Pump

2013
Pumps
DEFINITIONS AND CALCULATIONS
AMIR RAZMI

2

Total Dynamic Head The total dynamic head H of a pump is the total discharge head hd
minus the total suction head hs.
Total Suction Head This is the reading hgs of a gauge at the suction flange of a pump
(corrected to the pump centerline°), plus the barometer reading and the velocity head hvs at the
point of gauge attachment:
hs = hgs + atm + hvs (EQ-1)
If the gauge pressure at the suction flange is less than atmospheric, requiring use of a vacuum
gauge, this reading is used for hgs in Eq. (10-41) with a negative sign.
Before installation it is possible to estimate the total suction head as follows:
hs = hss − hfs (EQ-2)
where hss = static suction head and hfs = suction friction head.
Static Suction Head The static suction head hss is the vertical distance measured from the
free surface of the liquid source to the pump centerline plus the absolute pressure at the liquid
surface.
Total Discharge Head The total discharge head hd is the reading hgd of a gauge at the
discharge flange of a pump (corrected to the pump centerline*), plus the barometer reading and
the velocity head hvd at the point of gauge attachment:
hd = hgd + atm + hvd (EQ-3)
Again, if the discharge gauge pressure is below atmospheric, the vacuum-gauge reading is
used for hgd in Eq. (10-43) with a negative sign.
Before installation it is possible to estimate the total discharge head from the static discharge
head hsd and the discharge friction head hfd as follows:
hd = hsd + hfd (EQ-4)
Static Discharge Head The static discharge head hsd is the vertical distance measured from
the free surface of the liquid in the receiver to the pump centerline,* plus the absolute pressure
at the liquid surface. Total static head hts is the difference between discharge and suction
static heads.
Velocity Since most liquids are practically incompressible, the relation between the quantity
flowing past a given point in a given time and the velocity of flow is expressed as follows:
Q = Av (EQ-5)
Velocity Head This is the vertical distance by which a body must fall to acquire the velocity v.
hv = v2/2g (EQ-6)
Viscosity In flowing liquids the existence of internal friction or the internal resistance to
relative motion of the fluid particles must be considered. This resistance is called viscosity.
The viscosity of liquids usually decreases with rising temperature. Viscous liquids tend to
increase the power required by a pump, to reduce pump efficiency, head, and capacity, and to
increase friction in pipe lines.

3

Friction Head This is the pressure required to overcome the resistance to flow in pipe and
fittings.
Work Performed in Pumping To cause liquid to flow, work must be expended. A pump
may raise the liquid to a higher elevation, force it into a vessel at higher pressure, provide the
head to overcome pipe friction, or perform any combination of these. Regardless of the service
required a pump, all energy imparted to the liquid in performing this service must be accounted
for; consistent units for all quantities must be employed in arriving at the work or power
performed.
When arriving at the performance of a pump, it is customary to calculate its power output, which is
the product of (1) the total dynamic head and (2) the mass of liquid pumped in a given time.. Useful
work of the pump is called water (horse)power is defined as
WHP = HQρg (EQ-8)
WHP= HQsp.gr/3960
Where WHP is in horsepower, H is in feet and Q is in gallons/min. Also
WHP = HQρ/3.670*105
Where, WHP is in kW, H in m, Q in m3/hr and ρ in kg/m3
.
The power input to a pump (= brake horsepower, BHP) is greater than the power output (WHP)
because of internal losses resulting from friction, leakage, etc. The efficiency of a pump is therefore
defined as
Pump efficiency (η) = (power output)/(power input) = WHP / BHP (EQ-9)
For more study find below:
Attachment- Useful
Work and Pump Efficie
Pump Efficiency An equation developed for efficiency based on the GPSA Engineering Data Book
pumps efficiency curves is:
22222
QgHQfHeHdHQcHQbHaP  (EQ-10)
Where:
H: is developed head in m (meter)
Q: flowrate in l/s (litter/second)
a: +80
b: -0.9367
c: +1.97e-2
d: -1.96e-4

4

e: +5.80e-3
f: -1.09e-4
g: +1.08e-6
Ranges of applicability are H=15-90m and Q=6-63 l/s. Error documented at 3.5%.
The following efficiency can be used for initial estimation:
 Centrifugal pumps: efficiencies of 45% at 6.3 l/s, 70% at 31.5 l/s, 80% at 630 l/s.
 Axial pumps: efficiencies of about 65-85%.
 Rotary pumps: efficiencies of about 50-80%.
 Reciprocating pumps: efficiencies of 70% at 7.5 kW, 85% at 37 kW, and 90% at 373
kW.
Maximum Discharge Pressure (shut-off Pressure) sets the design pressure of a pump casing. This is
the sum of the maximum suction pressure and maximum differential pressure, which usually occurs
at zero flow (discharge isolation valve closed):
Shut off pressure = Ps.max + 125% × normal pump ΔP (EQ-11)
Where Ps.max = max suction pressure = design pressure of upstream item + maximum static head
Maximum static head= static head at HLL or HHLL and maximum specific gravity
Where the feed vessel is protected by a safety relief valve, the maximum suction pressure will be
equal to the sum of safety valve set pressure and the maximum suction head
Pump Minimum Flow to be considered for protection of pumps against shutoff. At shutoff,
practically all of a pump’s horsepower turns into heat, which can vaporize the liquid and damage the
pump. The minimum flow is a relatively constant flow going from discharge to suction.
The process engineer must plan for minimum flow provisions when making design calculations. For
preliminary work, approximate the required minimum flow by assuming all the horsepower at
blocked-in conditions turns into heat. Then, provide enough minimum flow to carry away this heat at
8°C rise in the minimum flow stream’s temperature.
As a worst case it can be assumed that the pump input power turns into heat. The minimum flow
at 8.33° C rise is calculated as:
Cp
BHP
flowMin
.
432

 (EQ-12)
Where BHP: Input power in kW and ρ: density in kg/m3 Cp: Specific heat in kJ/kg.°C
Suction Limitations of a Pump Whenever the pressure in a liquid drops below the vapor
pressure corresponding to its temperature, the liquid will vaporize. When this happens within an
operating pump, the vapor bubbles will be carried along to a point of higher pressure, where
they suddenly collapse. This phenomenon is known as cavitation. Cavitation in a pump should

5

be avoided, as it is accompanied by metal removal, vibration, reduced flow, loss in efficiency,
and noise. When the absolute suction pressure is low, cavitation may occur in the pump inlet
and damage result in the pump suction and on the impeller vanes near the inlet edges. To avoid
this phenomenon, it is necessary to maintain a required net positive suction head (NPSH)R,
which is the equivalent total head of liquid at the pump centerline less the vapor pressure p.
Each pump manufacturer publishes curves relating (NPSH)R to capacity and speed for each
pump.
When a pump installation is being designed, the available net positive suction head
(NPSH)A must be equal to or greater than the (NPSH)R for the desired capacity. The
(NPSH)A can be calculated as follows:
(NPSH)A = hss − hfs − p (EQ-13)
Where p = vapor pressure at operating pressure.
If (NPSH)A is to be checked on an existing installation, it can be determined as follows:
(NPSH)A = atm + hgs − p + hvs (EQ-14)
Practically, the NPSH required for operation without cavitation and vibration in the pump is
somewhat greater than the theoretical. The actual (NPSH)R depends on the characteristics of
the liquid, the total head, the pump speed, the capacity, and impeller design. Any suction
condition which reduces (NPSH)A below that required to prevent cavitation at the desired
capacity will produce an unsatisfactory installation and can lead to mechanical difficulty.
For more information use below:
Attachment-
NPSH.pdf
Attachment-
Cavitation1.pdf
Attachment-
Cavitation2.docx
NPSH Requirements for Other Liquids NPSH values depend on the fluid being pumped. Since
water is considered a standard fluid for pumping, various correction methods have been
developed to evaluate NPSH when pumping other fluids. The most recent of these corrective
methods has been developed by Hydraulic Institute and is shown in Fig. 1.
The chart shown in Fig. 1 is for pure liquids. Extrapolation of data beyond the ranges indicated in
the graph may not produce accurate results. Fig. 1 shows the variation of vapor pressure and
NPSH reductions for various hydrocarbons and hot water as a function of temperature. Certain
rules apply while using this chart. When using the chart for hot water, if the NPSH reduction is
greater than one-half of the NPSH required for cold water, deduct one-half of cold water NPSH
to obtain the corrected NPSH required. On the other hand, if the value read on the chart is less
than one-half of cold water NPSH, deduct this chart value from the cold water NPSH to obtain
the corrected NPSH.

6

Fig 1
Example : NPSH Calculation Suppose a selected pump requires a minimum NPSH of 16 ft (4.9
m) when pumping cold water; What will be the NPSH limitation to pump propane at 55°F
(12.8°C) with a vapor pressure of 100 psi? Using the chart in Fig. 1, NPSH reduction for propane
gives 9.5 ft (2.9 m). This is greater than one-half of cold water NPSH of 16 ft (4.9 m). The
corrected NPSH is therefore 8 ft (2.2 m) or one-half of cold water NPSH.
Dimensional Analysis with pump variables reveals that the functional relations of (EQ-18) and
(19) must exist:
gH/N2
D2
= f (Q/ND3
, D2
Nρ/µ, e/D) (EQ-15)
BHP/ρN3
D5
= f (Q/ND3
, D2
Nρ/µ, e/D) (EQ-16)
The group of D2
Nρ/µ is the Reynolds number and e/D is the roughness ratio. Three new groups
also have arisen which are named
Capacity coefficient CQ= Q/nD3
(EQ-17)
Head coefficient CH= gH/n2
D2
(EQ-18)
Power coefficient CP= BHP/ρn3
D5
(EQ-19)
Where n is rps (can be replaced by N which is rpm), and D is impeller diameter.

7

The hydraulic efficiency is expressed by these coefficients as
η=WHP/BHP=CHCQ/CP (EQ-20)
Although this equation states that the efficiency is independent of the diameter, in practice this is
not quite true. An empirical relation is due to Moody [ASCE Trans. 89, 628 (1926)]
η2=1- (1- η1 ) (D1/D2) 0.25
(EQ-21)
Scaling laws will be used for prediction of geometrically similar pumps and used for estimating
performance of
 a model in respect to a prototype pump
 expected plant condition in respect to test conditions (lower speed and different viscosity)
 efficiency gain with reducing roughness
the main formulas are as follows:
Where ή is overall efficiency and Z is No. of stages.
Subscripts:
a prototype
M model
V volumetric
H hydraulic
Derivation of these formulas is based on similarity laws or model according to various methods,
without going into the details of similarity theory, the model laws for pumps (and turbines) can
be derived directly from the velocity triangles and with the aid of dimensionless parameters (e.g
specific speed)

8

The performance of geometrically similar pumps also can be represented in terms of coefficients
CQ, CH, CP and η. For instance, the data of the pump Fig-2 are transformed into the plots as
dimensionless values.
Fig 2
Performance curves in dimensional and dimensionless forms: (a) Data of a pump with a specific diameter and rotation speed. (b)
Dimensionless performance curves of all pumps geometrically similar to (a). The dashed lines identify the condition of peak
efficiency. (After

9

The Affinity laws are simplified version of Scaling laws and a best estimate of the off-design
performance of pumps can be obtained through similarity relationship detailed manufacturer-
specified performance curves are not available for a different size of the pump or operating
condition.
Constant impeller diameter Constant impeller speed
Capacity Q1/Q2 = N1/N2 Q1/Q2 = D1/D2
Head H1/H2 = (N1/N2)2
H1/H2 = (D1/D2)2
Break horse power BHP1/BHP2 = (N1/N2)3
BHP1/BHP2 = (D1/D2)3
For more details see below attachment:
Attachment- The
Affinity Laws.pdf
Specific speed is another dimensionless parameter that is independent of diameter is obtained by
eliminating D between CQ and CH with the result
NS= NQ0.5
/ (gH)0.75
(EQ-22)
NS is a parameter that defines the speed at which impellers of geometrically similar design have
to be run to discharge one gallon per minute against a one-foot head. In general, pumps with a
low speed have a low capacity and high specific speed, high capacity. Specific speeds of different
types of pumps are shown in table-1 for comparison.

