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2. A parameter that describes the flow of water an an open channel, like an irrigation ditch, is called the discharge coefficient, K. If the cross-section of the channel is approximated as a parabola, K can be estimated from the engineering formula $$K = \frac{1.2}{x} \left[ \sqrt{16x^2 + 1} + \frac{1}{4x} ln(\sqrt{16x^2 + 1} + 4x) \right]^{\frac{2}{3}}$$ where x is the ratio of the maximum water depth to the width of the channel at the water surface. $x = \frac{d}{w}$ Investigate the behavior of K for a range of values of x from 0.05 to 1.0 in steps of 0.05. Display your results as a graph with your name and the date in the title. Make a screen capture (Start ? Snipping Tool) or copy the figure by going to the menu in the Figure window and clicking on Edit and then Copy Figure. Paste this figure into your Worksheet. 3. You will probably need to make reference to the class notes in solving the following problems. 3.1 What are the four roots of the following equation? $x^4 - 16x^3 + 78x^2 - 412x + 624 = 0$ 3.2 Find a solution for x in the equation in part 2 above for a value of K = 1.35. Which Matlab built-in function do you use to do this? What is the solution? x =

          2. A parameter that describes the flow of water an an open channel, like an irrigation ditch, is called the
discharge coefficient, K. If the cross-section of the channel is approximated as a parabola, K can
be estimated from the engineering formula
$$K = \frac{1.2}{x} \left[ \sqrt{16x^2 + 1} + \frac{1}{4x} ln(\sqrt{16x^2 + 1} + 4x) \right]^{\frac{2}{3}}$$
where x is the ratio of the maximum water depth to the width of the channel at the water surface.

$x = \frac{d}{w}$

Investigate the behavior of K for a range of values of x from 0.05 to 1.0 in steps of 0.05. Display your
results as a graph with your name and the date in the title. Make a screen capture (Start ? Snipping
Tool) or copy the figure by going to the menu in the Figure window and clicking on Edit and then Copy
Figure. Paste this figure into your Worksheet.
3. You will probably need to make reference to the class notes in solving the following problems.
3.1 What are the four roots of the following equation?
$x^4 - 16x^3 + 78x^2 - 412x + 624 = 0$

3.2 Find a solution for x in the equation in part 2 above for a value of K = 1.35.
Which Matlab built-in function do you use to do this?
What is the solution? x =

2. A parameter that describes the flow of water an an open channel, like an irrigation ditch, is called the
discharge coefficient, K. If the cross-section of the channel is approximated as a parabola, K can
be estimated from the engineering formula

K = (1.2)/(x)[ √(16x^2 + 1) + (1)/(4x) ln(√(16x^2 + 1) + 4x) ]^(2)/(3)

where x is the ratio of the maximum water depth to the width of the channel at the water surface.

x = (d)/(w)

Investigate the behavior of K for a range of values of x from 0.05 to 1.0 in steps of 0.05. Display your
results as a graph with your name and the date in the title. Make a screen capture (Start ? Snipping
Tool) or copy the figure by going to the menu in the Figure window and clicking on Edit and then Copy
Figure. Paste this figure into your Worksheet.
3. You will probably need to make reference to the class notes in solving the following problems.
3.1 What are the four roots of the following equation?
x^4 - 16x^3 + 78x^2 - 412x + 624 = 0

3.2 Find a solution for x in the equation in part 2 above for a value of K = 1.35.
Which Matlab built-in function do you use to do this?
What is the solution? x =

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