Glossary

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

A
Absolute pressure
Pressure above zero, given by the sum of the local atmospheric pressure and the gauge
pressure. [1]
Absolute roughness
Average height of undulations and imperfections on the inner surface of a pipe wall. [4]
Absolute viscosity
See Dynamic viscosity.
Acceleration due to gravity
See Gravitational acceleration.
Atmosphere
A standard atmospheric pressure of 1.01325 bar a. [5]
Atmospheric (barometric) pressure
Local pressure measured with a barometer. [1]

B
Barometer
A device that measures atmospheric pressure. [3]
Bernoulli equation
A useful reduction of conservation of momentum (and conservation of energy) that describes
a balance between pressure (work energy), velocity (kinetic energy), and position of fluid
particles relative to the gravity vector (potential energy) in regions of a fluid flow where
frictional force on fluid particles is negligible compared to pressure force in that region of the
flow. There are multiple forms of the Bernoulli equation for incompressible vs. compressible,
steady vs. no steady, and derivations through Newton's law vs. the first law of
thermodynamics. The most commonly used forms are for steady incompressible fluid flow
derived through conservation of momentum. [3]
 Piezometric and velocity head variation for flow through a venturi section. [11]

Bernoulli equation in head form.

Bernoulli equation in pressure form.

Best efficiency point (B.E.P.)

The point on a pump's performance curve that corresponds to the highest efficiency. [6]

Typical pump
performance
curves for a
centrifugal
pump with
backward
inclined
blades; the
curve shapes
for other
types of
pumps may
differ, and the
curves
change as
shaft rotation
speed is
changed. [3]

Bulk modulus of elasticity

The Bulk modulus of elasticity is synonymous with coefficient of compressibility. [3]
C
Cavitation
The formation of vapor bubbles in a liquid as a result of pressure going below the vapor
pressure. [3]
Centrifugal pump
Mechanical device used to transport fluids by way of an enclosed rotating impeller imparting
velocity to the fluid. [4]
Closed system
A closed system is a volume specified for analysis that encloses always the same fluid
particles. Therefore, no flow crosses any part of the volume's surface and a closed system
must move with the flow. Note that Newton's law analysis of solid particles is generally a
closed system analysis, sometimes referred to as a free body. [3]
Coefficient of compressibility
The coefficient of compressibility is the ratio of pressure change to relative change in volume
of a fluid particle. This coefficient quantifies compressibility in response to pressure change,
an important effect in high Mach number flows. [3]
Coefficient of contraction
The coefficient of contraction is the ratio of area or vena contracta to orifice area. [4]
Coefficient of discharge
The coefficient of discharge is the ratio of actual flowrate to theoretical flowrate through an
opening or restriction. [4]
Coefficient of velocity
The coefficient of velocity is the ratio of actual to theoretical velocity for a discharging jet of
fluid. [4]
Colebrook-White equation
Colebrook-White equation is used to calculate accurate Darcy friction factors fDarcy from the
internal diameter and internal roughness of a pipe and the Reynolds number for the flow
conditions. [5]

Re is the Reynolds number,

ε is the pipe's absolute roughness height,
Dh the pipe hydraulic diameter,
log function is understood to be base-10.
Computational fluid dynamics (CFD)
The application of the conservation laws with boundary and initial conditions in mathematical
discretized form to estimate field variables quantitatively on a discretized grid (or mesh)
spanning part of the flow field. [3]

D
Darcy friction factor
The Darcy friction factor is a dimensionless quantity used in the Darcy–Weisbach equation, for
the description of friction losses in pipe flow. [wiki]
This factor is a function of Reynolds number and relative roughness of the pipe wall.
Darcy friction factor formulae
In fluid dynamics, the Darcy friction factor formulae are equations that allow the calculation of
the Darcy friction factor, a dimensionless quantity used in the Darcy–Weisbach equation, for
the description of friction losses in pipe flow. The Darcy friction factor is also known as the
Darcy–Weisbach friction factor, resistance coefficient or simply friction factor; by definition it
 is four times larger than the Fanning friction factor. [wiki]
The formulas below may be used to obtain the Darcy friction factor for common applications:

Colebrook-White equation.

