CAPÍTULO 2 MODELOS DE REPRESENTACIÓN TEXTUAL
2.7 CÁLCULO DE SIMILITUD
10.7.1 Pump Hydraulic Selections and Specifications
10.7.1.1 Pump operating ranges Identify the minimum, maximum, and design flows for the pump based on the hydraulic analyses described above. See Fig. 10.14 as an example.
• The flow at 100 units would be defined as the design point.
• There is a minimum flow of 90 units.
• There is a maximum flow of 115 units.
In multiple–pump operation, the combination of varying static head conditions and the different number of pumps operating in parallel could very likely result in operating points as follows (100 units flow at BEP; see accompaning Table 10.7).
Table 10.7 Pump Operating Ranges
Operating Flow Condition Flow Comments
(per Pump)
Minimum 70 Maximum static head condition,
all pumps operating
Normal 1 100 Average or most frequent operating
condition: fewer than all pumps operating, average static head condition. Might also be the case of all pumps operating, minimum static head condition.
Normal 2 110 Fewer than all pumps operating,
minimum static head condition
Maximum 1 115 Maximum static head condition,
one pump operating
Maximum 2 125 Minimum static head condition,
one pump operating
FIGURE 10.14Determining the operating points for a single-speed pump with variation in values of hstat.
Some observations of the above example are:
• The flow range of an individual pump is about 1.8:1 (125 70).
• The pump was deliberately selected to have its most efficient operating point (Q 100) at the most frequent operating condition, not the most extreme condition. This will result in the minimum power consumption and minimum power cost for the system.
• The pump was selected or specified to operate over all possible conditions, not just one or two conditions.
In variablespeed pumping applications, the minimum flow can be much lower than what is shown in these examples. It is extremely important that the minimum flow be iden-tified in the pump specification so that the pump manufacturer can design the proper com-bination of impeller type and shaft diameter to avoid cavitation and vibration problems.
10.7.1.2 Specific pump hydraulic operating problems. Specific problems that can occur when operating a centrifugal pump beyond its minimum and maximum capacities include (Hydraulics Institute, 1994):
• Minimum flow problems. Temperature buildup, excessive radial thrust, suction recir-culation, discharge recirrecir-culation, and insufficient NPSHA.
• Maximum flow problems. Combined torsional and bending stresses or shaft deflection may exceed permissible limits; erosion drainage, noise, and cavitation may occur because of high fluid velocities.
10.7.2 Piping
Having selected a pump and determined its operating flows and discharge heads or pres-sures, it is then desirable to apply this data in the design of the piping. See Fig. 10.12 for typical piping associated with a horizontal centrifugal pump.
10.7.2.1 Pump suction and discharge piping installation guidelines. Section 1.4 in the Hydraulic Institute (HI) publication ANSI/HI 1.1–1.5 (1994) and Chap. 6 in API Recommended Practice 686 (1996) provide considerable discussion and many recom-mendations on the layout of piping for centrifugal pumps to help avoid the hydraulic prob-lems discussed above.
10.7.2.2 Fluid velocity. The allowable velocities of the fluid in the pump suction and dis-charge piping are usually in the following ranges:
Suction: 3–9 ft/s (4–6 ft/s most common) 1.0–2.7 m/s (1.2–1.8 m/s most common) Discharge: 5–15 ft/s (7–10 ft/s most common)
1.5–4.5 m/s (2–3 m/s most common)
Bear in mind that the velocities will vary for a given pump system as the operating point on a pump curve (i.e., intersection of the pump curve with the system curve) varies for the following reasons:
