Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 10: Problem 61

A rectangular brick-lined channel has a bottom slope of 0.0025 and is designed to carry a uniform water flow rate of \(300 \mathrm{ft}^{3} / \mathrm{s}\). Would the channel need fewer bricks if the channel were 2 ft wide, 6 ft wide, or \(10 \mathrm{ft}\) wide? Explain.

Short Answer

Expert verified
The 2 ft wide channel will require the fewest bricks, as it has the smallest hydraulic radius. This is because the hydraulic radius is inversely proportional to the wetted perimeter.

Step by step solution

01

Calculation of Flow Area and Hydraulic Radius for each Width

First, calculate the flow area (A) and the hydraulic radius (R) for each width using the formulas: For a rectangular channel, \(A=Width \times Depth\) \(R= \frac{A}{P}\) Where: A= Flow Area P= Wetted Perimeter; as there is no specific depth given, assume a unit depth Width = 2, 6, 10 ft respectively for each case.
02

Comparison of the Hydraulic Radius for each case

By comparing the hydraulic radius for each width, determine which width would lead to fewer bricks. The smaller the hydraulic radius, the fewer bricks would be needed for channel lining.
03

Answer the question

Finally, after analysis and comparison, state which channel width will require fewer bricks.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

\(\mathrm{A}\) trapezoidal channel with a bottom width of \(3.0 \mathrm{m}\) and sides with a slope of 2: 1 (horizontal:vertical) is lined with fine gravel \((n=0.020)\) and is to carry \(10 \mathrm{m}^{3} / \mathrm{s}\). Can this channel be built with a slope of \(S_{0}=0.00010\) if it is necessary to keep the velocity below \(0.75 \mathrm{m} / \mathrm{s}\) to prevent scouring of the bottom? Explain.

The depth downstream of a sluice gate in a rectangular wooden channel of width \(5 \mathrm{m}\) is \(0.60 \mathrm{m}\). If the flowrate is \(18 \mathrm{m}^{3} / \mathrm{s}\) determine the channel slope needed to maintain this depth. Will the depth increase or decrease in the flow direction if the slope is (a) \(0.02 ;\) (b) \(0.01 ?\)

An 8 -ft-diameter concrete drainage pipe that flows half full is to be replaced by a concrete-lined V-shaped open channel having an interior angle of \(90^{\circ} .\) Determine the depth of fluid that will exist in the \(V\) -shaped channel if it is laid on the same slope and carries the same discharge as the drainage pipe.

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.

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.
See all solutions

Recommended explanations on Physics Textbooks

Energy Physics

Read Explanation

Electric Charge Field and Potential

Read Explanation

Space Physics

Read Explanation

Oscillations

Read Explanation

Work Energy and Power

Read Explanation

Atoms and Radioactivity

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free