# Slender body theory for plates? (hydrodynamics, Stokes flow regime)

A basic question on low Reynolds number hydrodynamics. When a slender beam is moved through a fluid, the dynamics may be calculated using slender body theory (e.g. Slender-body theory for slow viscous flow J. B. Keller and S. I. Rubinow, J. Fluid Mech. 1976; https://en.wikipedia.org/wiki/Slender-body_theory). In effect, it allows one to calculate drag coefficient on a material element of the beam and thus avoid having to solve for the dynamics of the fluid around the beam. Essentially, drag per unit length ends up being proportional to viscosity of the ambient fluid, and, obviously, the dimensions work out ( viscosity is in Pa*s, multiplied by velocity leaves N/m which is the required drag per unit length of the beam). My question is if one can do something similar for a 2D plate? It appears to not be possible, since, if nothing else, dimensions don't work out correctly. Is there a simple reason for why this approach fails for the case of a plate?

• If the thickness of the plate is small then we can assume it as a beam and apply the slender-body theory. No? Jan 22, 2022 at 9:02
• See, slender body theory assumes one dimension is much larger than the other two. For a plate, this is not the case. Jan 24, 2022 at 20:02