Swamee–Jain equation.
Re is the Reynolds number,
ε is the pipe's absolute roughness height,
Dh the pipe hydraulic diameter,
log function is understood to be base-10.
Darcy-Weisbach equation
The Darcy-Weisbach equation is an empirical equation used to calculate the frictional head
loss ΔP due to fluid flow from the friction factor, the length and diameter of the pipe, the
velocity of the fluid and the density of the fluid. [5]

fD is the Darcy friction factor (also called flow coefficient l),

L is the length of the pipe,
Dh is the hydraulic diameter of the pipe,
ρ is the density of the fluid,
V is the flow velocity.
Density
The density is the measure of the quantity of a substance per unit volume. [4]
Differential-pressure
The differential-pressure is the pressure drop in pressure across a head device at specified
pressure tap locations. It is normally measured in inches or millimetres of water. [7]
The theory required for differential-pressure meters is given by Bernoulli’s Theorem. [9]

Discharge coefficient
The discharge coefficient is the ratio of the true flow to the theoretical flow. It corrects the
theoretical equation for the influence of velocity profile, tap location, and the assumption of
no energy loss with a flow area between 0.023 to 0.56 percent of the geometric area of the
inlet pipe. [7]
Discharge static head
The discharge static head is the difference in elevation between the liquid level of the
discharge tank and the centreline of the pump. This head also includes any additional
pressure head that may be present at the discharge tank fluid surface. [6]
Dynamic head
See Velocity head.
Dynamic pressure
When the Bernoulli equation in incompressible steady flow and/or the conservation of energy
equation along a streamline are written in forms where each term in the equations has the
dimensions force/area, dynamic pressure is the kinetic energy (per unit volume) term. [3].
See also Velocity pressure.
Dynamic viscosity
The dynamic viscosity is the measure of a fluid's intermolecular cohesive force's resistance to
shear per unit of time. [7]

E
Elevation head
The elevation head is the head due to the fluid's weight, the gravitational force acting on a
column of fluid. The elevation head is simply the elevation (h) of the fluid above an arbitrarily
designated zero point. [Wiki]
Effective roughness
See Absolute roughness.
Energy grade line
The energy grade line EGL is the line that represents the total head of the fluid. [3]

P/ρ.g is the pressure head; it represents the height of a fluid column that produces the
static pressure P,
V²/2g is the velocity head; it represents the elevation needed for a fluid to reach the velocity
V during frictionless free fall,
z is the elevation head; it represents the potential energy of the fluid.

The energy grade line (EGL) for free discharge from a reservoir through a
horizontal pipe with a diffuser. [3]
The difference between the heights of EGL and HGL is equal to the dynamic
head, V²/2g.

Equivalent length method

The equivalent length method (Le/D method) allows the user to describe the pressure loss
through an elbow or a fitting as a length of straight pipe.
This method is based on the observation that the major losses are also proportional to the
velocity head (v²/2.g).

f is the Darcy friction factor,

Leq is the equivalent length of the pipe,
D is the diameter of the pipe,
V is the flow velocity,
g is the local acceleration due to gravity.
 The conversion between equivalent pipe length and the resistance coefficient can be
expressed as:

The Leq/D method simply increases the multiplying factor in the Darcy-Weisbach equation (i.e.
f.Leq/D) by a length of straight pipe (i.e. Leq) which would give rise to a pressure loss
equivalent to the losses in the fittings, hence the name “equivalent length”. [thermal-
engineering.org]

The head loss caused by a

component (such as the angle
valve shown) is equivalent to the
head loss caused by a section of
the pipe whose length is the
equivalent length.. [3]

Euler’s equation
In fluid dynamics, the Euler equations are a set of quasilinear partial differential equations
governing adiabatic and inviscid flow. They are named after Leonhard Euler. In particular, they
correspond to the Navier–Stokes equations with zero viscosity and zero thermal conductivity.
The Euler equations can be applied to incompressible or compressible flow. [Wiki]

