First Principles - Sustainable Design: The Science of Sustainability and Green Engineering - page 62

discharge 3 of a stream of width w is the sum of the products of mean depth, s

mean width, and mean velocity:

n

1
2 ( h n

1
2 (

1) 1

= + − w + w − × v + v − +

Q h n 1)( 1)

2 ( h n

h n − 1 ) n n n n

n = 1

(2.11)

where

Q = discharge (m 3 s − 1 )
h n = n th water depth (m)

w n = n th distance from baseline or initial point of measurement (m)

n th velocity (m s − 1 ) from velocity meter v n =

Another important fluid property is pressure . A force per unit area is pressure:

F
A

p = (2.12)

So p is a type of stress that is exerted uniformly in all directions. It is common to
use pressure instead of force to describe the factors that influence the behavior
of fluids. The standard unit of p is the pascal (P), which is equal to1Nm − 2 .
The preferred pressure unit in this topic is the kilopascal (kP), since the standard
metric unit of pressure is the pascal, which is quite small.
Potential and kinetic energy discussions must consider the fluid acceleration
due to gravity. In many ways, it seems that acceleration was a major reason
for Isaac Newton's need to develop the calculus. 4 Known as the mathematics of
change , calculus is the mathematical means of describing acceleration and addressed
Newton's need to express mathematically his new law of motion. Acceleration is
the time rate of change in the velocity of a fluid particle. In terms of calculus, it
is a second derivative. That is, it is the derivative of the velocity function—and a
derivative of a function is itself a function, giving its rate of change. This explains
why the second derivative must be a function showing the rate of change of the
rate of change, which is readily apparent from the units of acceleration: length
per time per time (m s − 2 ).
The relationship between mass and volume is important in both environmental
physics and chemistry and is a fundamental property of fluids. The density of

a fluid is defined as its mass per unit volume. Its metric units are kg m − 3 . The
density of an ideal gas is found using the specific gas constant and applying the

ρ