Ratio Maximum Velocity To Average Velocity

Ratio Maximum Velocity To Average Velocity Assignment Help | Ratio Maximum Velocity To Average Velocity Homework Help

Ratio of Maximum Velocity to Average Velocity

The velocity will be maximum to y = ½.

Umax  = - 1/2μ ∂p / ∂x [ t x t / 2 - (t / 2)2] = - 1/2μ ∂p / ∂x [ t2 / 2 - t2 / 4 ]

Umax  =  - 1/ 8μ ∂p / ∂x t2

Average velocity      u  =  Q/A

dQ  = Velocity at a distance y x Area of strip

= - 1/2μ ∂p / ∂x  [ ty - y2 ] x dy x 1

Integrating from 0 to t

       t          t
Q = ∫ dQ = ∫ - 1/2μ ∂p / ∂x [ ty - y2 ]  dy x 1
      0         0

Q  = - 1/2μ ∂p / ∂x [ t ( y2 / 2)0t - (y3 / 3)01 ] = - 1/2μ ∂p / ∂x  [ t3 / 2 - t3 / 3 ]

Q = - 1/2μ ∂p / ∂x t3 / 6

Q = - 1/ 12μ ∂p / ∂x t3

u  = Q / A = - 1/12μ . ∂p / ∂x . t3 / t x 1

u = - 1/ 12μ ∂p / ∂x t2

Ratio Umax to u

Umax  = - 1 / 8μ (∂p / ∂x) t2 / 1/ 12μ ∂p / ∂x t2
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u

Umax  = 3 / 2
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u

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