10

Attachment- Specific
Speed.pdf
Suction specified speed helps in evaluating the pump suction limitations, such as cavitation.
S=NQ0.5
/(NPSH)0.75
(EQ-23)
Typically, for single-suction pumps, suction-specific speed above 11,000 is considered excellent.
Below 7000 is poor and 7000–9000 is of an average design. Similarly, for double-suction pumps,
suction specific speed above 14,000 is considered excellent, below 7000 is poor, and 9000–
11,000 is average.
Below figure shows the schematic of specific-speed variation for different types of pumps. The
figure clearly indicates that, as the specific speed increases, the ratio of the impeller outer
diameter D1 to inlet or eye diameter D2 decreases, tending to become unity for pumps of axial-
flow type.
Standards for upper limits of specific speeds have been established by vendors, when S are
exceeded, cavitation and resultant damage to the pump may occur.

12

The sump pump process parameter such as suction, discharge and differential pressures and
NPSH should be determined based on the procedure mentioned in Section 6.3. Other
parameters which are shown in the following figure depend on the pump Bell diameter. These
parameters should be calculated based on the equations presented in Table 1.
Figure 1: Recommended Intake Structure Layout (ANSI/HI 9.8-1998)

13

v
Q
D
v
Q
dv
d
vA
Q
dDDiameterOutsideBell



900
)2~5.1(900
4
.
3600
)2~5.1(
2 







Where:
Q: liquid design flowrate (m3
/h),
V: Inlet pipe velocity (m/s)
Table 1: Recommended Dimensions for Figures 2 (ANSI/HI 9.8-1998)
Variabl
e
Description Recommended Value
A
Distance from the pump inlet bell centerline to the intake
structure entrance
A = 5D minimum
B
Distance from the back wall to the pump inlet bell
centerline
B = 0.75D
C Distance between the inlet bell and floor C = 0.3D to 0.5 D
H Minimum liquid depth H = S + C
S Minimum pump inlet bell submergence S = D (1.0 + 2.3 FD)
Vx Pump bay velocity Vx= 0.5 m/s (max)
W Pump inlet bay entrance width W = 2D minimum
X Pump inlet bay length X = 5D minimum
Y
Distance from pump inlet bell centerline to the through-
flow traveling screen
Y = 4D minimum
Z Distance from inlet bell centerline to sloping floor Z = 5D minimum
α Angle of floor scope α = -10 to 10 degrees
β Angle of wall convergence β = 0 to 10 degrees

14

Figure 2: Sump Dimension versus Flow

16

Type and Applications
Table 2 and figure 4 shows types and application range of vacuum pumps.
Table 2: General Vacuum Limits
Vacuum Pump Type
Approx. Suction
Pressure
Attainable, mmHg abs
Centrifugal
Reciprocating
Steam jet ejector
Rotary displacement
Oil diffusion
Mercury or oil diffusion plus
rotary
6
0.3
0.05
10-5
10-7
Less than 10-7
Figure 3: Rough Estimates of Thermal Efficiency of Various Vacuum Producing
Systems

17

Liquid Ring Vacuum Pumps
The optimal operating range of such machines is about 20 mbar over vapor pressure of
the applied service liquid at ring liquid temperature. The suction capacity of these
machines ranges from 5m3
/h to 25000m3
/h with the main operating range lying
between 100m3
/h to 3000 m3
/h. With water as operating liquid, the operating range of
atmospheric pressure can be down to 33 mbar. If oil is used, final pressures between 10
mbar and 30 mbar are achieved.
The maximum gas suction temperature lies at approx. 100 C. If the suitable ring
liquids and sealing materials are used, also higher temperatures are permissible.
Evacuation Time and Suction Capacity of the Pump
The estimated pump-down capacity performance for a typical liquid-ring vacuum pump
is given in Figure 5 and below equations:
C
f×V=V
,
ex
ext,
eva
ext
t
V

Where:
V: Vessel Volume (m3
)
Vt,ex: Total Volume to be Extracted (m3
)
f : Working vacuum from figure 5.2
Cex: Capacity to be extracted (m3
/min)
teva: Evacuation time (min)

