Water Hydraulics - Mathematics and Statistics for the Environment - page 592

Liquid level

T

FIGURE 22.2 Hydrostatic pressure. (From Spellman, F.R. and Drinan, J., Water Hydraulics , Technomic,
Lancaster, PA, 2001.)

■ EXAMPLE 22.6
Problem: Find the height of water in a tank if the pressure at the bottom of the tank is 22 psi.

Solution:

22 psi
0.433 psi/ft

Height = = 51 ft (rounded)

22.2.4 h ydrostatiC p ressure
Figure 22.2 shows a number of differently shaped, connected, open containers of water. Note that
the water level is the same in each container, regardless of the shape or size of the container. This
occurs because pressure is developed within a liquid by the weight of the liquid above. If the water
level in any one container is momentarily higher than that in any of the other containers, the higher
pressure at the bottom of this container would cause some water to flow into the container having
the lower liquid level. In addition, the pressure of the water at any level (such as line T) is the same
in each of the containers. Pressure increases because of the weight of the water. The farther down
from the surface, the more pressure is created. This illustrates that the weight, not the volume, of
water contained in a vessel determines the pressure at the bottom of the vessel.

1. The pressure depends only on the depth of water above the point in question (not on the
water surface area).

2. The pressure increases in direct proportion to the depth.

3. The pressure in a continuous volume of water is the same at all points that are at the same
depth.

4. The pressure at any point in the water acts in all directions at the same depth.

22.2.5 h ead
Head is defined as the vertical distance the water/wastewater must be lifted from the supply tank
to the discharge or as the height a column of water would rise due to the pressure at its base. A
perfect vacuum plus atmospheric pressure of 14.7 psi would lift the water 34 ft. When the top of the
sealed tube is open to the atmosphere and the reservoir is enclosed, the pressure in the reservoir is
increased; the water will 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 . Consider
water in an open reservoir subjected to 14.7 psi of atmospheric pressure; subtracting this 14.7 psi
leaves a gauge pressure of 0 psi, indicating that the water would rise 0 feet above the reservoir sur-
face. If the gauge pressure in a water main were 120 psi, the water would rise in a tube connected
to the main: