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Pump Sizing And Hydraulic Losses Case Material

Pump Sizing And Hydraulic Losses Case Material

Introduction
Pump sizing involves matching the flow and pressure rating of a pump with the flowrate and pressure required for the process. The mass flowrate of the system is established on the process flow diagram by the mass balance. Achieving this mass flowrate requires a pump that can generate a
pressure high enough to overcome the hydraulic resistance of the system of pipes, valves, and so on that the liquid must travel through. This hydraulic resistance is known as the system head.
the system head is the amount of pressure required to achieve a given flowrate in the system downstream of the pump.
Pump sizing,  is the specification of the required outlet pressure of a rotodynamic pump (whose output flow varies nonlinearly with pressure) with a given system head (which varies nonlinearly with flow).

Understanding system head
The system head depends on properties of the system the pump is connected to — these include the static head and the dynamic head of the system.
The static head is created by any vertical columns of liquid attached to the pump and any pressurized systems attached to the pump outlet. The static head exists under static conditions, with the pump switched off, and does not change based on flow. The height of fluid above the pump’s centerline can be determined from the plant layout drawing.
FIG 1

The dynamic head varies dynamically with flowrate (and also with the degree of opening of valves). The dynamic head represents the inefficiency of the system — losses of energy as a result of friction within pipes and fittings and changes of direction. This ineffiency increases with the square of the average velocity of the fluid.
FIG 2
Dynamic head can be further split into two parts. The frictional loss as the liquid moves along lengths of straight pipe is called the straight-run headloss, and the loss as a result of fluid passing through pipe fittings such as bends, valves, and so on is called the fittings headloss.

Main principles of pumps selection
Selection of the pumping equipment is a crucial point that determines both process parameters
and in-use performance of the unit under development. During selection of the type of pump
three groups of criteria can be distinguished:
         1) Process and design requirements
         2) Nature of pumped medium
         3) Key design parameters

1- Process and design requirements:
In some cases the pump selection is determined by some stringent requirements for a number of
design or process parameters. The pump process and design requirements are seldom definitive, and ranges of suitable types of pumps for various specific cases of application are known as a matter of experience accumulated by humanity, and there is no need to enumerate them in detail.
2- Nature of pumped medium:
Characteristics of the pumped medium often become a decisive factor in pumping equipment
selection. Different types of pumps are suitable for pumping of various media differing in viscosity,
toxicity, abrasiveness and many other parameters.
3- Key design parameters:
Operational requirements specified by different industries can be satisfied by several types of
pumps.

What is friction in a pump system
Friction is always present, even in fluids, it is the force that resists the movement of objects.
FIG 3
When you move a solid on a hard surface, there is friction between the object and the surface. If you put wheels on it, there will be less friction. In the case of moving fluids such as water, there is even less friction but it can become significant for long pipes.
Friction can be also be high for short pipes which have a high flow rate and small  diameter as in the syringe example.
In fluids, friction occurs between fluid layers that are traveling at different velocities within the pipe (Figure 4). There is a natural tendency for the fluid velocity to be higher in
the center of the pipe than near the wall of the pipe. Friction will also be high for viscous
fluids and fluids with suspended particles.
FIG 4
Another cause of friction is the interaction of the fluid with the pipe wall, the rougher the pipe, the higher the friction.
Friction depends on:
     - average velocity of the fluid within the pipe
     - viscosity
     - pipe surface roughness

Determining frictional losses through fittings (minnor loss)
Dynamic, or friction, head is equal to the sum of the straight-run headloss and the fittings headloss.
The fittings headloss is calculated by what is known as the k-value method. Each type of valve, bend, and tee has a characteristic resistance coefficient, or k value
FIG 5