18

Figure 4: Total Volume to be Displaced to Evacuate a Close Vessel to a
Predetermined Vacuum
The evacuation time can be calculated from below equation or Figure 7.
2
1
ln60
P
P
S
V
teva 
Where:
teva: Evacuation time (min)
V: Volume of a completely dry and tight plant to be evacuated (m3
)
S: Suction capacity of the vacuum pump (m3
/h)
P1: Pressure at the beginning of the evacuation (mbar)
P2: Pressure at the end of the evacuation (mbar)

19

Figure 5: Projection of the Natural Logarithm Depending on the Pressure Ratio
The evacuation time of vessels and vacuum systems can also be determined with good
approximation according to the nomogram in Figure 7. The below procedure describe
the way to used nomogram.
 Scale 1: Vessel volume (V) in liters.
 Scale 2: Maximum of the effective suction capacity Seff,max on the vessel in (left)
liters per second or (right) cubic meter per hour respectively.
 Scale 3: Time constant (e-value time)  in seconds, =V/Seff,max
 Scale 4: Evacuation time tp in (right, above) seconds or (left, centre) minutes or
(right, below) hours, respectively.
 Scale 5: (right): Pressure PEND in millibar at the END of the evacuation time, if at the
START of the evacuation time, the atmospheric pressure PSTART  PN =1013 mbar
was prevailing. The desired pressure PEND has to be reduced by the end pressure of
the pump Pend,p , and the scale has to be entered at the differential value. If an
inflow qpV in exists, the scale has to be entered at the value
PEND – Pend,P – qpV in/ Seff ,max

20

On the left: Pressure reduction ratio R = (PSTART – Pend,p – qpV in/ Seff,max )/(PEND – Pend,p –
qpV in/ Seff, max), if at the beginning of the pumping process, the pressure PSTART prevails
and the vessel is to be evacuated to the pressure PEND.
The dependence of the suction capacity on the pressure enters the nomograph and is
expressed in the point Pend,p on scale 5. If the pump pressure Pend,p is low, compared
with the pressure PEND which is intended to be achieved at the end of the evacuation
process, this corresponds to the constant suction capacity S or Seff during the entire
pumping process.
Figure 6: Determination of the Evacuation Time of a Vessel (P1 mbar)
Air Leakage into System
Rates of air leakage into commercially tight systems calculated from below equation:

21

3
2
Vkm 
Where:
m: Air leakage Ib/hr, (0.4536 kg)
V: Volume of the system ft3
,(0.0283 m3
)
k: Coefficient is a function of the process pressure as follows :
Table 3: Air Leakage Coefficient
Pressure (Torr) >90 20-90 3-20 1-3 <1
k 0.194 0.146 0.0825 0.0508 0.0254
Note: For each agitator with a standard stuffing box, 5 Ib/hr(2.68 kg/h) of air leakage is
added. Use of special vacuum mechanical seals can reduce this allowance to 1-2 Ib/hr
(0.4536-0.9072 kg/hr).

23

Fig. 1 – Pump Classification
When selecting pumps for any service, it is necessary to know the liquid to be handled, the total
dynamic head, the suction and discharge heads, and, in most cases, the temperature, viscosity,
vapor pressure, and specific gravity. In the chemical industry, the task of pump selection is
frequently further complicated by the presence of solids in the liquid and liquid corrosion
characteristics requiring special materials of construction. Solids may accelerate erosion and
corrosion, have a tendency to agglomerate, or require delicate handling to prevent undesirable
degradation.
Range of Operation Because of the wide variety of pump types and the number of factors which
determine the selection of any one type for a specific installation, the designer must first
eliminate all but those types of reasonable possibility. Since range of operation is always an
important consideration, Fig. 2 & 3 should be of assistance. The boundaries shown for each
pump type are at best approximate, as unusual applications for which the best selection
contradicts the chart will arise. In most cases, however, Fig. 2 & 3 will prove useful in limiting
consideration to two or three types of pumps.

