NPSHA = Ha (ft.) - Hvp (ft.) + Hs (ft.)
NPSHA = Ha (ft.) - Hvp (ft.) - Hf (ft.) + Hs (ft.)
NPSHA = Ha (ft.) - Hvp (ft.) - Hf (ft.) + Hs (ft.)
Section 2 Power, Efficiency and Energy
Power. Power is defined as a time-rate of doing work. Horsepower (Hp) is the most common unit used to express power requirements for pumping equipment in the United States. One Hp is equal to the work performed over time when a weight of 33,000 lbs. is lifted on foot in one minute (ie. 1 Hp = 33,000 ft.-lbs./min. or 550 ft.-lbs./sec.).
WHp. Horsepower in pumping applications is a function of the fluid density, flow (Q or m) and total head (TH or H) or differential pressure to be developed. Taking water as the basis for calculation at 70∞F and atmospheric pressure (sg = 1.0 and density = 8.34 lbs./gal.), the following formulas can be used to express hydraulic/theoretical Hp (usually called water Hp (WHp) in water supply applications):
where; m = mass flow (lbs./min.)
or, Q = flow (gpm)
H = TH = total head (ft.) Note: (1) sg = 1.0 for most water supply applications and is normally not included
(2) 3960 gal.-ft./min. = (33,000 lbs.- ft./min.) / (8.34 lbs/gal.) = 1.0 Hp (3) WHp = (gpm x psi) / 1714
BHp. The actual or brake horsepower (BHp) of a pump will be greater than the WHp by the amount of losses incurred within the pump through friction, leakage and recirculation. Such losses are accounted for by the pump efficiency (PE). The BHp (shaft Hp - power delivered to the pump) can be expressed as:
where;
or PE = Pump efficiency
Note: (1) PE = WHp / BHP,
(2) BHp = gpm x psi / (1714 x PE)
EHp. Electrical Hp input (EHp) to the motor is used for calculating the overall efficiency (OE) of a pumping unit and motor under test conditions. Power and friction losses associated with cable, piping and fittings can be neglected as settings are generally less than 10’.
where;
or, or, Em = motor efficiency
Note: 1 Hp = 0.746 kW
IHp. Input horsepower (IHp) and EHp are approximately the same in booster applications, but can very significantly as setting depth increases. IHp is used to determine overall plant efficiency (OPE) and takes into account all installation losses (pump, motor, friction, cable, etc.). IHp can be expressed as follows.
where;
or, Hf = friction loss (ft.)
Hp (cable) = cable loss (Hp)
Note: If a variable frequency drive (VFD) is used between the pump and motor, the VFD efficiency should be included in the numerator. Typical VFD efficiencies range from 90-98%.
Efficiency. The efficiency concepts developed previously in the discussion of Horsepower are summarized as follows:
Pump efficiency (PE). PE is the ratio of energy delivered by the pump to the energy supplied to the pump shaft.
Section 2
Overall efficiency (OE). OE is the ratio of the energy delivered by the pump to the energy supplied to the motor input terminals, and generally takes into account only motor and pump efficiency (ie. OE = PE x ME).
Overall plant efficiency (OPE). OPE is the ratio of the energy delivered by the pump to the energy supplied to the entire pumping plant, and takes into account all installation losses.
The subject of efficiency is discussed in greater detail in Section 2D under the general heading of “testing”.
Energy. Energy is normally expressed in terms of kilowatt - hours (kWh) per unit volume. Typical units of measure and the associate calculations are presented as follows.
or
The subject of energy usage and the associated cost of pumping are discussed more completely in Section 2D, under the general heading of “power consumption and cost”.
Viscosity
The viscosity of a fluid (liquid or gas) is that property which offers resistance to flow due to the existence of internal friction within the fluid.
Pumping viscous liquids can present difficult problems for centrifugal pumps. Fortunately, the viscosity changes relative to water in the temperature range commonly encountered in water supply applications (50 - 85°F) can be neglected.
Water is classified as “Newtonial fluid,” which exhibits decreasing viscosity with temperature. Viscosity changes over the temperature range of interest has no direct impact on pump performance; however, pipe friction losses decrease from a maximum value at 32°F by approximately 40% over the temperature range of 32 - 212°F. Piping friction loss tables for water are typically based on a reference temperature of 60°F and require no correction for viscosity for most water supply applications. Refer to Table 2-1 below, for a listing of viscosity values for water at various temperatures at sea level.
OE = WHp/EHp
OPE = WHp/IHp
kWh/1000 gal. = H x 0.00315 OPE
kWh/acre-ft. = Q x H x 1.032 OPE
Table 2-1: Viscosity of Water from 32° to 212°F @ Sea Level
Temp. Absolute Viscosity Kimematic Viscosity Specific
°F °C Centipoises Centistokes SSU ft./sec. Gravity
32 0 1.79 1.79 33.00 0.00001931 .9999
40 4.4 1.54 1.54 32.3 0.00001664 1.000
50 10.0 1.31 1.31 31.6 0.00001410 .9997
60 15.6 1.12 1.12 31.2 0.00001217 .9990
70 21.1 0.98 0.98 30.9 0.00001059 .9980
80 26.7 0.86 0.86 30.6 0.00000930 .9960
90 32.2 0.77 0.77 30.4 0.00000826 .9950
100 37.8 0.68 0.69 30.2 0.00000739 .9931
120 48.9 0.56 0.57 30.0 0.00000609 .9888
140 60.0 0.47 0.48 29.7 0.00000514 .9833
160 71.5 0.40 0.41 29.6 0.00000442 .9773
180 83.0 0.35 0.36 29.5 0.00000385 .9702
212 100 0.28 0.29 29.3 0.00000319 .9592
Section 2 A fluid can be broadly classified as Newtonian, where viscosity remains constant regardless of changes in shear rate or agitation. As pump speed increases, flow increases proportionately. Liquids displaying Newtonian behavior include water, mineral oils, syrup, hydrocarbons and resins.
Viscosity is described in terms of absolute (dynamic) or kinematic values. Absolute viscosity is technically described as the shear stress (force) divided by the shear rate (velocity gradient - max fluid velocity divided by the distance from pipe wall). Kinematic viscosity is a product of the absolute viscosity divided by density of the fluid and is the most common viscosity reference in the pump industry.
One of the most common units of measure of kinematic viscosity is Saybolt seconds. This refers to the length of time it takes for a measured quantity of fluid at a specific temperature to drain from a container with a measured orifice in the bottom. Water has a viscosity of approximately 31 Saybolts seconds universal (SSU) at 60°F. Kinematic viscosity is also commonly expressed in metric units as stokes or centistokes.
Pumping Viscous Liquids with Centrifugal Pumps. Centrifugal pumps are generally not suitable for pumping highly viscous liquids. They can be used to pump liquids with viscosities less than 2000 SSU. The volume and pressure capabilities of the pump will be reduced with increasing viscosity. Table 2-2 lists the percent increase in power required along with the percent reduction in flow and head when pumping liquids of increasing viscosities.
Table 2-2: Viscosity Affect on Pump Performance
Viscosity (SSU) > > > > 30 100 250 500 750 1000 1500 2000
Flow reduction (gpm) % – 3 8 14 19 23 30 40
Head reduction (feet) % – 2 5 11 14 18 23 30
Horsepower increase % – 10 20 30 50 65 85 100
Note: Fluid should be corrected for specific gravity prior to applying viscosity corrections
Section 2