Final answer:
The correct relationship among displacement thickness, momentum thickness, and energy thickness in fluid dynamics is e > m > d, indicating that energy thickness is the greatest, followed by momentum thickness, and then displacement thickness.
Step-by-step explanation:
The correct relationship among displacement thickness (d), momentum thickness (m), and energy thickness (e) is directly related to the boundary layer concept in fluid dynamics. When considering a flow over a surface, the displacement thickness represents the distance by which the free stream is 'displaced' outwards due to the slower moving fluid near the surface. The momentum thickness is a measure of the loss of momentum in the boundary layer compared to the free stream, while the energy thickness represents the loss in kinetic energy in the boundary layer compared to the free stream.
The correct relationship is e > m > d, which signifies that the energy thickness is greater than the momentum thickness, which is in turn greater than the displacement thickness. This is due to the fact that even small differences in velocity near the surface can lead to large energy losses due to the nonlinear relationship between velocity and kinetic energy.