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Asolution 20 g/l concentration of a fluorescent tracer was discharged into a stream at a constant rate of 5 cm/s. The
background concentration of the dye in stream water was found to be zero. At a downstream section sufficiently far away, the
dye was found to reach an equilibrium concentration of 4 parts per billion. Estimated the stream discharge.
EXPLANATION
Stream Gauging & Hydrograph Analysis
- Streamflow Measurement via Constant-Rate Tracer Dilution:
- Mass Balance Principle:
Since stream background concentration $C_0 = 0$ and tracer injection rate $q \ll Q$:
$$Q = \frac{q \cdot C_1}{C_2}$$- Calculation:
- Tracer concentration $C_1 = 20\text{ g/L} = 20 \times 10^6\ \mu\text{g/L} = 20 \times 10^6\text{ ppb}$.
- Injection rate $q = 5\text{ cm}^3\text{/s} = 5 \times 10^{-3}\text{ L/s}$.
- Downstream equilibrium concentration $C_2 = 4\text{ ppb}$.
- Conclusion: Stream discharge is 25 m$^3$/s (Option 2).
Correct option: (2) 25 mls
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