Fundamental Chemistry and Hydraulics - Mathematics and Statistics for the Environment - page 369

14.2.1.4 Water at Rest
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 (14.16)

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 14.27
Problem: What is the pressure at a point 15 ft below the surface of a reservoir?

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

p = w × h = 62.4 lb/ft 3 × 15 ft = 936 lb/ft 2 , or 936 psf

Waterworks/wastewater operators 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 ):

2
22

936 lb/ft
144 in./ft

2

p = = 6. lb/in.orpsi

14.2.1.5 Gauge Pressure
Recall that head is the height that a column of water would rise due to the pressure at its base. We
demonstrated that a perfect vacuum plus atmospheric pressure of 14.7 psi would lift the water 34
feet. If we now open the top of the sealed tube to the atmosphere and enclose the reservoir, then
increase the pressure in the reservoir, the water will again rise in the tube. Because atmospheric
pressure is essentially universal, we usually ignore the first 14.7 psi of actual pressure measurements
and measure only the difference between the water pressure and the atmospheric pressure; we call
this gauge pressure.

■ EXAMPLE 14.28
Problem: Water in an open reservoir is subjected to the 14.7 psi of atmospheric pressure, but sub-
tracting this 14.7 psi leaves a gauge pressure of 0 psi. This shows that the water would rise 0 ft above
the reservoir surface. If the gauge pressure in a water main is 100 psi, how far would the water rise
in a tube connected to the main?

Solution:

100 psi × 2.31 ft/psi = 231 ft

14.2.1.6 Water in Motion
The study of water flow is much more complicated than that of water at rest. It is important to have
an understanding of these principles because the water/wastewater in a treatment plant and/or dis-
tribution/collection system is nearly always in motion (much of this motion is the result of pumping,
of course).