physics
posted by anna on .
water at 20°C has viscosity n=1.0*10^3 Ns/m^2. sand grains have density 2400kg/m^3. suppose a 1.1 mm diameter sand grain is dropped into a 51m deep lake whose water is a constant 20°C. If the sand grain reaches terminal speed almost instantly (a quite good approximation), how long will it take the sand grain to settle to the bottom of the lake?

Use Stokes' drag equation for the terminal velocity.
Stoke's equation says, for a sphere in a viscous fluid,
F=6(pi)RnVc,
where F is the force, R is the radius of the sphere, n is the viscosity, and V is the velocity through the fluid.
For the force F, use the weight minus the buoyancy force.
Divide the lake depth by that velocity. 
Make that last term V, not Vc

a) Vterm = (mg)/(6pi N R)
b)V term = ((4/3)pi R^3)pg))/(6pi N R)