CHAPTER 2 - BASIC CONCEPTS RELATED TO FLOWING WATER AND MEASUREMENT

4. Discharge-Area-Velocity Relationships

Flow rate or discharge, *Q*, is the volume of water in cubic feet
passing a flow section per unit time, usually measured in cubic feet per
second (ft^{3}/s). The distance, *d _{v}*, in feet
that water will travel at a given velocity in a pipe of constant diameter
is velocity,

(2-7)

The volume, *V _{o}*, in cubic feet passing from the upstream
to the downstream ends of this distance is the distance,

(2-8)

To get the time rate of flow or discharge, *Q*, in cubic feet per
second, divide the right and left sides of equation 2-8 by time, *t*,
in seconds, resulting in:

(2-9)

Flow in open channels of rectangular cross section is often expressed
in terms of unit discharge, *q*, in cubic feet per second per foot
of width which is discharge, *Q*, in cubic feet per second divided
by cross-sectional width, *L _{b}*, in feet or:

(2-10)

The area, *A,* is *L _{b}D,* where

(2-11)

where the subscript denotes any number of arbitrarily selected positions along the flowing system. This principle, known as continuity, is especially useful in the analysis of tube flow measurement devices such as the venturi meter.