Question $6.$

A laboratory study was performed in a sand column using NaCl as a tracer. Tracer

concentration $($C$)$ was measured for various pore volumes at the effluent. After $600$ seconds and $4000$ seconds, the effluent concentrations were found $16\%$ and $84\%$ of the initial concentration respectively. The following data were measured during the experiment:

Column length $=40$ cm

Column diameter $=5$ cm

Mean grain size $=0\mathrm{.}25$ mm

Uniformity coefficient of sand $=2\mathrm{.}3$

Porosity $=0\mathrm{.}3$

Flow rate $=10$ ml$/$min

Molecular diffusion of NaCl at $250$C $=2\mathrm{.}03$x$10-5$ cm$2/$sec

Tortuosity factor $=0\mathrm{.}5$

Using the above data,

a$.$ Calculate the hydrodynamic dispersion coefficient.

b$.$ Calculate the dispersivity of the sand in the column.