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The core objectives of this study encompass several key areas:

- To compute water surface profiles employing the direct step method efficiently.
- To accurately locate control points within the channel flow.
- To generate detailed water surface profiles and graphically represent these profiles for enhanced analysis.
- To utilize an Excel spreadsheet to facilitate the determination of normal depth and critical depth for a given channel section.

The study hinges on several fundamental hydraulic principles and definitions:

- Area – This is the cross sectional area of flow, normal to the direction of flow
- Wetted Perimeter, P – is the cross-sectional distance of the medium where it and the fluid that it carries are in contact.
- Normal depth – This is when the water depth stays constant, when the bottom of the channel and the water above ground level slope are synonymous.Normal depth is generally calculated using Manning’s Equation, it is the depth when the flow is unvarying.
- Critical depth – This is where the specific energy is at the least possible value given that a particular discharge is constant.
It is the lowest possible depth where the surface water’s flow speed is choppy and immense.

- Fr (Froude Number) – Froude number which is unit less measures the different flow conditions in an open channel. It is a ratio between inertial and gravitational forces.
- Sf (Friction Slope) – Friction slope is known as the amount of time taken to lose all the energy in the channel on a given distance.

The table below classifies gradually varied flow profiles based on channel slope conditions:

Channel Slope | Condition Type | Condition | Profile Type |
---|---|---|---|

Mild Slope | 1 | y>y0>yc | M1 |

Mild Slope | 2 | y0>y>yc | M2 |

Mild Slope | 3 | y0>yc>y | M3 |

Steep Slope | 1 | y>yc>y0 | S1 |

Steep Slope | 2 | yc>y>y0 | S2 |

Steep Slope | 3 | yc>y0>y | S3 |

Critical Slope | 1 | y>y0=yc | C1 |

In the excel spreadsheet the inputs such as So, b, Side Slope, Q, n, 𝛼, Δ y where placed for the Trapezoidal concrete lined channel.

The area of flow was calculated using the formulas :

A = b+T2 dn T = b+2dn

A = b +b+2 x 2 dn

=(2b + 2xdn)2dn

Wetted Perimeter was calculated using the formula :

Wp= b +2y √1+x2

The normal depth was calculated using the formulas.

QnSo1/2 = A5/3P2/3Since these equations are equal to one another and the values were known for this equation QnSo1/2 , it was then calculated. This equation A5/3P2/3 was calculated with the normal depth, this was done via trial and error since the normal depth is an unknown value.

The Top Width of the Trapezoidal channel was calculated using

T = b + (x * 2) dn

The Critical depth was calculated using the formula:

= 1

A3B = Q2g((2b + 2xdn)2dn)3b + (x * 2) dn = Q2gSince these equations are equal to one another and the values were known for this equation, Q2g it was then calculated. This equation A3B was calculated with the normal depth, this was done via trial and error since the critical depth is an unknown value.

The Water Surface Profile Computation table was created where to calculate the y (m), Area (m2), Wetted Perimeter (Pw), Froude Number (Fr), Friction Slope (Sf).

The formulas used in the calculation of the computation table are:

Froude Number

Fr = √Q2BgA3Friction Slope (Sf)

Sf=(n2Q2P4/3A10/3)

x(m)

Δ y = Δ x(1- Fr2So-Sf) mean

y (m)

y = Critical depth + Δ y

The type of water surface profile that would be expected since the constant bed slope is more than zero (So > 0), would be a mild slope profile.

The type of profile that was initially assumed is in fact the type of profile since dn (normal depth) which is 1.380 m is more than the critical depth which was calculated to be 1.108m which satisfy the condition of y0>y>yc. Hence it is a M2 Profile. Refer to Appendix for Sample Calculation

The locations of the control point was selected based on the free over fall since the critical depth is at the crest of the section or the brink of the section. After the water surface profile computations table was calculated for 13 steps it was shown The Critical depth which is the control point was then added to the Δ y to calculate the y (m) values since the flow in the upstream for the channel.

The integration of machine learning algorithms with hydraulic engineering principles presents a significant advancement in the analysis of water surface profiles. By automating the computation and visualization processes, this approach not only enhances accuracy but also significantly reduces the time and effort required for such analyses. The successful application of these techniques heralds a new era in hydraulic engineering, offering profound implications for the design and management of water conveyance systems.

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