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 ${\rm{U}} = {\rm{\;}} - \frac{{{{\rm{h}}^2}}}{{8{\rm{\mu }}}}\frac{{{\rm{dp}}}}{{{\rm{dx}}}}\left[ {1 - 4{{\left( {\frac{{\rm{y}}}{{\rm{h}}}} \right)}^2}} \right]$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

Question

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 ${\rm{U}} = {\rm{\;}} - \frac{{{{\rm{h}}^2}}}{{8{\rm{\mu }}}}\frac{{{\rm{dp}}}}{{{\rm{dx}}}}\left[ {1 - 4{{\left( {\frac{{\rm{y}}}{{\rm{h}}}} \right)}^2}} \right]$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

TuteeHUB · Accepted Answer

$ {{\rm{U}}_{{\rm{max}}}} = \frac{{{{\rm{h}}^2}}}{{8{\rm{\mu }}}}\frac{{{\rm{dp}}}}{{{\rm{dx}}}}$and ${{\rm{U}}_{{\rm{avg}}}} = \frac{2}{3}{{\rm{U}}_{{\rm{max}}}}$

TuteeHUB · Answer

${{\rm{U}}_{{\rm{max}}}} = {\rm{\;}} - \frac{{{{\rm{h}}^2}}}{{8{\rm{\mu }}}}\frac{{{\rm{dp}}}}{{{\rm{dx}}}}$and ${{\rm{U}}_{{\rm{avg}}}} = \frac{2}{3}{{\rm{U}}_{{\rm{max}}}}$

TuteeHUB · Answer

${{\rm{U}}_{{\rm{max}}}} = {\rm{\;}} - \frac{{{{\rm{h}}^2}}}{{8{\rm{\mu }}}}\frac{{{\rm{dp}}}}{{{\rm{dx}}}}$and ${{\rm{U}}_{{\rm{avg}}}} = \frac{3}{8}{{\rm{U}}_{{\rm{max}}}}$

TuteeHUB · Answer

$ {{\rm{U}}_{{\rm{max}}}} = \frac{{{{\rm{h}}^2}}}{{8{\rm{\mu }}}}\frac{{{\rm{dp}}}}{{{\rm{dx}}}}$and ${{\rm{U}}_{{\rm{avg}}}} = \frac{3}{8}{{\rm{U}}_{{\rm{max}}}}$

1.	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 \({\rm{U}} = {\rm{\;}} - \frac{{{{\rm{h}}^2}}}{{8{\rm{\mu }}}}\frac{{{\rm{dp}}}}{{{\rm{dx}}}}\left[ {1 - 4{{\left( {\frac{{\rm{y}}}{{\rm{h}}}} \right)}^2}} \right]\)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
A.	\({{\rm{U}}_{{\rm{max}}}} = {\rm{\;}} - \frac{{{{\rm{h}}^2}}}{{8{\rm{\mu }}}}\frac{{{\rm{dp}}}}{{{\rm{dx}}}}\)and \({{\rm{U}}_{{\rm{avg}}}} = \frac{2}{3}{{\rm{U}}_{{\rm{max}}}}\)
B.	\( {{\rm{U}}_{{\rm{max}}}} = \frac{{{{\rm{h}}^2}}}{{8{\rm{\mu }}}}\frac{{{\rm{dp}}}}{{{\rm{dx}}}}\)and \({{\rm{U}}_{{\rm{avg}}}} = \frac{2}{3}{{\rm{U}}_{{\rm{max}}}}\)
C.	\({{\rm{U}}_{{\rm{max}}}} = {\rm{\;}} - \frac{{{{\rm{h}}^2}}}{{8{\rm{\mu }}}}\frac{{{\rm{dp}}}}{{{\rm{dx}}}}\)and \({{\rm{U}}_{{\rm{avg}}}} = \frac{3}{8}{{\rm{U}}_{{\rm{max}}}}\)
D.	\( {{\rm{U}}_{{\rm{max}}}} = \frac{{{{\rm{h}}^2}}}{{8{\rm{\mu }}}}\frac{{{\rm{dp}}}}{{{\rm{dx}}}}\)and \({{\rm{U}}_{{\rm{avg}}}} = \frac{3}{8}{{\rm{U}}_{{\rm{max}}}}\)
Answer» B. \( {{\rm{U}}_{{\rm{max}}}} = \frac{{{{\rm{h}}^2}}}{{8{\rm{\mu }}}}\frac{{{\rm{dp}}}}{{{\rm{dx}}}}\)and \({{\rm{U}}_{{\rm{avg}}}} = \frac{2}{3}{{\rm{U}}_{{\rm{max}}}}\)

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