You are in charge to investigate the characteristic of a small river that can be assumed as a uniform and rectangular cross-section for modeling purpose. The width of the river is 10 ft, the depth is 1 ft, longitudinal slope of 0.001, and the Manning's coefficients is 0.03. To estimate travel times and dispersion coefficients, you injected 50 gm of rhodamine dye at one bank of the river because it will spread out soon enough. You also began the steady bubbling of propane, a gaseous tracer into the river at this location.
a. Your assistant is measuring the rhodamine concentration 1 km downstream. The data when converted to a spatial distribution at t = 2500 sec after dye release, show the following: 95% of the mass lies between 800 m and 1200 m at time t = 2500 sec. Estimate the longitudinal dispersion.
b. Your other assistant is measuring the propane (C3H8) concentrations, which are 75 microM at 200 m downstream and 52 microM at 1500 m downstream. What is the reaeration coefficient if it is assumed that no dilution occurred due to lateral flow?
c. How far downstream must your assistant go to collect the sample near shore that is representative of the entire channel cross-section?