Which term describes a flow profile with a parabolic velocity distribution?

• A. Laminar flow profile
• B. Parabolic flow profile
• C. Plug flow profile
• D. Spectral broadening flow profile

Answer: (B)

In fully developed laminar flow through a circular tube, the velocity distribution across the cross-section takes a parabolic shape because of viscous effects and the no-slip condition at the wall. Viscosity slows the fluid as you move toward the wall, so the velocity goes to zero at the boundary, while at the center it’s unimpeded and reaches a maximum. Mathematically, the velocity profile is described by u(r) = Umax[1 − (r/R)²], a parabola when you plot velocity versus radial position. This precise parabolic form is what defines a parabolic flow profile.

Other descriptors are too general or describe different profiles: a general laminar flow profile doesn’t specify its shape; plug flow implies a nearly uniform velocity across the cross-section, not parabolic; and spectral broadening flow profile isn’t a standard term for velocity distributions in this context.