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Dimensions and units of constant

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Reference no: EM132637399

A fluid flows between two stationary horizontal plates, 0.04 m apart, with its velocity described by a quartic (4th order) equation. (Note -- this is not Poiseuille flow.) V = A - Bη4 where η is distance [m] measured (up or down) from the centerline, and A and B are constants.

(a) What are the dimensions and units of constant B? Give your answer in both L-M-T-Θ dimensions and S.I. units.

(b) A = 2 m s-1; B = 1.25×107 [appropriate units]. Show that the no-slip condition is satisfied.

(c) Graph the velocity profile for the full 0.04 m of fluid thickness. (You may use Excel, Matlab, or a neat hand sketch.)

(d) Write the expression for shear stress in this flow.

(e) If the maximum shear stress in the fluid is 800 N m-2, what is the viscosity? (Hint: where does the maximum shear stress occur?)

(f) Calculate the shear stress on the lower wall, at 0.01 m from the lower wall, and at the centerline. (Note: τ is positive in the direction of flow.) Explain your steps.

Reference no: EM132637399

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