Water Hydraulics - Mathematics and Statistics for the Environment - page 589

22.2.1 s tevin ' s l aW
Stevin's law deals with water at rest. Specifically, it states: “The pressure at any point in a fluid at
rest depends on the distance measured vertically to the free surface and the density of the fluid.”
Stated as a formula, this becomes

p = w × h (22.1)

where
p = Pressure in pounds per square foot (lb/ft 2 or psf).
w = Density in pounds per cubic foot (lb/ft 3 ).
h = Vertical distance in feet.

■ EXAMPLE 22.2
Problem: What is the pressure at a point 18 ft below the surface of a reservoir?

Solution: To calculate this, we must know that the density of the water ( w ) is 62.4 lb/ft 3 :

p = w × h = 62.4 lb/ft 3 × 18 ft = 1123 lb/ft 2 (psf)

Environmental professionals involved with water and wastewater treatment generally measure
pressure in pounds per square inch rather than pounds per square foot; to convert, divide by 144 in. 2 /
ft 2 (12 in. × 12 in. = 144 in. 2 ):

1123 psf
144 in./ft

2

P = = 7.8 lb/in.orpsi ( rounded)

22

22.2.2 d ensity and s peCiFiC g ravity
When we say that iron is heavier than aluminum, we say that iron has greater density than alumi-
num. In practice, what we are really saying is that a given volume of iron is heavier than the same
volume of aluminum. Density is the mass per unit volume of a substance. Consider a tub of lard
and a large box of cold cereal, each having a mass of 600 grams. The density of the cereal would
be much less than the density of the lard because the cereal occupies a much larger volume than the
lard occupies. The density of an object can be calculated by using the formula:

Mass
Volume

(22.2)

Density =

In general use, perhaps the most common measures of density are pounds per cubic foot (lb/ft 3 )
and pounds per gallon (lb/gal):

• 1 ft 3 of water weighs 62.4 lb; density = 62.4 lb/ft 3 .
• 1 gal of water weighs 8.34 lb; density = 8.34 lb/gal.

The density of a dry material, such as cereal, lime, soda, or sand, is usually expressed in pounds
per cubic foot. The densities of plain and reinforced concrete are 144 and 150 lb/ft 3 , respectively.
The density of a liquid, such as liquid alum, liquid chlorine, or water, can be expressed either as
pounds per cubic foot or as pounds per gallon. The density of a gas, such as chlorine gas, methane,
carbon dioxide, or air, is usually expressed in pounds per cubic foot.
The density of a substance such as water changes slightly as the temperature of the substance
changes. This occurs because substances usually increase in volume as they become warmer.
Because of this expansion with warming, the same weight is spread over a larger volume, so the
density is lower when a substance is warm than when it is cold.