lent. For example, the ratio of inertia
forces to viscous forces within a fluid can
be expressed by what is called the Rey-
nold’s number; laminar fluid flow can be
described by the Navier-Stokes equations.
For no viscosity (or an ideal flow called
inviscid flow), the Bernoulli equation can
be used. Finally, when the flow is zero (or
static), the fluid is governed by the laws
and equations of fluid statics.
How oldis the studyof fluid mechanics?
According to many historians, fluid
mechanics may be the oldest subfield in
physics and engineering. In particular,
ancient civilizations needed to control
water flow for agricultural development,
drinking-water supplies, and transporta-
tion. Thus, the development of fluid
mechanics, which is the study of the
motion and behavior of fluids, led to even more (and complex) improvements. For
example, agricultural requirements led to irrigation waterways, dams, weirs, pumps,
and even crude forms of “sprinkler systems”; the need for a potable (drinkable) water
supply led to better wells, fountains, and water storage systems; and water transporta-
tion innovations included improved sails and rigs, as well as methods to build and
waterproof sailing vessels.
But early fluid mechanical studies did not end there. Over time, they extended
into almost every realm of science and engineering. For example, mechanical engi-
neering uses fluid mechanics because of the need to know about fluids used in com-
bustion (ships and automobiles), lubrication (from the smaller inner workings of a
wheel to larger mechanisms such as locks along a canal), and energy systems (hydro-
electric power). Civil engineering utilizes fluid mechanical studies to interpret how
fluid systems traveled over structures (aqueducts and pipes carrying drinking or waste
water). Electrical engineers use fluid flow to analyze how to cool electronic devices
with either air or water. Even early (and current) aeronautical engineers needed to
know how air flowed over an airplane wing, providing the much-needed lift that
allows a plane to become airborne.
How are studies of fluid mechanicsused today?
The list of engineering uses of fluid mechanics in the modern world seems endless—and
no wonder, since it is one of the most widely applied areas of mathematics and engineer- 329
MATH IN ENGINEERING
To understand the way lava flows from a volcano,
mathematicians apply their knowledge of fluid
mechanics. Science Faction/Getty Images.