Final answer:
The provided velocity profile indicates that the flow is attached to the solid surface because the velocity at the surface is zero and increases with height without reversing, which implies no flow separation and a healthy boundary layer.
Step-by-step explanation:
The student is asking about flow behavior in relation to a solid surface given a velocity profile equation, which is a topic in fluid dynamics, a subfield of engineering physics. According to the question, the velocity profile is given as u/U = 2(y/δ) - (y/δ)², where u is the fluid velocity at a distance y from the wall, U is the freestream velocity, and δ is the boundary layer thickness or a characteristic length.
To determine if the flow is attached to the solid surface, we observe that the velocity must be zero at the surface (y = 0), and should increase smoothly without any sign of reverse flow (negative velocity) as y increases. The provided velocity profile satisfies these conditions because for y=0, u=0, and the velocity increases with y without negative values, implying no flow separation. Thus, the flow is attached.