2.58 f the viscosity of the liquid is 10−3 𝑁 ∙ 𝑠/𝑚2 , what is the maximum shear stress in the liquid? b. Where will the minimum shear stress occur?
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(b) The flow of fluid satisfies the following law ̄̄ = ̄(du/dy)^1.3. The velocity distribution equation inside the fluid film is given by u/Umax = 2(y/h) - (1/3)(y/h)^3. Where h is the film thickness and Umax is the maximum velocity. The viscosity is 0.5 N.s/m^2. Calculate (i) The shear stress at the solid surface when Umax = 0.2 m/s and h = 1 cm. (ii) Estimate the viscosity of a Newtonian fluid to induce the same shear stress for the same velocity profile and the same maximum velocity.
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A fluid with a viscosity of $0.300 \mathrm{~Pa}$.s flows between parallel plates as illustrated in Figure $1.23 .$ The top and bottom plates each have an area of $1.5 \mathrm{~m}^{2},$ and the distance between the plates is $200 \mathrm{~mm}$. The distribution of velocity within the fluid is given by $$ u=0.8\left(1-100 y^{2}\right) $$ where $u$ is the velocity in $\mathrm{m} / \mathrm{s}$ and $y$ is the distance from the centerline in meters. (a) Determine the shear stress on the top and bottom plates. (b) Determine the shear forces exerted by the fluid on the top and bottom plates.
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