1. Variation in static heads, as the water surface elevations in both the suction and dis-charge reservoirs vary
2. Long-term variations in pipeline friction factors (Fig. 10.5) 3. Long-term deterioration in impeller (Fig. 10.7)
4. Variation in the number of pumps operating in a multipump system (Fig. 10.8).
A suggested procedure for sizing the suction and discharge piping is as follows:
1. Select an allowable suction pipe fluid velocity of 3–5 ft/s (1.0–1.5 m/s) with all pumps operating at the minimum static head condition. As fewer pumps are used, the flow output of each individual pump will increase (typically by about 20 to 40 percent with one pump operating compared to all pumps operating) with the resulting fluid veloci-ties in the suction piping also increasing to values above the 3–5 ft/s (1.0–1.5 m/s) nominal criteria;
2. Select an allowable discharge pipe fluid velocity of 5–8 ft/s (1.5–2.4 m/s) also with all pumps operating at the minimum static head condition. As discussed above, as fewer pumps are used, the flow output of each individual pump will increase with the result-ing fluid velocities in the discharge pipresult-ing also increasresult-ing in values above the 5–8 ft/s (1.5–2.4 m/s) nominal criteria.
10.7.2.3 Design of pipe wall thickness (pressure design) Metal pipes are designed for pressure conditions by the equation for hoop tensile strength:
t 2
D inside diameter, in or mm (although in practice, the outside diameter is often conservatively used, partly because the ID is not known initially and because it is the outside diameter (OD) that is the fixed dimension: ID then varies with the wall thickness)
P design pressure (psi or kPa)
S allowable design circumferential stress (psi or kPa) E longitudinal joint efficiency
The design value for S is typically 50 percent of the material yield strength, for “nor-mal” pressures. For surge or transient pressures in steel piping systems, S is typically allowed to rise to 70 percent of the material yield strength (American Water Works Association 1989).
The factor E for the longitudinal joint efficiency is associated with the effective strength of the welded joint. The ANSI B31.1 (American Society for Mechanical Engineers, 1995) and B31.3 (American Society for Mechanical Engineers, 1996) codes for pressure piping recommend the values for E given in Table 10.8
TABLE 10.8 Weld Joint Efficiencies
Type of Longitudinal Joint Weld Joint
Efficiency Factor (E) Arc or gas weld (steel pipe)
Single-butt weld 0.80
Double-butt weld 0.90
Single-or double-butt weld with 100% radiography 1.00
Electric resistance weld (steel pipe) 0.85
Furnace butt weld (steel pipe) 0.60
Most steel water pipelines 0.85
Ductile iron pipe 1.0
The wall thickness for plastic pipes [polyvinyl chloride (PVC), high-density polyeth-ylene (HDPE), and FRP] is usually designed in the United States on what is known as the hydrostatic design basis or HDB:
Pt D
where Pt total system pressure (operating surge), t minimum wall thickness (in), D average outside diameter (in), HDB hydrostatic design basis (psi) anh F factor of safety (2.50–4.00)
10.7.2.4 Design of pipe wall thickness (vacuum conditions). If the hydraulic transient or surge analysis (see Chap. 12) indicates that full or partial vacuum conditions may occur, then the piping must also be designed accordingly. The negative pressure required to col-lapse a circular metal pipe is described by the equation:
∆P (1
where∆P = difference between internal and external pipeline pressures (psi or kPa) , E = modulus of elasticity of the pipe material (psi or kPa),µ = Poisson's ratio, SF = safety fac-tor (typically 4.0), e = wall thickness (in or m) anh D = outside diameter (in or m)
Because of factors such as end effects, wall thickness variations, lack of roundness, and other manufacturing tolerances, Eq. (10.3b) for steel pipe is frequently adjusted in practice to
10.7.2.5 Summary of pipe design criteria. The wall thickness of the pump piping sys-tem is determined by consideration of three criteria:
1. Normal operating pressure [Eq. (10.34)], with S 50 percent of yield strength 2. Maximum pressure due to surge (static dynamic transient rise), using Eq. (10.34)
with S 70 percent of yield strength (in the case of steel pipe)
3. Collapsing pressure, if negative pressures occur due to surge conditions (Eq. 10.36).
10.8 IMPLICATIONS OF HYDRAULIC TRANSIENTS