Many great rivers flow towards the equator, what effect does the sediment they carry to sea have on the rotation of the earth? 
 

In the absence of external torque, angular momentum of the system is conserved.
$\mathrm{L}=\mathrm{I\omega }=\mathrm{constant}$
Due to the flow of river towards equator, the sediments also move towards the equator which in result increases the Moment of  inertia  I of the earth, thus decreasing angular velocity w of the earth so that angular momentum remains constant.

$\text{ As }\mathrm{w}=\frac{2\mathrm{\pi }}{\mathrm{T}}$

Hence when w decreases, then time period (T) of rotation increases.