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Chapter 1: Problem 18

A commercial advertisement shows a pearl falling in a bottle of shampoo. If the diameter \(D\) of the pearl is quite small and the shampoo sufficiently viscous, the drag 9 on the pearl is given by Stokes's law, \\[ \mathscr{P}=3 \pi \mu V D \\] where \(V\) is the speed of the pearl and \(\mu\) is the fluid viscosity. Show tha: the term on the right side of Stokes's law has units of force.

Short Answer

Expert verified
The term on the right side of Stokes's law has units of force (kg.m/s²) as shown by the breakdown and simplification of the individual terms' units.

Step by step solution

01

Identify Units

In this step identify the units of each variable according to the International System of Units (SI). Here, the diameter \(D\) is given in meters (m); the speed \(V\) in meters per second (m/s); and the viscosity \(\mu\) is measured in Pascal-seconds (Pa.s) which can be further reduced to (kg/(m.s)).
02

Substitute units into Stokes’s law

The next step substitutes the units identified into Stokes’s law. Accordingly, \(\mathscr{P}=3 \pi \mu V D\) becomes \(kg.m/s² = 3 \pi (kg/(m.s)) (m/s) m\).
03

Performing Evaluation

In this last step, the multiplication is performed, which results to \(kg.m/s² = 3 \pi kg.m/s²\). This confirms that the right side of the equation does indeed come out to be in units of force.

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Most popular questions from this chapter

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