# Engineering of Water Systems

### Part 17(a)—Mechanical Design, Piping, Part 1

By Ed Butts, PE, CPI

As we proceed with this series on engineering water systems, we have now arrived at one of the most important, but often overlooked, elements of a complete design. Namely, effective and efficient design of the required mechanical equipment including the piping, valving, and related equipment needed to complete connection to a pumping installation or plant.

This four-part subseries will introduce you to the fundamental concepts of good mechanical subsystem design. This first installment will primarily outline underground piping design, including selection of the appropriate material and wall thickness for both internal and external loads.

Part 2 will outline and provide an overview of the many methods of corrosion protection, including coatings and linings and a review of above-ground piping. Part 3 will outline the variables and options available for effective valving on both suction and discharge sides for pumps and water systems as well as the needed support equipment. Part 4 will go over the multitude of control valves available for all types of water applications.

### Mechanical Systems

The mechanical subsystem for a pumping plant can consist of various elements, each with a specific duty, purpose, and placement. For purposes of this discussion, the mechanical subsystem will consist of the piping, including manifolds and underground piping; specialized and typical valving; and support equipment like pressure switches and gauges for both inlet and discharge sides of a typical plant.

Conduits for water transmission can take many forms. They consist of closed pipelines and open flow channels such as ditches, flumes, and triangular and partial circular open channels.

Closed conduits are generally circular in cross-sectional shape, owing to the superior carrying capacity per diameter relationship. However, they can be configured from several types of materials such as aluminum, steel, copper, cast and ductile iron. Also, various types of thermoplastics including polyvinyl chloride (PVC), chlorinated polyvinyl chloride (CPVC), low density polyethylene (LDPE), medium density
polyethylene (MDPE), high density polyethylene (HDPE), and cross-linked polyethylene (PEX or XLPE).

Closed channel conduits, commonly referred to as pipelines, are the most common type of water transmission and distribution conveyance method in use today. They are able to effectively transmit the flow of water and other liquids in heads from just a few feet or less (1-2 psig) up to a thousand feet or more of head or pressures exceeding 500 psig. This discussion will largely surround flexible materials, such as PVC and PE.

### Piping

The piping design for a water pumping station or water system primarily involves three separate factors:

1. The required internal and external pressure (head) the piping must withstand
2. The specific short- and long-term corrosive or incrusting properties of the fluid being pumped onto the pipe’s interior surfaces that affect the roughness (i.e., friction) of the interior pipe wall along with the impact burial and underground conditions may have on the pipe and exterior surfaces, to be covered in Part 17(b)
3. Designer preference, cost, and local customs plus environmental and/or code limitations, (Part 17b).

### Internal Pressure Design

The ability of a pipe to withstand a given internal pressure is a direct function involving the type of material used, the allowable unit stress in the material, and the wall thickness of the pipe. This stress is called hoop stress and illustrated in Figure 1.

The basic determination of the required wall thickness is a factor involving the outside diameter and allowable unit stress and is figured through an equation called Barlow’s Formula:

t =

where:
t = Required wall thickness in inches
P = Internal maximum design or operating pressure, in psi
(for head: multiply feet of head × 0.433)
D = Outside diameter of pipe in inches
S = Allowable design stress in psi
Variations on this formula are:
P = [(2)(S)(t)]/D or
S = (2)(t)(P)(D) or
D = [(t)(2)(S)]/P

It is important to note the values in Table 1 reflect the maximum allowable unit stress in the applicable pipe material only and do not include any factoring or derating for corrosion or the method of connection to flanges, fittings, joints, etc.

Where pressurized pipes are to be used, an additional factor should be included for corrosion (recommended minimum is 1/16 inch = 0.0625 inch) and weld or joint efficiency allowances, as required for both.

Example: What wall thickness is required for a 16-inch outer diameter pipe manifold to be made using ASTM/ANSI A106-Grade B steel with a maximum internal design pressure of 125 psi? No ASME correction is required.

Wall thickness =

= 2000 = 0.0571 inch + 0.0625 inch corrosion allowance 35,000
= 0.1196 inch

Even though the use of ⅛-inch (0.125 inch) wall thickness would technically be permitted, I would tend to err on the side of caution and probably go up in thickness to use ¼-inch (0.250 inch) wall thickness steel pipe. And using this thicker pipe wall will also provide easier welding and fabrication than using a thinner wall pipe and provide some allowance for possible future corrosion.