24

Fig. 2: Pump Selection Guide (SI Unit)
Fig. 3: Pump Selection Guide (US Unit)
Solid lines: use left ordinate, head scale; dshed lines: use right ordinate, pressure scale

25

Below criteria can be used for pump selection also:
Centrifugal Pumps (Process Pumps)
 Medium to high capacity for low to medium head requirements
 Higher head requirements can be met by using multistage impellers.
 General Service for all liquids, hydrocarbons, products, water, and boiler feed.
 Simple, low cost, even flow, small floor space, quiet, easy maintenance
Rotary Pumps
 Many proprietary designs available for specific services
 Essentially can handle clean fluids only with small suspended solids if any. Can
pump liquids with dissolved gases or vapor phase.
 Can handle wide range of viscosities – up to 500 000 SSU at high pressures.
 Typical fluids pumped: mineral, vegetable, animal oils, grease, glucose, viscose,
paints, molasses, alcohol, and etc.
Reciprocating pumps
 Positive displacement pumps operate with approximately constant capacities over
wide variations in head; hence they usually are installed for services which require
high heads at moderate capacities.
 Pumps produce virtually any discharge head up to limit of driver power and strength
of pistons and casings.
 Overall efficiency is higher than centrifugal pumps. Flexibility is limited.
 A special application of small reciprocating pumps in gas processing plants is for
injection of fluids (e.g. methanol and corrosion inhibitors) into process streams,
where their constant-capacity characteristics are desirable.
Piston pumps
 Can be single or double acting.
 Used for low pressure light duty or intermittent services.
 Less expensive than plunger design but cannot handle gritty fluids.
Plunger pumps
 High pressure, heavy duty or continuous service usage.
 Suitable for gritty or foreign material.
 Expensive.
Diaphragm pump
 Driven parts are sealed from fluid by plastic or rubber diaphragm.
 No seals no leakage.
 Ideal for toxic or hazardous material.
 Can be pneumatically driven at slow speeds for delicate fluids.

38

System Curves In addition to the pump design, the operational performance of a pump depends
upon factors such as the downstream load characteristics, pipe friction, and valve performance.
Typically, head and flow follow the following relationship:
(10-56)
where the subscript 1 refers to the design condition and 2 to the actual conditions. The above
equation indicates that head will change as a square of the water flow rate. Figure 10-32 shows
the schematic of a pump, moving a fluid from tank A to tank B, both of which are at the same
level. The only force that the pump has to overcome in this case is the pipe function, variation of
which with fluid flow rate is also shown in the figure. On the other for the use shown in Figure
10-33, the pump in addition to pipe friction should overcome head due to difference in elevation
between tanks A and B. In this case, elevation head is constant, whereas the head required to
overcome friction depends on the flow rate. Figure 10-34 shows the pump performance
requirement of a valve opening and closing.
Attachment - The
System Curve.pdf
Attachment -
Understanding Pump
Pumps chart.pdf

39
Maintenance and Troubleshooting

40

Attachment- Pump
Problems.pdf
Attachment- Pump
Maintainance.pdf
Attachment-
Vibration Monitoring.d

41

Jet pumps
(Ejectors)

42

JET PUMPS
Jet pumps are a class of liquid-handling device that makes use of the momentum of one fluid to
move another.
Ejectors and injectors are the two types of jet pumps of interest to chemical engineers. The
ejector, also called the siphon, exhauster, or eductor, is designed for use in operations in which
the head pumped against is low and is less than the head of the fluid used for pumping.
The injector is a special type of jet pump, operated by steam and used for boiler feed and similar
services, in which the fluid being pumped is discharged into a space under the same pressure as
that of the steam being used to operate the injector.
Fig-1 shows a simple design for a jet pump of the ejector type. The pumping fluid enters through
the nozzle at the left and passes through the venturi nozzle at the center and out of the discharge
opening at the right. As it passes into the venturi nozzle, it develops a suction that causes some of
the fluid in the suction chamber to be entrained with the stream and delivered through this
discharge.
The efficiency of an ejector or jet pump is low, being only a few percent. The head developed by
the ejector is also low except in special types. The device has the disadvantage of diluting the
fluid pumped by mixing it with the pumping fluid. In steam injectors for boiler feed and similar
services in which the heat of the steam is recovered, efficiency is close to 100 percent.
The simple ejector or siphon is widely used, in spite of its low efficiency, for transferring liquids
from one tank to another, for lifting acids, alkalies, or solid-containing liquids of an abrasive
nature, and for emptying sumps.

Fig-1: Simple ejector using a liquid-motivating fluid
Attachment- Ejector
Sample 1.pdf

Attachment- Ejector
Sample 2.pdf

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