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 = - h²/(8μ) dp/dx [1 - 4(y/h

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
u = - h²/(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

Accepted Answer

(A) u_max = - h²/(8μ) dp/dx and u_average = 2/3 u_max. The maximum velocity, u_max, is correctly expressed as - h²/(8μ) dp/dx, reflecting the negative gradient of pressure in the flow direction, while the average velocity is derived from the parabolic profile, resulting in u_average being 2/3 of u_max.

Solution

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