We should count the number of valves on the piping and instrumentation diagram (P&ID), and the fittings, bends, and tees on the plant layout drawing for the relevant suction or delivery line. Multiply the number of each type of fitting by the corresponding k value, and add the k values for the various types of fittings to get the total k value. Use the total k value to calculate the headloss due to fittings:

hm = k × (ρ v²)/2
where :
hm  = is the fittings headloss (Pa (N/m²), psf (lb/ft²))
k   = is the minor loss coefficient k value, 
v   = is the superficial velocity (m/sec,), 
ρ   is the density of the fluid,kg/m³,slugs/ft³

Summarized Minor Losses

Minor head loss can be expressed as:

hm = k v²/ 2 g 
where
k = minor loss coefficient
hm  = is the fittings headloss (m, ft)


Calculating straight-run headloss

Pressure loss in steady pipe  flow is calulated using the Darcy-Weisbach equation.
This equation includes the Darcy friction factor. The exact solution of the Darcy friction factor in turbulent flow is got by looking at the Moody diagram or by solving it from the Colebrook equation.
The Darcy-Weisbach equation, for calculating the friction loss in a pipe, uses a dimensionless value known as the friction factor (also known as the Darcy-Weisbach friction factor or the Moody friction factor) and it is four times larger than the Fanning friction factor.
FIG 6


Reynolds Numbers
Fluid flow in a pipe encounters frictional resistance due to the internal roughness (e) of the pipe wall, which can create local eddy currents within the fluid. Calculation of the Reynolds Number helps to determine if the flow in the pipe is Laminar Flow or Turbulent Flow.
Pipes that have a smooth wall such as glass, copper, brass and polyethylene cause less fritional resistance and hence they produce a smaller frictional loss than those pipes with a greater internal roughness, such as concrete, cast iron and steel.
The velocity profile of fluid flow in a pipe shows that the fluid at the centre of the stream moves more quickly than the fluid flow towards the edge of the stream. Therefore friction occurs between layers within the fluid.
Fluids with a high viscosity flow more slowly and generally not produce eddy currents, thus the internal roughness of the pipe has little or no effect on the frictional resistance to flow in the pipe. This condition is known as laminar flow.

Kinematic viscosity = dynamic viscosity/fluid density
Reynolds number = (Fluid velocity x Internal pipe diameter) / Kinematic viscosity
where :
ρ   is the density of the fluid,kg/m³,lbm/ft³
D  is the pipe internal diameter (hydraulic diameter), m,mm
μ  is the fluid dynamic viscosity. Ns/m², lbm/s ft)
𝜈 = μ/ρ is the kinematic viscosity. (cSt ,m²/s, ft²/s)
V  is the average velocity. m/sec ft/sec,   
𝖰  is volumetric flow rate (m³/sec.ft³/sec)
𝘮 is mass flow  rate (kg/sec,lb/sec)

If the flow is transient - 2300 < Re < 4000 - the flow varies between laminar and turbulent flow and the friction coefiicient is not possible to determine. The friction factor can usually be interpolated between the laminar value at Re = 2300 and the turbulent value at Re = 4000.


Pipe Roughness  

Absolute Roughness
The roughness of a pipe is normally specified in either mm or inches and common values range from 0.0015 mm for PVC pipes through to 3.0 mm for rough concrete pipes.
Relative Roughness
The relative roughness of a pipe is its roughness divided by its internal diameter or ε/D, and this value is used in the calculation of the pipe friction factor, which is then used in the Darcy-Weisbach equation to calculate the friction loss in a pipe for a flowing fluid.
e = ε/D

where :
ε is Absolute Roughness . (mm,m) the absolute roughness of the pipe inner wall.
D is the pipe internal diameter (hydraulic diameter), (mm,m)

For turbulent flow the friction coefficient depends on the Reynolds Number and the roughness of the duct or pipe wall. Roughness for different materials can be determined by experiments.
Absolute roughness - ε - for some common materials :

Friction Factor Calculations
The Darcy-Weisbach equation, for calculating the friction loss in a pipe, uses a dimensionless value known as the friction factor (also known as the Darcy-Weisbach friction factor or the Moody friction factor) and it is four times larger than the Fanning friction factor.

