CHAPTER 12 - DISCHARGE MEASUREMENTS USING TRACERS

4. Discharge Equations for Tracer Methods

The following equations apply to both open channel and closed conduit flow.

**(a) Velocity-Area Tracer Discharge Equation**

The discharge using velocity-area method is computed by:

where:

Q=AL/T (12-1)

*Q* = discharge in cubic feet per second (ft^{3}/s)

*A* = average cross-sectional area of reach length in square feet
(ft^{2})

*L* = reach length between detection stations in feet (ft)

*T* = recorded time required for the tracer solution to travel
between the detection stations at each end of the measurement reach in
seconds (s)

**(b) Tracer-Dilution Discharge Equation**

The dilution method equation for discharge is:

QC_{0}+qC_{1}=(Q+q)C_{2 } (12-2a)

Solving for discharge in equation 12-2a results in:

Q=q(C_{1}-C_{2})/(C_{2}-C_{0}) (12-2b)

where:

*C*_{0} = the natural or background concentration of the
tracer of the flow

*C*_{1} = the concentration of the strong injected tracer
solution

*C*_{2} = the concentration of tracer after full mixing
at the sampling station, including the background concentration of the
stream

*Q* = the discharge being measured

*q* = the discharge of the strong solution injected into the flow

Equation 12-2 can be modified for use in terms of weight by substituting percent of dry weight of tracer for concentrations and weight of water per second for discharges.

The discharge of the channel flow, *Q*, is measured by determining
*C*_{0}, *C*_{1}, *C*_{2}, and the
injection rate, *q*. These required variables and equation 12-2 show
that the dilution method does not need measurement of channel geometry
or time measurement. Only the final plateau value or *C*_{2},
the downstream concentration, must be recorded rather than a complete record
of the passing cloud that is needed with the salt-velocity-area method.