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A circular painted-steel channel, of radius $50 \mathrm{cm},$ is running half-full at $1.2 \mathrm{m}^{3} / \mathrm{s}$ on a slope of $5 \mathrm{m} / \mathrm{km} .$...

Question

A circular painted-steel channel, of radius $50 \mathrm{cm},$ is running half-full at $1.2 \mathrm{m}^{3} / \mathrm{s}$ on a slope of $5 \mathrm{m} / \mathrm{km} .$ Determine $(a)$ whether the slope is mild or steep and $(b)$ what type of gradually varied solution applies at this point. (c) Use the approximate method of Eq. $(10.52),$ and a single depth increment $\Delta y=5 \mathrm{cm},$ to calculate the estimated $\Delta x$ for this new $y$.

A circular painted-steel channel, of radius $50 \mathrm{cm},$ is running half-full at $1.2 \mathrm{m}^{3} / \mathrm{s}$ on a slope of $5 \mathrm{m} / \mathrm{km} .$ Determine $(a)$ whether the slope is mild or steep and $(b)$ what type of gradually varied solution applies at this point. (c) Use the approximate method of Eq. $(10.52),$ and a single depth increment $\Delta y=5 \mathrm{cm},$ to calculate the estimated $\Delta x$ for this new $y$.



Answers

A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of
60 cm/s. Find the rate at which the area within the circle is increasing after
(a) 1 s, (b) 3 s, and (c) 5 s. What can you conclude?


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