### Design (Safety) Factor

Although the stated design stress values indicate the maximum allowable stress for all thermoplastics, copper, and cast/ductile iron, many of the steel materials shown in Table 1 reflect fairly conservative values to allow for manufacturing variations. They also allow for chemical composition and field tolerances for cyclic stress from varying pressures and assume a maximum operating temperature of 200°F with underground conditions, and therefore may be lower than and not coincide with published values.

In many cases, particularly with cold water and adequate engineering supervision, most of the allowable steel stresses can be increased to higher values, up to 20%. Although the use of Barlow’s Formula provides a reliable and reasonably accurate determination of wall thickness for circular pressurized vessels or pipe, many applications require the further consideration of environmental or exposure factors as additional safety factors.

These added factors are usually applied where American Society of Mechanical Engineers (ASME) codes apply and are described as Class 1 through Class 4 locations with applicable design factors ranging from 0.72 to 0.40, respectively. These additional design factors are particularly important to apply for underground or under-structure pipelines that carry high pressure commodities, such as gas or steam. In these cases, the resulting pressure determined from Barlow’s Formula is multiplied (or divided) by the appropriate design factor to arrive
at the maximum allowable or design pressure.

For example, in a Class 4 exposure with a design factor of 0.40, a calculated or design pressure of 125 psi used in Barlow’s Formula would be modified as follows.

### Designing for Water Hammer and Surge Pressures

All pressure piping must include a factor for water hammer and pressure surges from thrust developed from internal pressure and fluid velocity.

Even though you will not likely find this in any texts, my definition of water hammer is: “The rise in pressure due to changes in pipeline velocity resulting in a surge pressure which, in turn, contributes to the combined pressure that occurs from the water hammer event along with the background pressure.”

Although the velocity component is minor compared to the thrust developed from pressure, it must be considered nonetheless at changes of direction, such as ells or tees.

The surge or rise in pressure developed in a pipeline is a function of the material’s elasticity; initial and final fluid velocity in feet per second; wave speed, generated from valve closure time; and the bulk modulus of the fluid under transit. Typically, the more flexible a material, the lower the surge pressure.

An obvious example of this is comparing steel pipe to PVC pipe. PVC, with a modulus of elasticity of 400,000 psi, is around 75 times less than steel. This means PVC will expand more than steel pipe during a surge event, generating much lower water hammer pressure. The information in Table 2 has been prepared as a shortcut method of determining the approximate pressure rise and wave speed in a pipeline for different materials for each foot per second (fps) of velocity change.

Based on the rule of thumb estimate, an instantaneous change of velocity of 6 feet per second would result in a pressure rise of approximately 90 psi (i.e., ΔV = 6 fps × 15 psi/Δfps) with Class 160 psi IPS PVC pipe.

With AWWA C-900 DR 25 (Class 165 psi) PVC pipe, this same change in velocity will also result in an estimated surge pressure of 90 psi. At matched velocities, this indicates the pressure rise is due to roughly the same degree of elasticity of the material in pressure rated Class 160 psi IPS PVC pipe as it is with Class 165 psi pressure-rated C-900 PVC pipe. Simply put, the IPS will stretch to accommodate a surge in the same manner and approximate amount as the C-900 pipe class at the same pressure rating.

A steel pipe under comparable conditions will experience an estimated surge of 6 fps of ΔV × 60 psi = 360 psi, or around four times the PVC surge. This advantage of lower surge pressures with PVC must always be tempered with the knowledge that thinner-wall PVC pipe is inherently weaker in strength than thicker-wall PVC or steel pipe, and may not withstand the same degree of higher pressures.

However, if we use the Table 1 estimated value of 20 psi for each 1 fps of ΔV for DR 14 (Class 305 psi) C-900 PVC pipe from the first example, it is apparent the estimated surge of 6 fps of ΔV × 20 psi = 120 psi is considerably higher than the original estimated value of 90 psi. Therefore, it is obvious that with the material and diameter being virtually equal, the only real variable—wall thickness—plays a significant role in the actual surge value even when using the same type of pipe.