Friction Factor for Laminar Flow
The friction factor for laminar flow is calculated by dividing 64 by the Reynold's number.
Friction factor (for laminar flow) 
fD = 64 / Re
Friction Factor for Turbulent Flow
The Colebrook-White approximation can be used to estimate the Darcy friction factor (fD) from Reynolds numbers greater than 4,000:

where
fD     is Darcy-Weisbach friction coefficient
D    is the hydraulic diameter of the pipe,(m,ft)
ε    is the surface roughness of the pipe, (m,ft)
Re  is the Reynolds number
FIG 7
Blasius
The Blasius equation is the most simple equation for solving the Darcy friction factor. Because the Blasius equation has no term for pipe roughness, it is valid only to smooth pipes. However, the Blasius equation is sometimes used in rough pipes because of its simplicity. The Blasius equation is valid up to the Reynolds number 10⁵ . The Blasius equation is
Swamee-Jain
Swamee and Jain  have devoloped the following equation to the Darcy friction factor
Haaland
Haaland  has deduced the equation
In the Haaland equation there is no need to iterate the Darcy friction factor. The accuracy of the Darcy friction factor solved from this equation is claimed to be within about 2 %, if the Reynolds number is greater than 3000
Major Head Loss
Darcy Weisbach Formula
The Darcy formula or the Darcy-Weisbach equation as it tends to be referred to, is now accepted as the most accurate pipe friction loss formula, and although more difficult to calculate and use than other friction loss formula, with the introduction of computers, it has now become the standard equation for hydraulic engineers.
Weisbach first proposed the relationship that we now know as the Darcy-Weisbach equation or the Darcy-Weisbach formula, for calculating friction loss in a pipe.

where
hf  is  pressure loss (Pa (N/m²), psf (lb/ft²))
fD   is the Darcy friction factor
L  is length of pipe or pipe part (m,ft)
D is inner diameter of the pipe
ρ   is the density of the fluid,kg/m³,slugs/ft³)
V  flow velocity (m/sec,ft/sec)

Summarized Major Losses

The major head loss for a single pipe or duct can be expressed as:
hf = fD (L/ D) (v² / 2 g) 

where

hf = head loss (m, ft)
fD= Darcy-Weisbach friction coefficient
L = length of duct or pipe (m)
D= hydraulic diameter (m)
v = flow velocity (m/s, ft/s)
g = acceleration of gravity (m/s2, ft/s2)

Hazen-Williams Formula
Before the advent of personal computers the Hazen-Williams formula was extremely popular with piping engineers because of its relatively simple calculation properties.

However the Hazen-Williams results rely upon the value of the friction factor, C hw, which is used in the formula, and the C value can vary significantly, from around 80 up to 130 and higher, depending on the pipe material, pipe size and the fluid velocity.

Also the Hazen-Williams equation only really gives good results when the fluid is Water and can produce large inaccuracies when this is not the case.

The imperial form of the Hazen-Williams formula is:

hf = 0.002083 x L x (100/C)¹′⁸⁵ x (gpm¹′⁸⁵/ D⁴′⁸⁶⁵⁵)

where:
hf = head loss in feet of water
L = length of pipe in feet
C = friction coefficient
gpm = gallons per minute (USA gallons not imperial gallons)
D = inside diameter of the pipe in inches

The empirical nature of the friction factor C hw means that the Hazen-Williams formula is not suitable for accurate prediction of head loss. The friction loss results are only valid for fluids with a kinematic viscosity of 1.13 centistokes, where the velocity of flow is less than 10 feet per sec, and where the pipe diameter has a size greater than 2 inches.

Notes: Water at 60° F (15.5° C) has a kinematic viscosity of 1.13 centistokes.

