with the horizontal position. Outside of the boundary layer, the flow is uniform and equal to the free stream velocity Uco. Show that for two fluids of different viscosities (₁, ₂) and densities (P₁, P2) and flowing at the same free stream velocity, the ratio of the drag force they generate on the plate is proportional to the square root of the ratio of the viscosities and densities: FD2 FD1 = H₂P₂ H₁P₁

When a viscous fluid flows parallel to a horizontal plate, it leads to the development of a thin boundary layer on the plate surface. The velocity within the boundary layer varies with the vertical direction as u(y) = Uwhere 8(x) = 3.5 / is the boundary layer thickness that increases with the horizontal position. Outside of the boundary layer, the flow is uniform and equal to the free stream velocity Uco. Show that for two fluids of different viscosities (₁, ₂) and densities (P₁, P2) and flowing at the same free stream velocity, the ratio of the drag force they generate on the plate is proportional to the square root of the ratio of the viscosities and densities: FD2 FD1 = H₂P₂ H₁P₁