F
Fanning friction factor
This friction factor is one-fourth of the Darcy friction factor, so attention must be paid to note
which one of these is meant in the "friction factor" chart or equation consulted. Of the two, the
Fanning friction factor is the more commonly used by chemical engineers and those following
the British convention. [Wiki]
This factor is a function of Reynolds number and relative roughness of the pipe wall. [x]
Fanning friction factor formulae
In fluid dynamics, the Fanning friction factor formulae are equations that allow the calculation
of the Fanning friction factor, a dimensionless quantity used in the Fanning equation, for the
description of friction losses in pipe flow. The Fanning friction factor is four times smaller
than the Darcy friction factor. [wiki]
Many formulations exist to calculate the Fanning friction factor. The following formulas are
two of the most used formulas. [x]
 Colebrook-White equation.

Swamee–Jain equation.

Re is the Reynolds number,

ε is the pipe's absolute roughness height,
Dh the pipe hydraulic diameter,
log function is understood to be base-10.
Fittings
xxx [x]
Flow velocity
The flow velocity V is the mean velocity in a given cross-section across which the medium
flows, e.g. a pipe cross-section. [Lexicon]

Q is the volumetric flowrate,

A is the cross-sectional area of the flow.
Flow work energy
The Flow work energy WE is the energy required for the fluid to flow and is expressed as: [?]

P is the xxx,
ρ is the density of the fluid.
Flowmeters
Flowmeters are the devices that are used to measure the flow of liquid & gases that pass
through them [appropedia.org]
Friction loss
In fluid flow the friction loss is the head loss that occurs in a containment such as a pipe or
duct due to the effect of the fluid's viscosity near the surface of the containment. [Wiki]

G
Gate valve
Device used to regulate flow in a pipe. consisting of a vertical moving section across the f1ow
area. [4]
Gravitational acceleration
At different points on Earth's surface, the free fall acceleration ranges from 9.764 to 9.834
m/s2 (32.03 to 32.26 ft/s2), depending on altitude, latitude, and longitude. A conventional
standard value is defined exactly as 9.80665 m/s2 (32.1740 ft/s2). The gravitational
acceleration is also called gravitational constant. [Wiki]

H
Hazen–Williams equation
The Hazen–Williams equation is an empirical relationship which relates the flow of water in a
pipe with the physical properties of the pipe and the pressure drop caused by friction. It is
used in the design of water pipe systems such as fire sprinkler systems, water supply
networks, and irrigation systems. [Wiki]
The general form of the equation relates the mean velocity of water in a pipe with the
geometric properties of the pipe and slope of the energy line.
 V is the cross-sectional average velocity,
k is a conversion factor for the unit system,
CHW is a roughness coefficient,
Rh is the hydraulic radius,
S is the slope of the energy line.
Head loss
The term in the head form of conservation of energy that contains frictional losses and other
irreversibilities. Without this term, the energy equation for streamlines becomes the Bernoulli
equation in head form. [3]
Head loss coefficient
See Resistance coefficient.
Head loss equation
See Major head losses and Minor head losses.
Hydraulic diameter
The hydraulic diameter is a commonly used term when handling flow in non-circular tubes.
Using this term, one can calculate many things in the same way as for a round tube. When the
cross-section is uniform along the tube or channel length, it is defined as: [Wiki]

A is the cross-sectional area of the flow,

P is the wetted perimeter of the cross-section.

Ajouter dessin et formules (voir Idelchik)

Hydraulic grade line
The hydraulic grade line HGL is the line that represents the sum of the static pressure and the
elevation heads. [3]

P/ρ.g is the pressure head; it represents the height of a fluid column that produces the
static pressure,
z is the elevation head; it represents the potential energy of the fluid.

