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) = US where 8(x) = 3.5vX/U is the boundary layer thickness that increases with the 8(x) horizontal position. Outside of the boundary layer, the flow is uniform and equal to the free stream velocity U... Show that for two fluids of different viscosities (₁, 2) and densities (P₁, P2₂) 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

Elements Of Electromagnetics
7th Edition
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Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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Problem6
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
y
u(y) = U∞ (x) where 8(x) = 3.5 x/Uis 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 U...
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
Transcribed Image Text:Problem6 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 y u(y) = U∞ (x) where 8(x) = 3.5 x/Uis 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 U... 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
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