Final answer:
The student's question concerns the verification of a given velocity profile as an exact solution to the boundary layer equations in fluid dynamics, focusing on a laminar flow between two plates. To show this, the given profiles must be substituted into the equations, implying meeting certain boundary conditions like Couette flow. The constant C can be determined from the viscosity of the fluid.
Step-by-step explanation:
The question relates to verifying whether a given two-dimensional laminar flow pattern is an exact solution to the boundary layer equations. To confirm this, one must insert the given velocity profiles into the boundary layer equations and show that they're satisfied.
Assuming the pressure gradient dp/dx is zero, the momentum conservation equation in the x-direction simplifies and must be checked against the given u-velocity profile u = U*(1 - e^(C*y)). Since v = V and we're told V = 0, the continuity equation is also satisfied.
By performing the differentiation and substitution steps of u and v into the boundary layer equations, we find that C must be related to the flow's viscosity μ. The exact relationship depends on the problem's specifics, which are not fully provided.
This solution satisfies the boundary condition of having no slip at the bottom plate (u(0) = 0) and a constant velocity at the top plate when y tends to infinity, which is characteristic of a Couette flow.
This flow might represent a situation where a fluid is trapped between two plates and the top plate is dragged to the right, moving the fluid along with it, while the bottom plate remains stationary. This is a classical physics problem often discussed in fluid dynamics courses and illustrates how fluid viscosity contributes to generating velocity profiles.