The hydraulic grade line (HGL) for free discharge from a reservoir through a horizontal pipe
with a diffuser. [3]
The difference between the heights of EGL and HGL is equal to the dynamic
head, V²/2g.

hydrostatic pressure
The hydrostatic pressure is the component of pressure variation in a fluid flow that would
exist in the absence of flow as a result of gravitational body force. This term appears in the
hydrostatic equation and in the Bernoulli equation. See also dynamic pressure and static
pressure. [3]

I
Ideal fluid
See Perfect fluid.
Incompressible flow
A fluid flow where variations in density are sufficiently small to be negligible. Flows are
generally incompressible either because the fluid is incompressible (liquids) or because the
Mach number is low (roughly < 0.3). [3]

K
Several ways exist to determine the pressure drop caused by fluid flow through a fitting or valve.
PypeFlow supports four different methods: [github.com/TomLXXVI/pypeflow]

the K-method uses a single resistance coefficient zeta that is coupled to the velocity pressure in
the section in which the fitting or valve is present.

the 3K method uses a set of three resistance coefficients zeta, zeta_inf and zeta_d to determine
the pressure loss more precisely.

the Crane-K-method which is an adaptation of the K-method (see CRANE, Flow of Fluids
Through Valves, Fittings and Pipe, Technical Paper No. 410M).

using a flow coefficient Kv instead of a resistance coefficient, which is especially the case for
valves.

K method
xxx [x]
The resistance coefficient (K) method (sometimes called the "loss coefficient" method)
The Crane "2 friction factor" Method for Determining the Resistance Coefficient (K)
2-K (Hooper) Method
3-K (Darby) Method

The resistance coefficient method (or K-method, or Excess head method)

There are following methods:

Equivalent length method

K-method (resistance coeff. method)
2K-method
3K-method [thermal-engineering.org]

2-K Method
The 2-K method is a technique developed by Hooper B.W. to predict head loss in an elbow,
valve, or tee. The 2-K method improves the excess head method by characterizing the change
in pressure loss due to varying Reynolds number. The 2-K method is advantageous over other
methods, especially in the laminar flow region. [thermal-engineering.org] www.nuclear-
power.com
 D : Internal diameter of the pipe (in inches)
K : Pressure loss coefficient
K1 : Resistance coefficient for fitting at Re=1
K∞ : Resistance coefficient for large fitting at Re=∞
Re : Reynolds number

Example bend

3-K Method
The 3-K method (by Ron Darby in 1999) further improves the accuracy of the pressure loss
calculation by also characterizing the change in geometric proportions of a fitting as its size
changes. This makes the 3-K method particularly accurate for a system with large fittings.
[thermal-engineering.org] www.nuclear-power.com

D is the nominal diameter of the pipe (in inches)

K : Pressure loss coefficient
Kd : Diameter correction coefficient for diameter scale 3K method
constant (in inches0.3)
K1 : Resistance coefficient for fitting at Re=1
Ki : Resistance coefficient for large fitting at Re=∞
Re : Reynolds number

Kinematic viscosity
The kinematic viscosity is a measure of a fluid's internal resistance to flow under gravitational
forces. It is determined by measuring the time in seconds, required for a fixed volume of fluid
to flow a known distance by gravity through a capillary within a calibrated viscometer at a
closely controlled temperature. [wikipedia.org]
The kinematic viscosity is the ratio of dynamic viscosity of a fluid divided by the fluid density.

Kinetic Energy
The kinetic energy is the energy that a system possesses as a result of its motion. When all
parts of a system move with the same velocity, the kinetic energy per unit mass is expressed
as: [3]

KE is the kinetic energy,

V is the cross-sectional average velocity.
L
Laminar flow
Laminar flow is the flow that occurs when adjacent layers of fluid move relative to one
another in smooth streamlines. Flow occurs in pipes for Reynolds numbers below 2000. [4]
Losses
Frictional head losses in pipe flows are separated into those losses in the fully developed pipe
flow regions of a piping network, the major losses, plus head losses in other flow regions of
the network, the minor losses. Minor loss regions include entry lengths, pipe couplings, bends,
valves, etc. It is not unusual for minor losses to be larger than major losses. [3]

