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Crude oil, with specific gravity $\mathrm{SG}=0.85$ and viscosity $\mu=2.15 \times 10^{-3}\ \mathrm{lbf} \cdot \mathrm{s} / \mathrm{ft}^2$, flows steadily down a surface inclined $\theta=45$ degrees below the horizontal in a film of thickness $h=0.1\ \text{in.}$ The velocity profile is given by $$ u=\frac{\rho g}{\mu}\left(h y-\frac{y^2}{2}\right) \sin \theta $$ (Coordinate $x$ is along the surface and $y$ is normal to the surface.) Plot the velocity profile. Determine the magnitude and direction of the shear stress that acts on the surface.

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physics

Some electro-optic materials can change their index of refraction in response to an applied voltage. Suppose a planoconvex lens (flat on one side, a 15.0 cm radius of curvature on the other), made from a material whose normal index of refraction is 1.500, is creating an image of an object that is 50.0 cm from the lens. By how much would the index of refraction need to be increased to move the image 5.0 cm closer to the lens?

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computer science

Repeat earlier Example in the text, but assume that node N5 needs to find the responsible node for key k16. Hint: Remember that interval checking needs to be done in modulo 32 arithmetic.

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chemistry

Write the formula for each of the following substances. k. barium acetate

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Atkins Physical Chemistry

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