Static head.head loss and total head 
The head loss of a pipe, tube or duct system, is the same as that produced in a straight pipe or duct whose length is equal to the pipes of the original systems plus the sum of the equivalent lengths of all the components in the system. This can be expressed as
hloss = Σ hmajor_losses + Σ hminor_losses
hloss  = Σhf +Σhm
where :
hloss   is total head loss 
hf      is head loss of each straigth pipe
hm     is head loss of each compenent (fitting )
FIG 8
Total dynamic head 
As in figure 8
H = (hd -hs) + hloss
where :
H is total head
hd is discharge static head 
hs is suction static head

And as in figure 9
FIG 9
H = (hd +hs) + hloss
Hydraulic power, pump shaft power 
The hydraulic power which is also known as absorbed power, represents the energy imparted on the fluid being pumped to increase its velocity and pressure. The hydraulic power may be calculated using one of the formulae below, depending on the available data
FIG 10

Hydraulic power
Ph = (Q ×H × ρ ×g)/1000 
Where:
Ph = input power of the centrifugal pump (Kw)
ρ = density of water (Kg/m³)
g = acceleration due to gravity (m/sec²)
H =  total head (m)
Q = capacity (m³/s)

or 

SHAFT POWER
The shaft power is the power supplied by the motor to the pump shaft. Shaft power is the sum of the hydraulic power (discussed above) and power loss due to inefficiencies in power transmission from the shaft to the fluid. Shaft power is typically calculated as the hydraulic power of the pump divided by the pump efficiency as follows:

P= Ph/η 

Where :
η = pump efficiency

MOTOR POWER
The motor power is the power consumed by the pump motor to turn the pump shaft. The motor power is the sum of the shaft power and power loss due to inefficiencies in converting electric energy into kinetic energy. Motor power may be calculated as the shaft power divided by the motor efficiency
Pump curves
A pump curve is a plot of outlet pressure as a function of flow and is characteristic of a certain pump. The most frequent use of pump curves is in the selection of centrifugal pumps, as the flowrate of these pumps varies dramatically with system pressure. Pump curves are used far less frequently
for positive-displacement pumps. A basic pump curve plots the relationship between head and flow for a pump (Figure 11 ).
On a typical pump curve, flowrate (Q) is on the horizontal axis and head (H) is on the vertical axis. The pump curve shows the measured relationship between these variables, soit is sometimes called a Q/H curve. The intersection of this curve with the vertical axis corresponds to the closed valve head of the pump. These curves are generated by the pump manufacturer under shop test conditions and ideally represent average values for a representative sample of pumps
FIG 11
More-advanced curves usually incorporate efficiency curves, and these curves define a region of highest efficiency. At the center of this region is the best efficiency point (BEP).
We can often generate acceptable pump curves using the curves you have and the following approximate pump affinity relationships:
CALCULATION OF PUMP SPECIFIC SPEED
Pump specific speed is calculated using the relationship below

Ns  = specific speed (rpm)
n    = rotational speed rpm)
Q   = Capacity (m³/sec)
H   =head (m)
for multi-stage pumps the specific speed is calculated for the first stage only. For pumps with a double-suction inlet the flow rate Q, should be half the total flow rate for the pump.


Dimensionless Form

The traditional pump specific speed is not a dimensionless number, thus it is critically important that the units used are reported along with the pump specific speed value. A dimensionless form can be created by multiplying the pump head by the gravitation constant and measuring the shaft rotation in radians.
The resulting Nd . N​d​​ will be dimensionless provided consistent units are used. Rotational speed nrad ​​ should be measured in radians per second. The metric units m³/s, m/s² and m for Q, g and h respectively are consistent. The imperial units ft³/s, ft/s² and ft as the units of Q, g and h respectively also result in a dimensionless number.
The typical ranges of pump specific speed and the corresponding impeller diameter to eye diameter ratios for several impeller types are shown
FIG 12
Piston pumps (positive displacement pumps)
For single-acting piston pump the flow rate formula will look like the following:

