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.
1 answer:
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Answer:
48.7 J
Explanation:
For a mass-spring system, there is a continuous conversion of energy between elastic potential energy and kinetic energy.
In particular:
- The elastic potential energy is maximum when the system is at its maximum displacement
- The kinetic energy is maximum when the system passes through the equilibrium position
Therefore, the maximum kinetic energy of the system is given by:
where
m is the mass
v is the speed at equilibrium position
In this problem:
m = 3.6 kg
v = 5.2 m/s
Therefore, the maximum kinetic energy is:
