By C.F. ‘Chubb’ Michaud, CWS-VI

In Part 2 of this series, we will address the relationship between flow and pressure through pipes. This should help the reader understand that pushing high flows through small pipes not only takes more energy but is a big waste of money.

To avoid higher energy consumption , it is always better to use a larger pipe than a larger pump.

Water flows at different rates through different sections of a pipe
Fluid flowing through a pipe does not flow uniformly from edge to edge. Just like a river, flow is faster through mid-stream and almost nonexistent towards the edges. This is illustrated in Figure 1.

The boundary layer of water right against the pipe wall (also called the ‘Nernst’ layer) has a linear velocity of zero represented by the red areas. As water moves towards the center of the pipe, the flow increases, which is illustrated by the transition to yellow. Green represents full flow. If we envision the fluid flow through a conduit as sheets or cylinders of molecules sliding over one another, we can appreciate that there is friction between the layers, which contributes to a loss of energy and a subsequent drop in pressure through the pipe. If we increase the pressure, the flow increases and the transition zone against the pipe becomes thinner and more turbulent. Fluid flow with high turbulence consumes far more energy than does laminar (smooth) flow. It takes four times the energy (pressure) to double the flowrate, as illustrated in Figure 2 (note that yellow boxes indicate pipe diameters). In designing systems, we try to avoid high linear flow because it costs more in power and the added turbulence adds to the wear factors on the pipe, tanks, valves and media.

The red outlined rectangle shown in Figure 2 represents relative pressure drops of 10 to 20 psi of pressure drop (23.2 to 46.2 ft of head) for the equivalent of 100 feet of straight pipe. This is also called ‘delta P’ (change in pressure) and is represented by the Greek letter delta (D) and the letter P or DP. This is at linear flow velocities of around 3 to 15 ft per second, considered the normal flow range for pipe. To translate this from linear flow to volumetric flow we show the conversion in Table 1. This table shows the flow range corresponding to the parts of the curves in Figure 2 that fall within the red box. The blue line shows a specific 15 psi DP.

We have all used the general rule of thumb that flow through a pipe should be no more than 8 to 10 linear feet per second (fps). Here we note that the larger the diameter, the more easily it can tolerate the turbulence induced by the drag of fluid flowing within the pipe. This is because the Nernst layer is nearly constant in terms of its thickness and it becomes a lower percentage relative to the total flow through the pipe as the pipe size increases. This allows for a more laminar flow transit of fluid. Table 1 shows that water flowing at 3 gpm through a half-inch pipe will have the same DP as water flowing 19.3 gpm through a one- inch pipe (more than six times the flow and only four times the cross-sectional area). Obviously, when the pressure in the system is furnished from city water, it makes a lot more sense to use a larger pipe for keeping customers happy. The pressure is free.

The factors that come into play in fluid flow and energy use are the viscosity of the water (determined by temperature but usually considered to be constant), the size of the pipe and the linear flowrate. Total energy use (as determined by pressure requirements) also takes into account the number of joints, the length of travel and elevation change. Colder water will produce more resistance to flow and require more energy to move than will warmer water. You might consider upsizing the pipe if the water temperatures are less than 40°F (5°C). Also, a larger home will have more long runs of pipe and pressure losses as well (more to come in Part 3).

The relationship between flowrate and pressure drop
The relationship of flow to DP states that the pressure increases by the square of the value of flow. If the flow doubles, the DP increases by four (2 x 2 = 4). If it triples, DP goes up by nine (3 x 3 = 9). If you cut the flow in half, the DP decreases by a factor of four (1/2 x 1/2 = 1/4). Keep in mind that the DP shown in Figure 2 is per 100 feet of straight and perfectly smooth pipe. A six-foot run of half-inch copper pipe to connect a 2.5-gpm shower off a three-quarter-inch line decreases the pressure by about 1 psi. On the other hand, if you run a half-inch line from the kitchen to the barn 200 feet away, you may not be able to fill a bucket with water before the cows come home.

Inside the pipe, flowing water causes an energy loss due to the friction. It takes energy to push past the pipe surface, no matter how smooth the pipe is. This reduces the pressure available to push water out the end of the pipe. The pressure loss due to friction occurs at every point along the pipe; when water starts to flow, the pressure is highest at the source and decreases every inch along the way and is lowest right at the tap. If we wanted to move 3 gallons per minute (gpm) through half-inch-diameter pipe, 100 feet long, we might lose about 7 psi of pressure. If the pressure at the beginning of the pipe is 60 psi, the pressure at the end would be 53 psi. Flows (or flowrates) are measurements of the volume of water that comes out of the tap every minute. Hydraulic design must take into account the dynamic pressure available under flowing conditions at the point of use and not the static pressure available in a non-flowing condition.

NOTE: An easy rule I follow in determining pipe size is that 4-inch pipe with an internal flow velocity of 10 ft/sec is rated at 400 gpm. Therefore, 2-inch pipe (half the size) would handle one-fourth the flow or 100 gpm. It would follow that 1-inch pipe would do 25 gpm and half-inch pipe would be at 6.25 gpm. Figure 2 illustrates that smaller pipe diameters are less forgiving.

Are there negatives for running high linear flows through pipes besides the higher pressure drop and energy costs? Yes, there are. Higher water flow induces higher wear and corrosion inside pipes, as well as increased noise levels. This is especially true if the water is forced to change direction, such as going through an elbow. In addition, high flowrates increase the DP, which releases more carbon dioxide from the water, which in turn, will corrode pipes and fixtures more rapidly and cause dezincification of brass.

Pressure versus flow
Pressure is a measure of the force of water per unit of area (psi). Flow is a measure of the volume per unit time (gpm). The flow and pressure are related by the following equation:

Equation 1.
q = 20d2 p½
Where:
q = rate of flow at the outlet (in gpm)
d = actual inside diameter (ID) of outlet (in inches)
p = flow pressure (in psi)

Example 1.
Assume a hose bib with a three-quarter-inch supply line and the flow pressure is 9 psi. Calculate the expected flowrate.
q = 20 x (3/4)2 x (9)½
q = 20 x 9/16 x 3
q = 33.8 gpm

Example 2.
Assume a faucet connected to a three-eighths-inch line and a flow pressure of 16 psi
q = 20 x (3/8)2 x (16)½
q = 20 x 9/64 x 4
q = 11.25 gpm

Summary
Long runs of pipe can take a drastic toll on available working pressure at the point of use. This DP does not show up with a static pressure test done at an outside hose bib. At 10 gpm, a three-quarter-inch line will show a DP of 20 psi/100 feet of pipe run. A half-inch irrigation run suffers a 35 psi drop in pressure if trying to deliver 10 gpm. A one-inch pipe will see 15 psi at those flows.

References

1. www.pressure-drop.com/online-calculator/index