M
Mach number
The Mach number Ma is defined as: [3]

V is the speed of flow,

c is the speed of sound.
The following rough classifications are commonly used for the value of the Mach number:
[12]
Ma < 0.3 incompressible flow, where density effects are negligible.
0.3 < Ma < 0.8 subsonic flow, where density effects are important but no shock waves
appear.
0.8 < Ma < 1.2 transonic flow, where shock waves first appear, dividing subsonic and
supersonic regions of the flow. Powered flight in the transonic region
is difficult because of the mixed character of the flow field.
1.2 < Ma < 3.0 supersonic flow, where shock waves are present but there are no
subsonic regions.
3.0 < Ma hypersonic flow, where shock waves and other flow changes are
especially strong.
Major head losses
The major head losses are the head losses due to frictional effects in fully developed flow in
constant area pipes. [Wiki]
Major head losses equation
The major head losses is expressed as: [x]

fD is the Darcy friction factor (also called flow coefficient l),

L is the length of the pipe,
Dh is the hydraulic diameter of the pipe,
V is the flow velocity,
g is the local acceleration due to gravity.
By observation, the major head loss is roughly proportional to the square of the flowrate in
most engineering flows (fully developed, turbulent pipe flow).
Major pressure losses
The major pressure losses are the pressure losses due to frictional effects in fully developed
flow in constant area pipes. [Wiki]
Major pressure losses equation
The major pressure losses is expressed as: [x]
 fD is the Darcy friction factor (also called flow coefficient l),
L is the length of the pipe,
Dh is the hydraulic diameter of the pipe,
ρ is the density of the fluid,
V is the flow velocity.
By observation, the major pressure loss is roughly proportional to the square of the
flowrate in most engineering flows (fully developed, turbulent pipe flow).
Mach number
The Mach number is expressed as: [x]
Manning formula
The Manning formula is an empirical formula estimating the average velocity of a liquid
flowing in a conduit that does not completely enclose the liquid. [Wiki]

V is the cross-sectional average velocity,

k is a conversion factor between SI and English units,
n is the Gauckler–Manning coefficient,
R is the hydraulic radius,
S is the slope of the hydraulic grade line or the linear hydraulic head loss.
Manometer
A manometer is a device that measures the height (head) of liquid in a tube at the point of
measurement. [7]
Mass density
See Density
Mass
The property of a body that measures the amount of material it contains and causes it to have
weight in a gravitational field. [7]
Mass flowrate
The mass of a substance which passes per unit of time. [wikipedia.org]
Mass flowrate in the pipe line is the product of the volumetric flowrate by density of the fluid.

ρ is the density of the fluid,

Q is the volume flowrate.
Minor head losses
The minor head losses (also called local head losses) are the head losses which occur at
entrances, sudden area changes, bends, elbows, fittings, valves, contraction and diffusers,
etc.. . [Wiki]
Minor head losses equation
The minor head losses are expressed as. [x]

z is the head loss coefficient,

V is the flow velocity,
g is the local acceleration due to gravity.
Minor pressure losses
The minor pressure losses (also called local pressure losses) are the pressure losses which
occur at entrances, sudden area changes, bends, elbows, fittings, valves, contraction and
diffusers, etc.. . [Wiki]
Minor pressure losses equation
The minor pressure losses are expressed as: [x]

z is the Pressure loss coefficient,

ρ is the density of the fluid,
V is the flow velocity.
Moody chart
A commonly used plot of the friction factor as a function of the Reynolds number and
roughness parameter for fully developed pipe flow. The chart is a combination of flow theory
for laminar flow with a graphical representation of an empirical formula by Colebrook to a
large set of experimental data for turbulent pipe flow of various values of "sandpaper"
roughness. [3]

Pipe friction factor λ as a function of the Reynolds number Re and the relative roughness
k/d. [8]

