First Principles - Sustainable Design: The Science of Sustainability and Green Engineering - page 61

Figure 2.6 Classification of
fluids based on continuum fluid
mechanics.
Adapted from Research and Education
Association, The Essentials of Fluid
Mechanics and Dynamics I , REA,
Piscataway, NJ, 1987.

Continuum fluid mechanics

Inviscid

Viscous

Compressible Incompressible

Laminar Turbulent

Compressible Incompressible Compressible Incompressible

Fluids can be classified according to observable physical characteristics of flow
fields. A continuum fluids mechanics classification is shown in Figure 2.6. Laminar
flow is in layers, whereas turbulent flow has random movements of fluid particles
in all directions. In incompressible flow , the variations in density are assumed to be
constant, whereas compressible flow has density variations, which must be included
in flow calculations. Viscous flows must account for viscosity, whereas inviscid
flows assume that the viscosity is zero.
The time rate of change of a fluid particle's position in space is the fluid velocity
V . This is a vector field quantity. Speed V is the magnitude of the vector velocity
V at some given point in the fluid, and average speed V is the mean fluid
speed through a control volume's surface. Therefore, velocity is a vector quantity
(magnitude and direction), whereas speed is a scalar quantity (magnitude only).
The standard units of velocity and speed are meters per second (m s − 1 ).
Velocity is important when determining pollution, such as mixing rates after
an effluent is discharged to a stream, how rapidly an aquifer will become con-
taminated, and the ability of liners to slow the movement of leachate from a
landfill toward the groundwater. The distinction between velocity and speed is
seldom made, even in technical discussion. Surface water flow, known as stream
discharge Q , has units of volume per time. Although the appropriate units are
m 3 s − 1 , most stream discharge data in the United States are reported as the num-
ber of cubic feet of water flowing past a point each second (cfs). Discharge is
derived by measuring a stream's velocity at numerous points across the stream.
Since heights (and volume of water) in a stream change with meteorological
and other conditions, stream-stage/stream-discharge relationships are found by
measuring stream discharge during different stream stages. The flow of a stream
is estimated based on many measurements. The mean of the flow measurements
at all stage heights is reported as the estimated discharge. The calculation of