Always remember the value of surge pressure must be added to the working pressure to determine the total pressure the pipe must withstand. Even when using the same material, this variance to balance the selection of a pipe’s wall thickness with the amount of a pressure spike generally requires careful judgment and appraisal with a full system evaluation and surge analysis by the system designer.

### Thrust Restraint

Thrust is a component in all pressurized pipelines and some gravity and open channel flows resulting from the combined forces of internal pressure and fluid flow (velocity). It does not generally cause any issue with low pressure circular pipelines or open channel flow since the pressure forces are uniformly distributed throughout the full circumference and the generated head values are low enough that extreme thrust due to operating pressure is not a concern.

It does, however, result in unbalanced forces in pressurized conduits at changes of direction such as ells and tees, reductions in flow area as those that occur in pipe size reducers or cones, or reductions in pressure across a valve.

There are two separate components that together create the total thrust: the first is the force due to flow mass (pipeline velocity) and the second results from the internal pressure. The sum of these two forces are considered as the total thrust.

Although the materials that go into a pressurized pipeline may easily handle the internal stress resulting from the applied pressure—per Newton’s third law of “for every action there is an equal and opposite reaction”—this is the reason piping must be restrained in some manner. The flow component of thrust (i.e., velocity) is relatively low compared to the much greater value associated with the static or dynamic line pressure.

Generally, thrust values for pipelines are determined for various pressures and pipe sizes and shown on prepared charts or graphs to reflect the soil-bearing area in square feet or concrete mass (for gravity thrust blocks) in volume of cubic feet required to resist the thrust. Therefore, the ordinary daily use of these formulas is usually not necessary, but it is helpful to understand their relationship to pipe thrust nonetheless.

Thrust must be resisted to prevent lateral pipe movement and resulting joint separation even in normal service, and if severe enough, can result in dangerous and damaging surge conditions usually referred to as water hammer.

Thrust is generally resisted using the following methods:

1. Bearing thrust blocks: This method of thrust restraint uses a counteracting material, generally concrete, that is placed between the pipe fitting and earth. The block is distributed over an adequate area of bearing surface to maintain the soil stress to 2000 psf or lower. Bearing thrust blocks can be placed directly against soil or used as cutoff collars as intermediate thrust resistance.
2. Gravity thrust blocks: This type of thrust block is generally used when the bearing capacity or projected area of the soil is inadequate to provide primary thrust resistance. In this case the block, almost always composed of concrete, uses the dead weight (145 pounds per cubic foot or approximately 3900 pounds per cubic yard) of the concrete to counteract the imposed thrust with little or no contribution from the soil-bearing strength.
3. Pipe joint restraint: This method uses specialized joint restraints to maintain the integrity of the connection. The restraint can consist of tie-rods around the joint to a coupling or a compression sleeve engaged onto the pipe, serrated teeth, wedges, or pins that bite into the pipe’s wall, or mechanical resistance between the pipe and joint from PVC solvent weld joints.
4. Backfill resistance: The weight imposed from backfill can provide some partial resistance against thrust, but this value should never be used as a primary resistance factor since the friction coefficient placed against the pipe is an unpredictable and unreliable value.

### External Pressure Design

In addition to the internal pressures pipe must handle, there is often a factor involving external stress the pipe must also handle.

Depending on the pipe material, diameter, and wall thickness— as well as trench type, burial depth, presence or lack of overlying groundwater, and type of backfill—a pipe may not experience any undue external stress or could suffer enough to result in collapse of the pipe.

The behavior of rigid and flexible pipe in a buried condition is widely different. Rigid pipes such as steel, concrete, and small-diameter ductile iron use their inherent ring strength characteristics and load distribution to resist backfill weight and usually fail suddenly due to crushing forces from overloading. Flexible buried pipe such as PVC and HDPE meanwhile depend on a combination of factors to withstand the potential crushing or collapse from the imposed weight of backfill. Among these are the strength developed by the pipe as an arch,
the depth of backfill, and the type of backfill.

