ing. Some of today’s uses of fluid mechanics in various fields include: understanding the
movement of molten (liquid) rock, or lava, in volcanic eruptions; studying the flow of air
over objects to help design airplanes, the space shuttle, and even spacecraft that fly
through the atmospheres of other planets; air flow studies in the automobile industry to
design cars with more aerodynamic profiles; analyzing the ups and downs of the stock
market; examining natural hazards, such as snow conditions that result in an avalanche;
interpreting turbulent flow in sewer and water pipes, and in river channels; studying
complicated flow of weather patterns in the atmosphere; researching the effects of gravi-
ty (and other) waves in space; and using fluid mechanics applications to study the deep
oceans and coastal shorelines, including waves and currents.CIVIL ENGINEERING AND MATHEMATICS
How do civil engineersuse mathematics?
Although most civil engineers actually spend only a small portion of their time doing
calculations, mathematics is essential to this field. For example, civil engineers may
use math to carry out the technical calculations in order to plan a construction pro-
ject. They may use math to model and simulate the possible behavior of a structure
before it is actually built. They also use math to understand the necessary chemistry
(the strength of a material) and/or physical components (how strong parts need to be)
of a construction project.How do surveyorsuse mathematics?
Surveyors use mathematics—especially geometry and trigonometry—because they
need to measure angles and distances on the ground. They then interpret the data,
accurately plotting such information as boundaries and locations of structures on a
map. These maps are then used for personal or legal means, such as a survey of a per-
son’s lot showing ownership boundaries in order to obtain a mortgage. The traditional
method of surveying is called plane surveying, which does not take into consideration
the curvature of the Earth because, for most small projects, this curvature doesn’t
really matter. When it does, especially for projects measuring greater distances, the
method used is called geodetic surveying.How do surveyorsmake measurements?
Most of a surveyor’s measurements are gathered with a theodolite, an instrument that
acts as a telescope, ruler, and protractor. The theodolite is set up over a known spot,
such as a previously surveyed corner of a lot; its telescope then sights a specific spot,
such as another corner of a lot, and the distance is measured (most modern theodo-
lites use lasers to measure distance), supplemented by angular measurements in both
330 the horizontal and vertical planes. The surveyor then uses trigonometry to analyze the