A crude but useful approximation for an incompressible boundary layer is a cubic variation from u = 0 at the surface (y = δ) to
the freestream velocity, U, at the edge of the boundary layer (y = 0). The equation for the profile is u/U = 3/2(y/δ) – 1/2(y/δ)3, where δ = cx1/2 and c is a constant. Derive the simplest expression for v/U, the y component of velocity ratio. Determine the y/δ location for the maximum value of the ratio v/U. Determine v/U for y = 1 mm, δ = 5 mm and x = 0.87 m. Determine vmax/U for δ = 5 mm and x = 0.87 m.
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Answer:
- 1.07 ft
Explanation:
V1 = (-5, 7, 2)
V2 = (3, 1, 2)
Projection of v1 along v2, we use the following formula
=\frac{\overrightarrow{V1}.\overrightarrow{V2}}{V2}
So, the dot product of V1 and V2 is = - 5 (3) + 7 (1) + 2 (2) = -15 + 7 + 4 = -4
The magnitude of vector V2 is given by
=
So, the projection of V1 along V2 = - 4 / 3.74 = - 1.07 ft
Thus, the projection of V1 along V2 is - 1.07 ft.
so we need to find the direction of v2