As seen in Figure 2, external pressure is generally applied from the height of backfill material (C) over a buried pipe (underground) condition and the presence of groundwater over the pipe (HW). In other situations, also shown in the figure, depending on the offset distance (D) from the pipe, superimposed loads from other sources such as vehicular traffic, railway, or other loads (PS) may also increase the pipe load.

Proper pipeline installation involves much more than just covering up the pipe. Always remember a buried pipe is a quasi-structure that incorporates the combined properties of the pipe to resist the surrounding backfill. The structural design of a pipeline is based on specific soil conditions and intense control of the construction process, which is important to ensure the design conditions and intent are met.

There are two basic types of pipe in common use: rigid and flexible. Rigid pipe includes reinforced concrete pipe (RCP) and ductile iron (DI) pipe under 24 inches diameter while flexible pipe includes all thermoplastics such as PVC, CPVC, HDPE, PE, and fiberglass as well as steel, corrugated metal pipe (CMP), pretensioned concrete cylinder pipe (PCCP), and ductile iron pipe greater than 24 inches in diameter.

While rigid pipe must be primarily supported on the bottom portion of the pipe, flexible pipe must be supported on both the bottom and on the sidewalls of the pipe, as illustrated in Figure 3.

Proper soil support under and around the pipe is critical to the proper performance and longevity of both types of pipe. Likewise, proper installation and inspection of the pipe installation is essential in obtaining the required support.

Verification for proper soil support involves checking the following factors:

• Adequacy of the parent soil in the trench walls and foundation to support the pipe, particularly the support soil
• Type and consistency of the soil used for bedding, embedment, and backfill. (Soil classification is generally based on the Modulus of Soil Reaction-Table 6 (ASTM Designation D 2487, USBR Designation E-3.)
• Distribution and compaction of the backfill around the pipe
• Density of backfill soil around and over the pipe
• Permissible and actual deflections of flexible pipe (shown as ΔY and ΔX in Figure 4).

The weight from the soil load is often the sole dead load consideration. However, forces from high groundwater and nearby permanent foundations are also types of dead loads and should be incorporated into the design whenever appropriate.

Live loads change in position or magnitude, whereas dead loads are assumed to remain reasonably constant throughout the design life of the pipe. The determination of live load is important for pipe with a shallow burial depth of less than 8 feet, as the effects of live loads decrease as the depth of cover increases and the load is distributed across a wider area.

There are two distinct types of dead and live loads that impact buried pipe. The first load, considered a dead load and called the prism load, is based on the progressive prismatic or triangular type of loading that occurs on the pipe from the increasing deadweight of soil due to the accumulated effects of additional depths of backfill pressing down on the pipe. It is shown for depths between 1 foot to 40 feet and soil unit weights in Table 3.

The second load conditions are the live loads. There are many methods used to calculate live loads, and Table 4 has been developed for the three standard types of live-load conditions: highway or vehicular, railroad, and airport.

Variable, or live, loads are usually considered as transitory or temporary loads—as they pass over the pipe and then rapidly diminish. However, the cyclic condition of these loads can cause increased fatigue in the pipe wall from repeated cycles of stress followed by immediate relaxation.

This is particularly evident in applications where the pipe is adjacent to or under a roadway and buried at a relatively shallow depth as it can experience an additional force from the rolling motion of the vehicle traveling over it. To account for this additional force, the stationary vehicular load is multiplied by an impact factor.

For highway loads, the American Association of State Highway and Transportation Officials (AASHTO) establishes a range of impact factors from 1.30 at 1 foot (0.3 m) of cover to 1.10 at depths just under 3 feet (1 m) that should be used. However, impact has negligible influence at burial depths over 3 feet (1 m) and can generally be disregarded.

Table 4 provides information about the resultant H-20, E-80, and airport forces at various cover heights from 1 to 30 feet with impact factors included in the shallow cover situations.

Resultant loads for H-25 vehicle loads can be estimated by increasing the tabular values by 20%. Typically, live loads at burial depths exceeding 30 feet are considered negligible and can usually be disregarded. In other cases, particularly with flexible pipe dead loads, burial depths over 20 feet are often contraindicated as even the normal stress to the pipe may be too great.

These values are widely used throughout the industry, even though values based on alternative computation methods can be substituted. As opposed to prism loads, the intensity of the vehicular load decreases as the depth increases, but the area over which the force acts increases.

