With reference to a standard Cartesian (x, y) plane, the parabolic velocity distribution profile of fully developed laminar flow in x-direction between two parallel, stationary and identical plates that are separated by distance, h, is given by the expression
\({{U}} = {\rm{}} - \frac{{{{{h}}^2}}}{{8{{\mu }}}}\frac{{{{dp}}}}{{{{dx}}}}\left[ {1 - 4{{\left( {\frac{{{y}}}{{{h}}}} \right)}^2}} \right]\)
In this equation, the y = 0 axis lies equidistant between the plates at a distance h/2 from the two plates, p is the pressure variable and µ is the dynamic viscosity term. The maximum and average velocities are, respectively
1
\({{\rm{U}}_{{\rm{max}}}} = - \frac{{{{\rm{h}}^2}}}{{8{\rm{\mu }}}}\frac{{{\rm{dp}}}}{{{\rm{dx}}}}\) and \({{\rm{U}}_{{\rm{avg}}}} = \frac{2}{3}{{\rm{U}}_{{\rm{max}}}}\)
2
\( {{\rm{U}}_{{\rm{max}}}} = \frac{{{{\rm{h}}^2}}}{{8{\rm{\mu }}}}\frac{{{\rm{dp}}}}{{{\rm{dx}}}}\) and \({{\rm{U}}_{{\rm{avg}}}} = \frac{2}{3}{{\rm{U}}_{{\rm{max}}}}\)
3
\({{\rm{U}}_{{\rm{max}}}} = - \frac{{{{\rm{h}}^2}}}{{8{\rm{\mu }}}}\frac{{{\rm{dp}}}}{{{\rm{dx}}}}\) and \({{\rm{U}}_{{\rm{avg}}}} = \frac{3}{8}{{\rm{U}}_{{\rm{max}}}}\)
4
\( {{\rm{U}}_{{\rm{max}}}} = \frac{{{{\rm{h}}^2}}}{{8{\rm{\mu }}}}\frac{{{\rm{dp}}}}{{{\rm{dx}}}}\) and \({{\rm{U}}_{{\rm{avg}}}} = \frac{3}{8}{{\rm{U}}_{{\rm{max}}}}\)