   Chapter 15, Problem 1PA

Chapter
Section
Textbook Problem

A stream flowing out of a canyon mouth onto the apex of an alluvial fan has a discharge of 12 cubic meters per second, flow depth of 2 meters, and flow width of 3 meters. What is the flow velocity at the fan apex? If the velocity decreases downfan by 0.1 meter per second, at what distance from the apex will it reach a velocity of zero?

To determine

The flow velocity at the fan apex and distance it will reach from the apex at a velocity of zero if a stream flowing out of a canyon mouth onto the apex of an alluvial fan with a discharge of 12 cubic meters per second, flow depth of 2 meters, and flow width of 3 meters.

Explanation

Given information:

Stream discharge (Q)=12Channel cross-sectional width (w)=3Depth (d)=2Decrease in velocity = 0.1

The equation used to calculate stream discharge is as follows:

Stream discharge (Q) is the channel cross-sectional width (w) and depth (d) multiplied with the flow velocity (v). It is expressed as follows:

Q=wdv

Velocity(v)=Stream discharge(Q)Width(w)×Depth(d)=12

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