How to calculate dean number and wommerslay number for blood
Answers
Answer:
The Dean number is typically denoted by De (or Dn). For a flow in a pipe or tube it is defined as:
{\displaystyle {\mathit {De}}={\frac {\sqrt {({\text{centripetal forces}})({\text{inertial forces}})}}{\text{viscous forces}}}={\frac {\sqrt {(\rho \,{\frac {r}{d}}{\frac {v^{2}}{(r/d)^{2}}})(\rho \,v^{2})}}{\mu {\frac {v}{d}}}}={\sqrt {\frac {d}{2r}}}{\frac {\rho v\!d}{\mu }}={\sqrt {\frac {d}{2r}}}{\textit {Re}}}
where
\rho is the density of the fluid
\mu is the dynamic viscosity
v is the axial velocity scale
d is the diameter (for non-circular geometry, an equivalent diameter is used; see Reynolds number)
r is the radius of curvature of the path of the channel.
{\displaystyle {\textit {Re}}} is the Reynolds number.
The Dean number is therefore the product of the Reynolds number (based on axial flow v through a pipe of diameter d) and the square root of the curvature ratio.