By C.F. ‘Chubb’ Michaud CWS-VI

Pressure is the driving force of fluid flow, but how is it measured and what does it mean? Part 1 of this series introduces the concept of pressure and how it is transmitted from point to point.

Hydrodynamics: the applied science of fluid flow
There are two very important considerations in the design of a water filter. One is that the performance characteristics of the media selected are matched to the job. If you don’t do that part right, there is absolutely nothing you can do to remedy the situation short of changing the media. The second is in giving that media a chance to perform. The latter has to do with the flowrates of the water relative to the media, tanks and pipes. That technology is called ‘hydrodynamics’ and it is governed both by the laws of physics and the laws of common sense. This article is Part 1 in a series and will address the design considerations for sizing based on sound hydraulic principles.

Pressure: the driving force of fluid flow
No presentation on fluid flow would be complete without a brief discussion on a few fundamental terms. Pressure is the driving force of all fluid flow. It is reported as units of force per unit of area; i.e., pounds per square inch (psi) or kilograms per square centimeter. Picture a cylinder of cross-sectional area of 10 inches squared and a height of 20 feet or 240 inches, filled with water. We can calculate the volume of the water as the area times the height or 10 in2 x 240 in = 2,400 in3. Since a cubic foot (cu. ft.) of water weighs 62.4 lbs. and contains (12 x 12 x 12 =) 1,728 in3, we can determine the weight of the water as 2,400 in3/1,728 in3/ cu. ft. x 62.4 lbs./cu. ft. = 86.67 lbs. So there is 86.67 lbs. of force sitting at the bottom of the cylinder. Since the bottom of the cylinder has a surface area of 10 in2, we therefore have a pressure of 86.67 lbs./10 in2 = 8.67 psi.

The 20 feet represents head pressure measured in feet and referenced as feet of head (pressure). Since 20 feet of head is equal to 8.67 psi, 1 psi is therefore equal to 20 ft. of head/8.67 psi = 2.31 feet of head per 1 psi. A reservoir, 25 feet deep whose bottom is located at the top of a hill 120 feet above a fire hydrant would apply a pressure of 120 + 25 = 145/2.31 = 62.8 psi at the hydrant. This is referred to as static head pressure or no-flow pressure. It doesn’t really matter how large or long the pipe is connecting the reservoir and the hydrant. The static pressure will be 62.8 psi purely due to the level of water above the hydrant, its density and the forces of gravity.

Gauge versus absolute pressure
The Earth’s atmosphere contains molecules of air and water vapor that have measureable mass that is pulled downward by gravity. The force applied at sea level can be measured at 14.7 psi, referred to as 1 atmosphere (1 atm). This pressure is also represented as 1 bar or 1,000 millibars (mbars)* or the metric term 100,000 pascals (Pa) or 100 kPa (kilopascals). This pressure is not read on a pressure gauge and is referred to as absolute pressure. Since the same additional (atmospheric) pressure is applied equally at both the top and bottom of our reservoir and hydrant, they cancel each other out mathematically. Pressure gauges are set to measure zero for this reason. This is referred to as gauge or gage pressure and is sometimes written as psig to differentiate it from absolute (psia). Unless you are installing a water filter in outer space, stick with the gauge reading.

Since 1 atm = 14.7 psi, how many feet of head pressure does this amount to? With 2.31 ft. of head = 1 psi, we can calculate the equivalent as 2.31 x 14.7 = 33.9 ft. Because mercury (Hg) is 13.55 times denser than water, 1 atm also = 33.9 ft. x 12 in./ft. = 406.8 inches and divided by 13.6, we have an equivalent of 29.92 in. of Hg. Barometric pressure reports atmospheric pressure in inches of Hg absolute because the original measuring devices were mercury-filled tubes called manometers which could measure atmospheric pressure versus a near-perfect vacuum. References to barometric pressure in connection to a weather report are still in use. Aircraft use barometric pressure to determine altitude (the less air overhead, the less pressure).

Pump lift limitations
If you have worked with wells, you will know that well pumps push water up to the surface; they don’t suck it up. Since atmospheric pressure is only equal to about 33 ft. of head, that becomes the maximum height the atmosphere can push water, even into a perfect vacuum. This is something one has to think about. If you took a 35-foot-long transparent glass pipe, capped on one end, filled it with water and stood it on end in a bucket of water, the water in the pipe would drop down to a level of about 33 feet with a near perfect vacuum above it. No matter how much suction a pump could apply to the top of a pipe, it would be impossible to draw water any farther up the pipe than about 33 feet.

Italian physicist Evangelista Torricelli (1608-1649) made a discovery in 1643 while trying to solve the problem of limited pump lift. He sealed one end of a one-meter-long glass tube, filled it with mercury and inverted it into a bath of mercury. The level of the mercury in the tube fell to about 76 centimeters (29.92 inches). He had just invented the barometer and the vacuum above the mercury became a Torricellian vacuum.1 This same vacuum can form inside the suction side of a pump head if the feed inlet is too small or restricted as a means of flow control. Throttle pump flow from the pressure side, not the suction side to avoid cavitation and destroying your pump. Table 1 presents a handy guide for converting various pressure units.2

Static pressure versus dynamic pressure
Now let’s imagine that we have two hydrants. Hydrant A is connected to a six-inch-diameter pipe and across the street is hydrant B, which is connected using a one-inch-diameter pipe; both pipes run all the way to the top of the hill. Both have a static pressure of 62.8 psi. With both hydrants wide open, which supports the higher flow?

The pressure available to hydrant A will be considerably higher than that of hydrant B because the smaller pipe connecting B will present more resistance to flow (friction losses). The working pressure available at the point of use is called net or dynamic pressure and refers to the original pressure (static), less the losses of energy due to flowrate and distance. A point to keep in mind when designing or installing filtration equipment is that it is the dynamic pressure that counts. This really comes into play on twin alternating systems (more on that later).

When measuring the water pressure at a convenient hose bib at the front of a customer’s house, static pressure is being measured. If there are flow restrictions in the pipe or the plumbing layout is long, there may not be sufficient pressure at the point of use to support a POU filtration device. Pressure at the point of use should be measured with at least one faucet turned on to accurately measure the dynamic pressure that will drive the device. Keep in mind that a second-floor bathroom will not have the same operating pressure as the first floor and a guest bath on the third floor might not support a high-flow shower.

Pressure transmission
Within a vessel, fluid pressure is transmitted equally in all directions. A garden hose under 80 psi from a city water inlet can lift a 5,000-pound automobile when connected to a hydraulic cylinder about nine inches in diameter. Pressure, in psi, means exactly that. You have 80 pounds of static pressure for every square inch. A six-foot-diameter tank has a surface area of 19.6 ft2 or 2,826 in2. At 80 psi, 226,080 pounds to the top of your filter bed, or 113 tons is being delivered! Is it any wonder that resin beads break?

Summary
Pressure is the driving force of fluid flow. It is transmitted equally in all directions. Friction within the flow circuit causes a loss of pressure that has to be taken into account when designing any in-line water filtration device. There must be enough residual pressure to allow the device to function properly both in service and regeneration.

*Hurricane Sandy in October 2012 came ashore with a barometric pressure reading of 943 mbar. This is the equivalent of 13.86 psi atmospheric. This reduced atmospheric pressure is what caused the ocean surges and the rise in sea level.

References