### Pipe External Load Design Factors—Deflection

When the other salient design elements of pipeline selection such as hydraulic efficiency, pressure rating, and friction losses have been satisfied, the remaining design issue is generally the external pipe load.

As discussed earlier, this factor includes both dead and live loads and is usually not a major concern unless the pipe is buried very deep or very shallow.

For flexible pipe, the ultimate deciding factor for external loads is not breakage or fracture common to rigid pipes, but overflexing of the pipe, generally measured by the pipe’s deflection. Deflection (indicated by Δy and Δx in Figures 3 and 4), is the amount of vertical and horizontal movement the crown or top of the pipe (Δy) and the sidewalls (Δx), respectively, experience when fully buried and in service.

To gauge the degree of deflection in an existing or new pipeline design, a designer will typically use an empirical formula called the Modified Iowa Equation. A simplified and conservative form of this equation is shown here:

Deflection (in %) =

where:
Deflection = Percentage of diametric offset distance
LL = Live load on pipe in lbs./in2 (psi) from vehicular or
other loads found in Table 4
PL = Prism load in lbs./in2 found in Table 3
PS = Pipe stiffness in lbs./in2 found in Table 5
E1 = Modulus of soil reaction in lbs./in2 found in Table 6

Example: What is the projected and maximum pipe deflections for the following pipe and backfill conditions?

Pipe size and type: 8-inch Class 160 psi IPS, pipe stiffness = use 115 psi from Table 5

Modulus of soil reaction: Class III with 90% (moderate) proctor backfill density = use 1000 psi from Table 6

Prism soil load: At soil unit weight of 125 lbs./ft3 and a 6-foot burial depth = use 5.21 psi from Table 3

Live loads: next to highway, so vehicular loads apply = use 1.39 psi from Table 4

Deflection (%) =

=

$\frac{66}{78.13}$

= 0.84% (less than 1%)

This value reflects the projected deflection. However, in practice, the maximum deflection at any point within the pipeline length may vary due to inadequate or unconsolidated backfill, variations in backfill unit weight, pipe depths, or the modulus of soil reaction values. Therefore, an appropriate safety factor (percentage of deflection) should be applied to all solutions obtained from the Modified Iowa Equation.

This varies with the degree of compaction shown in Table 6. In this case, referring again to the table, a safety factor value of + 1.0% will apply to 90% backfill density within the moderate density column to estimate the maximum deflection.

Thus, for this problem, the projected maximum deflection would be 0.84% + 1.0% = 1.84%. The generally accepted value of maximum deflection for PVC water service and water well casing type (IPS, C-900, Schedule 40 and 80) pipes is 5.0%, with 7.5% used for PVC sewer (ASTM D3034-SDR 35, ASTM D2729) pipes. Therefore, this value is acceptable as 1.84% < 5.0%.

### Summary

The primary elements of underground pipe design must include four basic considerations:

1. For hydraulic conveyance, limiting the friction loss to an economically viable value against pipe cost
2. Limiting the velocity to a value to reduce the incidence and exposure to water hammer damage (also impacts the friction factor)
3. Limiting the working pressure to a safe level below the maximum material unit stress to avoid pipe failure
4. Limiting the pipe deflection to prevent sidewall splitting or failure or pipe collapse.

With flexible pipe, limiting the deflection is largely a matter of ensuring adequate support under the pipe along with well distributed and compacted backfill to the pipe’s springline as well as sufficient compaction levels above the pipe zone (refer again to Figure 3). By providing good compaction around the pipe and in the pipe zone, the applied loads will be distributed evenly against the pipe and the trench wall and limit the degree of deflection.

_____________________

In the next installment of The Water Works, we will discuss rigid pipe theory in greater detail, the corrosion aspects of pipe selection, and miscellaneous factors such as designer and client preference in pipe selection and design, economic pipe sizing and selection, and code and environmental considerations.

Until then, keep them pumping!

Ed Butts, PE, CPI, is the chief engineer at 4B Engineering & Consulting, Salem, Oregon. He has more than 40 years of experience in the water well business, specializing in engineering and business management. He can be reached at epbpe@juno.com.