Final answer:
The two boundary conditions related to velocity for solving the velocity profile equation are the no-slip condition and constant viscosity. These conditions simplify the differential equations in fluid mechanics. (Option B).
Step-by-step explanation:
The two boundary conditions related to velocity that are used to solve the velocity profile equation are b) No-slip condition and constant viscosity. The no-slip condition implies that the fluid velocity relative to the boundary is zero (i.e., the fluid does not 'slip' over the surface). This is typically applied at solid boundaries where the fluid is in contact with a surface.
The assumption of constant viscosity leads to a velocity profile that is solely a function of the distance from the boundary and the pressure gradient, not the varying viscosity of the fluid.
The use of these boundary conditions makes the mathematics of solving fluid flow problems much simpler, as it provides concrete values or relationships at the boundaries, reducing the complexity of the differential equations governing the flow. This concept is key in the field of fluid mechanics, which is part of engineering studies.