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(Solved): Boundary layer For a steady laminar flow over a flat plate, the velocity profile of the boundary lay ...



Boundary layer For a steady laminar flow over a flat plate, the velocity profile of the boundary layer is defined as

(u)/(U)={(sin((\pi y)/(2\delta (x))),y<=\delta (x)),(1,y>\delta (x)):}

When there exists two parallel plates with gap thickness

h

as shown below, the two boundary layers meet at a distance

x

away from

x=0

. Show that

x=10h

when

Re

based on gap thickness

h

is

80(\pi ^(2))/(5-\pi )

.[Hint:

\int sin(ax)dx=-(cos(ax))/(a)+

const.,

\int sin^(2)(ax)dx=

(x)/(2)-(sin(2ax))/(4a)+

const.]



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