Physical Chemistry Third Edition

10.2 Transport Processes 457

EXAMPLE10.8

Calculate the Reynolds number for the flow of water in Example 10.6. Is the flow laminar?

Solution

R

R〈u〉ρ

η



(0. 500 × 10 −^3 m)(2.48 m s−^1 )(998.2kgm−^3 )

(0.001002 kg m−^1 s−^1 )

 1234

The flow is probably laminar.

Exercise 10.7

Estimate the Reynolds number for the flow of blood in a typical human capillary. Is the flow

laminar? The average diameter of a red blood cell is roughly 7μm, which is the same as the

assumed diameter of the capillaries. Comment on this fact.

EXAMPLE10.9

Water flows through a tube of length 0.420 m and radius 0.00520 m. If the pressure difference

is 0.0500 atm and the temperature is 20◦C, find the volume of water that flows in 1.000 hour,

assuming laminar flow.

Solution

dV

dt



(P 2 −P 1 )πR^4

8 Lη



(0.0500 atm)(101325 Pa atm−^1 )π(0.00520 m)^4

8(0.420 m)(0.001002 kg m−^1 s−^1 )

 3. 457 × 10 −^3 m^3 s−^1  3 .457 L s−^1

V(3. 457 × 10 −^3 m^3 s−^1 )(3600 s) 12 .4m^3

Exercise 10.8

Estimate the Reynolds number for the flow in the previous example. Is the answer to this example

usable? What is the maximum value of the pressure difference that would correspond to laminar

flow?

Stokes’ Law

If a spherical object moves through a fluid or if the fluid flows past it, there is a frictional

force on the object. If the flow is laminar and if the object moves with a velocityv

through a fluid with viscosityη, Stokes’ law is

Stokes’ law was derived from the laws
of hydrodynamics by George Gabriel
Stokes, 1819–1903, an Anglo-Irish
mathematician and physicist who
pioneered the science of
hydrodynamics.

Ff− 6 πηrv (Stokes’ law) (10.2-27)