Concept:
Lacey's silt factor is used in the design of stable alluvial channels.
It is given by
\[
\boxed{
f=1.76\sqrt{d}
}
\]
where
\[
d=\text{Mean particle size (mm)}.
\]
Step 1: Write the given data.
\[
d=0.16\text{ mm}
\]
Step 2: Calculate the silt factor.
\[
f
=
1.76\sqrt{0.16}
\]
\[
=
1.76\times0.4
=
0.704
\]
\[
\boxed{f\approx0.70}
\]
Therefore, the correct option is
\[
\boxed{(C)\;0.70.}
\]