Q – flow rate (m /s)
F – piston cross-sectional area, m
S –piston stroke length, m
n – shaft rotation speed, s
ηv – volumetric efficiency

Gear pumps (positive displacement pumps)
Gear pump performance capacity can be calculated in the following way:

Q – gear pump performance capacity, m /s
f – cross-sectional area of space between adjacent gear teeth, m
z – number of gear teeth
b – gear tooth length, m
n – teeth rotation speed, s⁻¹
ηv – volumetric efficiency

Screw pumps (positive displacement pumps)
Single-screw pump performance capacity can be calculated in the following way:

Q – screw pump performance capacity, m /s
e – eccentricity, m
D – diameter of rotor screw, m
Т – pitch of stator screw surface, m
n – rotor rotation speed, s⁻¹
ηv– volumetric efficiency

Pump Selection Considerations 

Pumps transfer liquids from one point to another by converting mechanical energy from a rotating impeller into pressure energy (head). The pressure applied to the liquid forces the fluid to flow at the required rate and to overcome friction (or head) losses in piping, valves, fittings, and process equipment. The pumping system designer must consider fluid properties, determine end use requirements, and understand environmental conditions. Pumping applications include constant or variable flow rate requirements, serving single or networked loads, and consisting of open loops (nonreturn or liquid delivery) or closed loops (return systems). 

Fluid Properties 
The properties of the fluids being pumped can significantly affect the choice of pump. Key considerations include: 
     • Acidity/alkalinity (pH) and chemical composition. Corrosive and acidic fluids can degrade                 pumps, and should be considered when selecting pump materials. 
     • Operating temperature. Pump materials and expansion, mechanical seal components, and                     packing materials need to be considered with pumped fluids that are hotter than 200°F.             
     • Solids concentrations/particle sizes. When pumping abrasive liquids such as industrial                       slurries,  selecting a pump that will not clog or fail prematurely depends on particle size,                      hardness, and  the  volumetric percentage of solids. 
     • Specific gravity. The fluid specific gravity is the ratio of the fluid density to that of water under           specified conditions. Specific gravity affects the energy required to lift and move the fluid, and            must be considered when determining pump power requirements. 
      • Vapor pressure. A fluid’s vapor pressure is the force per unit area that a fluid exerts in an                  effort  to change phase from a liquid to a vapor, and depends on the fluid’s chemical and                      physical properties. Proper consideration of the fluid’s vapor pressure will help to minimize the           risk of cavitation. 
     • Viscosity. The viscosity of a fluid is a measure of its resistance to motion. Since kinematic                   viscosity normally varies directly with temperature, the pumping system designer must know the         viscosity of the fluid at the lowest anticipated pumping temperature. High viscosity fluids result         in reduced centrifugal pump performance and increased power requirements. It is particularly             important to consider pump suction-side line losses when pumping viscous fluids.

System Flow Rate and Head
The design pump capacity, or desired pump discharge in gallons per minute (gpm)or  m3/sec is needed to accurately size the piping system, determine friction head losses, construct a system curve, and select a pump and drive motor. Process requirements may be met by providing a constant flow rate (with on/off control and storage used to satisfy variable flow rate requirements), or by using a throttling valve or variable speed drive to supply continuously variable flow rates. The total system head has three components: static head, elevation (potential energy), and velocity (or dynamic) head. Static head is the pressure of the fluid in the system, and is the quantity measured by conventional pressure gauges. 
The height of the fluid level can have a substantial impact on system head. The dynamic head is the pressure required by the system to overcome head losses caused by flow rate resistance in pipes, valves, fittings, and mechanical equipment. Dynamic head losses are approximately proportional to the square of the fluid flow velocity, or flow rate. If the flow rate doubles, dynamic losses increase fourfold. 

Environmental Considerations 
Important environmental considerations include ambient temperature and humidity, elevation above sea level, and whether the pump is to be installed indoors or outdoors.

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MECHANICAL INFORMATION.S SOURCE

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