Let be a flow whose longitudinal speed is given: $u(y) = 3y^3 + 2y^2$. Knowing that the dynamic viscosity of the fluid is $\mu = 3.5 \times 10^{-2} \text{ N.s/}m^2$, calculate the value of the stress at the wall as well as the stress at 30 cm from the wall.
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The velocity gradient is given by du/dy. In this case, du/dy = 9y^2 + 4y. Show more…
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(a) Show that for Poiseuille flow in a tube of radius $R$ the magnitude of the wall shearing stress, $\tau_{r}$, can be obtained from the relationship $$\left|\left(\tau_{r_{z}}\right)_{\mathrm{will}}\right|=\frac{4 \mu Q}{\pi R^{3}}$$ for a Newtonian fluid of viscosity $\mu .$ The volume rate of flow is $Q$ (b) Determine the magnitude of the wall shearing stress for a fluid having a viscosity of $0.004 \mathrm{N} \cdot \mathrm{s} / \mathrm{m}^{2}$ flowing with an average velocity of $130 \mathrm{mm} / \mathrm{s}$ in a $2-\mathrm{mm}$ -diameter tube.
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