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CE 4353/5360 Design of Hydraulic Systems
Fall 2022 Exercise Set 3

LAST NAME, FIRST NAME

R00000000


Purpose :

Apply principles of specific energy in open channel transitions

Assessment Criteria :

Completion, results plausible, format correct, calculations (Jupyter Notebook) are shown.


Problem 1

A subcritical transition from an upstream rectangular flume that is 49 $ft$ wide to a downstream trapezoidal channel with a width of 75 $ft$ and side slopes of 2:1. The transition bottom drops 1 $ft$ from the upstream flume to the downstream trapezoidal channel. The steady discharge is 12,600 $cfs$ and the depth of flow in the downstream channel is 22 $ft$. For a head loss coefficient of 0.5

Determine:

  • The approach flow depth (in the rectangular flume).
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Problem 2

A circular culvert with 1.0 $m$ diameter is placed on a steep slope. The upstream head is 1.3 $m$ with an unsubmerged entrance. Neglect entrance losses and

Determine:

  • The discharge through the culvert.
  • The critical depth at the entrance.
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Problem 3

A 1.0 $m$ by 1.0 $m$ box culvert is placed on a steep slope. The upstream head is 1.3 $m$ with an unsubmerged entrance. Neglect entrance losses and

Determine:

  • The discharge through the culvert.
  • The critical depth at the entrance.
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Problem 4

A study of natural channel shapes in the western United States reported an average ratio of maximum depth to hydraulic depth ($D=\frac{A}{T}$) in the main channel (with no overflow) of $\frac{y}{D} = 1.55$ for 761 measurements.

Determine:

  • The calculated ratio of maximum depth to hydraulic depth for a triangular channel.
  • The calculated ratio of maximum depth to hydraulic depth for a parabolic channel.
  • The calculated ratio of maximum depth to hydraulic depth for a rectangular channel.
  • The significance of these calculated results to the study's reported average.
  • The discharge for a channel at a critical depth of $y=10.0~ft$ if $\frac{y}{D} = 1.55$ and $T=100~ft$.
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Problem 5 (Application of ENGR-1330 Computational Thinking)

Prepare a function (within a JupyterLab Notebook) to compute head-discharge relationships for a rectangular, sharp-crested weir, and another function to compute head-discharge relationship for a 90$^o$ V-notch sharp-crested weir.

Incorporate your functions into a supervisory script (a main program) and apply to a situation where the weir is placed in a 5 $ft$ wide channel with the weir crests are 1 $ft$ above the channel bottom.

Determine:

  • Head vs discharge for the rectangular weir with a crest width of 1 $ft$ for approach head in the range $0 - 0.5~ft$
  • Head vs discharge for the V-notch weir for approach head in the range $0 - 0.5~ft$
  • Plot both relationships on the same figure (2 curves, 1 graph); properly label the axes of the plot including units,include a plot title, and include a plot legend altering both color and marker type to distinguish between the two different weirs.
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