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 = −\frac{h^{2}}{8\mu }\frac{dp}{dx} [1−4 (\frac{y}{h}) ^{2}] 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

Correct Answer is : Umax=−h28µdpdx and Uavg=23Umax

U_{\max} = −\frac{h^{2}}{8\mu }\frac{dp}{dx} and U_{avg} = \frac{2}{3}U_{\max}

U_{\max} = \frac{h^{2}}{8\mu }\frac{dp}{dx} and U_{avg} = \frac{2}{3}U_{\max}

U_{\max} = −\frac{h^{2}}{8\mu }\frac{dp}{dx} and U_{avg} = \frac{3}{8}U_{\max}

U_{\max} = \frac{h^{2}}{8\mu }\frac{dp}{dx} and U_{avg} = \frac{3}{8}U_{\max}

GATE Civil Engineering (CE) 2014 Shift 2 Solved Paper

Question : 55 of 65

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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 = −\;{h^{2}}/{8µ\;}\;{dp}/{dx} [1−4 (\;{y}/{h}) ^{2}]

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

$U_{max} = −\;{h^{2}}/{8µ\;}\;{dp}/{dx}$ and $U_{avg} = \;{2}/{3}U_{max}$
$U_{max} = \;{h^{2}}/{8µ\;}\;{dp}/{dx}$ and $U_{avg} = \;{2}/{3}U_{max}$
$U_{max} = −\;{h^{2}}/{8µ\;}\;{dp}/{dx}$ and $U_{avg} = \;{3}/{8}U_{max}$
$U_{max} = \;{h^{2}}/{8µ\;}\;{dp}/{dx}$ and $U_{avg} = \;{3}/{8}U_{max}$

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