GATE Civil Engineering
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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

$$u= - \frac{h^2}{8 \mu} \: \frac{dp}{dx} \bigg[1-4 \bigg( \frac{y}{h} \bigg) ^2 \bigg]$$

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 $\mu$ is the dynamic viscosity term. The maximum and average velocities are, respectively

  1. $u_{max} = - \dfrac{h^2}{8 \mu} \: \dfrac{dp}{dx} \text{ and } u_{average} = \dfrac{2}{3} u_{max} \\$
  2. $u_{max} = \dfrac{h^2}{8 \mu} \: \dfrac{dp}{dx} \text{ and } u_{average} = \dfrac{2}{3} u_{max} \\$
  3. $u_{max} = - \dfrac{h^2}{8 \mu} \: \dfrac{dp}{dx} \text{ and } u_{average} = \dfrac{3}{8} u_{max} \\$
  4. $u_{max} = \dfrac{h^2}{8 \mu} \: \dfrac{dp}{dx} \text{ and } u_{average} = \dfrac{3}{8} u_{max}$
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