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Chapter 10: Problem 78

At a given location in a 12 -ft-wide rectangular channel the flowrate is \(900 \mathrm{ft}^{3} / \mathrm{s}\) and the depth is \(4 \mathrm{ft}\). Is this location upstream or downstream of the hydraulic jump that occurs in this channel? Explain.

Short Answer

Expert verified
The given location is upstream of the hydraulic jump as it is in a supercritical flow regime.

Step by step solution

01

Understanding the provided data

The given data in the exercise is: width of channel (b) = 12 ft, flow rate (Q) = 900 ft³/s and depth of flow (h) = 4 ft. The goal is to determine if the given location is upstream or downstream of the hydraulic jump.
02

Calculate velocity

Start by calculating the velocity (v) of the flow. Velocity can be computed using the formula: \(v = Q / (b \times h)\). By substituting the given values, \(v = 900 / (12 \times 4)\) which equals 18.75 ft/s.
03

Compute the Froude number

Next, calculate the Froude number (Fr) that describes the flow regime. The Froude number is the ratio of inertial force to gravitational force and is calculated using the formula: \(Fr = v / \sqrt{g \times h}\), where g is the acceleration due to gravity (32.2 ft/s²). Plugging in the previous computed value of velocity and the known values of acceleration due to gravity and depth, the Froude number equals 1.32.
04

Interpret the result

The Froude number helps identify the flow regime. Flow is typically classified as subcritical (Fr < 1), critical (Fr = 1), or supercritical (Fr > 1). Here, since Fr = 1.32 > 1, the flow is supercritical. In the phenomenon of hydraulic jump, the flow changes from supercritical to subcritical. Hence the given location (with supercritical flow) is upstream of the hydraulic jump.

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Most popular questions from this chapter

An old, rough-surfaced, 2 -m-diameter concrete pipe with a Manning coefficient of 0.025 carries water at a rate of \(5.0 \mathrm{m}^{3} / \mathrm{s}\) when it is half full. It is to be replaced by a new pipe with a Manning coefficient of 0.012 that is also to flow half full at the same flowrate. Determine the diameter of the new pipe.

Water flows down a wide rectangular channel having Manning's \(n=0.015\) and bottom slope \(=0.0015 .\) Find the rate of discharge and normal depth for critical flow conditions.

Find the diameter required for reinforced concrete pipe laid at a slope of 0.001 and required to carry a uniform flow of \(19.3 \mathrm{ft}^{3} / \mathrm{sec}\) when the depth is \(75 \%\) of the diameter.

A channel has a rectangular cross section, a width of \(40 \mathrm{m}\) and a flow rale of \(4000 \mathrm{m}^{3} / \mathrm{s}\). The normal water depth is \(20 \mathrm{m}\). The flow then encounters a 4.0 -m-high dam. Find the water depth directly above the dam if the flow is critical. Assume frictionless flow.

A rectangular, unfinished concrete channel of 28 -ft width is laid on a slope of \(8 \mathrm{ft} / \mathrm{mi}\). Determine the flow depth and Froude number of the flow if the flowrate is \(400 \mathrm{ft}^{3} / \mathrm{s}\)
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