Question

Using Stokes’ law, verify that the units for viscosity are kilograms per meter per second.

a) kg/m²
b) kg/(m·s)
c) kg/m³
d) kg·m/s²

Answer 1

The units for viscosity, as determined by Stokes' law, are kilograms per meter per second (kg/(m·s)).

Step-by-step explanation:

Stokes' law states that the drag force experienced by a small sphere moving through a viscous fluid is proportional to the sphere's velocity and the fluid's viscosity. Mathematically, it can be expressed as Fd = 6πηrv, where Fd is the drag force, η is the viscosity, r is the radius of the sphere, and v is its velocity.

To verify that the units for viscosity are kilograms per meter per second, we can substitute the units of the different variables in the equation:

Fd = (kilograms) * (1/meter) * (meter/second)

This simplifies to:

Fd = kilograms / (meter * second)

Therefore, the units of viscosity are kilograms per meter per second, which corresponds to option b) kg/(m·s).