Question

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?

Answer 1

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.

Answer 2

Make that last term V, not Vc

Answer 3

a) Vterm = (mg)/(6pi N R)

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