Open Channel Flow: Numerical Methods and Computer Applications 1st. Edition by Roland Jeppson | 9781482282160 | 148228216X | Holooly

Numerical Methods

Open Channel Flow: Numerical Methods and Computer Applications

194 SOLVED PROBLEMS

Question: C.4

As an example, consider the flow from a reservoir whose water surface is 8 ft above the bottom of a trapezoidal channel with a bottom width b = 10 ft, a side slope m = 1.5, a Manning’s roughness n = .013 and a bottom slope So = 0.0008. The entrance loss coefficient for the water entering the ...

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This problem involves the simultaneous solution of...

Question: C.3

As a third example, consider the flow from a reservoir whose water surface is 8 ft above the bottom of a trapezoidal channel with a bottom width, b = 10 ft, a side slope m = 1.5, a Manning’s roughness coefficient, n = .013 and a bottom slope So = 0.0008. The entrance loss coefficient for the water ...

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This problem involves the simultaneous solution of...

Question: 6.15

A trapezoidal channel with a bottom width b = 10 ft, and a side slope of m = 1.0 initially has a uniform depth of Yo = 4.2 ft, and a velocity Vo = −3.517 fps. (The velocity is negative because the origin for the unsteady solution is at the downstream end of the channel.) The gate at the downstream ...

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First, compute

Y^{\prime }_{o}

= (1)...

Question: A.1

Find the area of flow if the depth is Y = 1.2 m in a pipe with a 1.8 m diameter. ...

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Let us obtain the solution by four different proce...

Question: A.2

Evaluate the first moment of area around the water surface for the previous problem in which the depth is 1.2 m in a pipe with a diameter of D = 1.8 m (R = 0.9 m). ...

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Substituting D = 1.8 and β = 1.910633 rad in Equat...

Question: B.1

Integrate the function f(x) = x²(x² − 2)sin(x) between the limits of 0 and π/2 using first the trapezoidal rule and then Simpson’s rule and compare the results with the exact integral. ...

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The integral is F(x) = 4x(x² − 7)sin(x) − (x[latex...

Question: B.2

Find the vertical component of force (including its location) on the bottom surface that is 3 m long with water standing to a height of 6 m. The surface is defined by the equation y = x + 0.5(1 − cos x). The distance between vertical walls is 3 m. ...

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The method of components allows the hydrostatic fl...

Question: B.3

The bottom of the tank is defined by the ODE dy/dx = x + y/2 minus x sin(45°). In other words, the depth of water at any position x is 5 + x sin(45°) − y where y is the solution to the above ODE. The gate exists between two vertical walls 2/cos(45°) = 2.828427 m apart as shown, and the tank is 5 m ...

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This problem requires that the ODE dy/dx = x + y/2...

Question: B.4

The bottom of the tank is defined by the ODE dy/dx = x + 0.5y from a coordinate system that is rotated downward 45° from the horizontal. The gate exists between two vertical walls 2 m apart as shown, and the tank is 5 m long and contains water that is 5 m deep at the left wall. Find the vertical ...

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The program below obtains the solution. Because of...

Question: B.5

We want to generate a smooth function for plotting x versus y using cubic splines through the following six pairs of (Xj, Yj) values: (0, 0), (5, 2), (9, 9), (14, 15), (18, 17), and (22, 19). ...

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To use the above programs the following input woul...

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