# Tracer process

The tracer method , also known as the dilution method , especially in the case of groundwater marking experiments, is a form of discharge measurement , a hydrological method for measuring flow velocity. The discharge is determined by the targeted addition of a so-called tracer (marking substance) into a flowing water and by subsequent measurement of the concentration drop further downstream. At the same time, the dwell time is also measured, which is important information for groundwater - there it is also the most important method for waterway mapping itself, as it allows you to determine which paths the water takes even underground.

## Measuring principle

The tracer is fed to the flowing water at an input point. On the subsequent mixing section, the tracer is distributed over the entire flow cross-section. The concentration of the marking substance is determined at a specified sampling point further downstream. The lower the concentration there, the more the tracer was diluted and the greater the flow.

## scope of application

The dilution method is mainly used to determine the discharge of torrents, since conventional measurement methods such as wing measurement cannot be carried out due to the strong turbulence and the high flow of debris and debris and the measurement cross-section cannot be clearly determined due to large stones. However, these are ideal prerequisites for the tracer process, as the strong turbulence results in thorough mixing of the marking substance supplied.

## Variants of the method of dilution

The tracer measurement can be done in the following ways:

• Constant input method
• Integration method

### Constant input method

With this method, the marking substance is added to the flowing water at the input point over a longer period of time at a constant input rate and constant concentration until a tracer concentration constant over time is reached in the entire flow cross-section at the sampling or measuring point . ${\ displaystyle Q_ {1}}$${\ displaystyle C_ {1}}$${\ displaystyle C_ {2}}$

Provided that the water is not preloaded with the marking substance, the following formula applies:

${\ displaystyle Q_ {1} \ cdot C_ {1} = (Q + Q_ {1}) \ cdot C_ {2}}$

From this it follows through transformation:

${\ displaystyle Q = Q_ {1} \ cdot {\ frac {C_ {1}} {C_ {2}}} - Q_ {1}}$

Since the input inflow is generally very small in relation to the desired flow , the calculation can be simplified: ${\ displaystyle Q_ {1}}$${\ displaystyle Q}$

${\ displaystyle Q = Q_ {1} \ cdot {\ frac {C1} {C_ {2}}} = Q_ {1} \ cdot N}$

The following applies:

${\ displaystyle Q_ {1} \ cdot C_ {1} = {\ text {const.}}}$
${\ displaystyle C_ {2} = {\ text {const.}}}$

With:

${\ displaystyle Q \ colon}$ Flow
${\ displaystyle Q_ {1} \ colon}$ Tracer addition
${\ displaystyle C_ {1} \ colon}$ Concentration of the input solution
${\ displaystyle C_ {2} \ colon}$ constant tracer concentration in the sampling area
${\ displaystyle N \ colon}$ Concentration ratio ${\ displaystyle C_ {1} / C_ {2}}$

### Integration method

A certain input quantity of the marking substance is fed into the flowing water within a very short time at the tracer input point. As a result, the marking substance spreads in the direction of flow and is increasingly evenly distributed over the cross section. The tracer cloud then passes the sampling point as a so-called transit curve. This is generally characterized by a steep increase in concentration and a long, gradual decrease in concentration. At the sampling point, the course of the tracer concentration over time is measured - this can be done with as many individual samples as possible at small time intervals, or better, with continuous measurement, which is also possible today with modern measuring probes. The flow curve determined is then integrated over time to calculate the flow rate . ${\ displaystyle M}$

Provided that the water is not preloaded with the marking substance and that the tracer has been completely mixed, the following applies to every point of the sampling cross-section:

${\ displaystyle M = \ int Q \ cdot C_ {2} \, \ mathrm {d} t}$

From this it follows for constant : ${\ displaystyle Q}$

${\ displaystyle Q = {\ frac {M} {\ int C_ {2} (t) \, \ mathrm {d} t}}}$

With:

${\ displaystyle Q \ colon}$ Drain
${\ displaystyle M \ colon}$ amount of tracer added
${\ displaystyle C_ {2} (t) \ colon}$ Course of concentration at the extraction point
${\ displaystyle t \ colon}$ time

## Mixing range

It is crucial for the tracer measurement that the marking substance is completely mixed in the mixing section (that is the flow section between the tracer addition and sampling point). Mixing is complete when, in the case of the constant addition method, the concentration is the same at every point of the extraction cross-section or, in the case of the integration method, the integral of the concentration (integrated over time) is constant for every point of the extraction cross-section. On the one hand, the mixing section must be at least long enough to ensure complete mixing, but on the other hand, it must not be too long, as a loss of the marking substance results in an excessively high discharge calculation. Furthermore, the flowing water in the area of ​​the mixing section must not have any above or below ground inflows or outflows. Areas with dead spaces, pools , eddies , widenings and flooded foreland are also unfavorable and should therefore be avoided when choosing the mixing route. ${\ displaystyle C_ {2}}$