Open Channel Flow: Non-Uniform Flow - Examples & Applications

$Problem 1: Critical Depth and Minimum Specific Energy$

A rectangular channel is $4.00\text{ m}$ wide and carries $10.0\text{ m}^3/\text{s}$ . Determine critical depth and minimum specific energy using $\alpha=1$ .

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$Problem 2: Specific Energy, Froude Number, and Flow Regime$

A $3.00\text{ m}$ wide rectangular channel carries $6.00\text{ m}^3/\text{s}$ at depth $1.00\text{ m}$ . Determine mean velocity, specific energy, Froude number, and flow regime.

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$Problem 3: Alternate Depths at Equal Specific Energy$

In a rectangular channel, unit discharge is $q=2.00\text{ m}^2/\text{s}$ and specific energy is $E=1.50\text{ m}$ . Determine the two possible depths and identify their regimes.

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$Problem 4: Maximum Bed Rise before Choking$

A $4.00\text{ m}$ wide rectangular channel carries $10.0\text{ m}^3/\text{s}$ at an upstream depth of $1.50\text{ m}$ . Neglect losses and take $\alpha=1$ . Determine the maximum bed rise that can occur before the raised section becomes critical.

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$Problem 5: Sequent Depth of a Hydraulic Jump$

Supercritical flow in a rectangular channel has upstream depth $y_1=0.500\text{ m}$ and velocity $V_1=8.00\text{ m/s}$ . Determine the upstream Froude number and downstream conjugate depth.

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$Problem 6: Hydraulic-Jump Energy and Power Dissipation$

For $y_1=0.500\text{ m}$ and $y_2=2.316\text{ m}$ , determine the specific-energy loss. If total discharge is $10.0\text{ m}^3/\text{s}$ , estimate hydraulic power dissipated.

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$Problem 7: Tailwater Check for Hydraulic-Jump Location$

A calculated free hydraulic jump requires downstream conjugate depth $y_2=2.32\text{ m}$ . At the same discharge, the actual tailwater depth at the proposed basin is only $1.80\text{ m}$ . What does this imply?

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$Problem 8: Broad-Crested Weir at Critical Flow$

Water passes over a broad-crested weir with available specific head $H=1.50\text{ m}$ above the crest. Neglect approach-velocity correction and losses. The crest is $4.00\text{ m}$ wide. Determine critical depth and discharge.

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$Problem 9: Critical Slope and Mild-Slope Classification$

A $4.00\text{ m}$ wide rectangular channel carries $10.0\text{ m}^3/\text{s}$ with Manning $n=0.0150$ . Determine the critical slope and classify an actual reach with $S_0=0.00100$ .

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$Problem 10: Water-Surface Profile Classification$

Classify each case: (a) $y_n=2.00\text{ m}$ , $y_c=1.20\text{ m}$ , $y=3.00\text{ m}$ ; (b) $y_n=0.800\text{ m}$ , $y_c=1.50\text{ m}$ , $y=1.10\text{ m}$ .

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$Problem 11: Local GVF Depth Gradient$

At a channel section, $S_0=0.00100$ , $S_f=0.000400$ , and $Fr=0.500$ . Determine $dy/dx$ and interpret its sign.

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$Problem 12: Direct-Step Reach Length and Sign Convention$

For two states in a prismatic channel, $E_2-E_1=0.120\text{ m}$ , $S_0=0.00100$ , and $\bar S_f=0.000400$ . Determine the signed distance from section 1 to section 2.

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$Problem 13: One Standard-Step Update in a Rectangular Channel$

A $4.00\text{ m}$ wide rectangular channel carries $10.0\text{ m}^3/\text{s}$ with $n=0.0150$ and bed slope $S_0=0.00100$ . At an upstream station, $y_1=2.00\text{ m}$ . The next station is $100\text{ m}$ downstream. Using the average of endpoint friction slopes, determine the downstream depth $y_2$ by iteration with $\alpha=1$ .

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$Problem 14: Spatially Varied Flow with Uniform Lateral Inflow$

A channel enters a $100\text{ m}$ reach with $Q_0=2.00\text{ m}^3/\text{s}$ and receives uniform lateral inflow $q_l=0.0300\text{ m}^2/\text{s}$ . Determine discharge at the downstream end.

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