The Moody diagram, friction factor vs. Reynolds number for laminar and turbulent flow at
various pipe roughness-values. [6]
N
Newton's law
xxx. [x]
Newtonian fluids
A newtonian fluid is a fluid in which viscosity is independent of shear stress and/or time. [4]
Nominal pressure
xxx. [x]
Nominal speed of rotation
xxx. [x]
Non-Newtonian fluid
A non-newtonian fluid is a fluid in which the viscosity depends on shear stress and/or time. [4]
Nozzle
A nozzle is a flow device with an elliptical inlet profile along its centerline and made to a
specified standard; usually used for high-velocity flows. Resistant to erosion because of its
shape. [7]
NPSHa
Net Positive Such Head available is the absolute pressure at the inlet of a centrifugal pump
and is a function of elevation, temperature and pressure. [4]

Illustration of a suction piping

Application of the extended Bernoulli equation for a real fluid

where (as for the Total Dynamic Head):

Static pressure head.

Dynamic head.

Pressure loss head.

Total static head.

NPSHr
Net Positive Such Head required by a centrifugal pump is a function of the pump
characteristics and must be exceeded by NPSHa. [4]

O
Operating point
See Pump operating point
Orifice equation
xxx. [xx]
Orifice flowmeter
Device used to measure flowrate by the pressure drop through a small hole. [4]
Orifice plate
An orifice plate is a device used for measuring flow rate, for reducing pressure or for
restricting flow (in the latter two cases it is often called a restriction plate). [Wiki]

Cd is the coefficient of discharge, typically between 0.6 and 0.85, depending on the orifice
geometry and tappings,
β is the diameter ratio of orifice diameter to pipe diameter,
ϵ is the expansibility factor, 1 for incompressible gases and most liquids, and decreasing with
pressure ratio across the orifice,
d is the internal orifice diameter under operating conditions,
ρ is the fluid density in plane of upstream tapping,
Δp is the differential pressure measured across the orifice.
The overall pressure (also called Net pressure loss, Unrecoverable pressure loss or
Permanent pressure loss) loss in the pipe due to an orifice plate is lower than the measured
pressure.[4]

Obstruction flowmeters
Devices used to measure flowrate of gases and liquids. [3]

Common types of obstruction flowmeters. [3]

 The performance and application areas of common differential pressure flowmeters.
[10]

P
Perfect fluid
Also called an ideal fluid, the concept of a fictitious fluid that can flow in the absence of all
frictional effects. There is no such thing as a perfect fluid, even as an approximation, so the
engineer need not consider the concept further. [3]
Performance curve
A plot of total head vs. flow for a specific pump model, impeller diameter and speed. [6]
Permanent pressure loos
Pressure loss across a flowmeter (not the differential-pressure). [9]
See Orifice plate.
Potential Energy
The energy that a system possesses as a result of its elevation in a gravitational field is called
potential energy PE and is expressed on a per-unit mass basis as: [3]

g is the local acceleration due to gravity,

z is the elevation of the center of gravity of the system relative to some arbitrarily selected
reference plane.
Power
Work per unit time; time rate at which work is done. [3]
Pressure
Force of a fluid applied over a given area. [4]
Pressure head
See Static pressure head.
Pressure head difference
xxx. [x]
Pressure drop
xxx. [x] or Orifice meter

The variation of pressure along a

flow section with an orifice meter
as measured with piezometer
tubes; the lost pressure and the
pressure recovery are shown. [3]
Pressure loss coefficient
The pressure loss coefficient characterizes pressure loss of a certain hydraulic system or a
part of a hydraulic system. It can be easily measured in hydraulic loops. The pressure loss
coefficient can be defined or measured for both straight pipes and especially for local (minor)
losses. [nuclear-power.com] xxxxxxxxxx
See Resistance coefficient.
Pressure loss equation
See Major pressure losses equation and Minor pressure losses equation.
Pump characteristic curves
Unlike positive displacement pumps (such as piston pumps), centrifugal pumps deliver a
variable flow rate (increasing with decreasing head) when operating at constant speed. They
are therefore able to accommodate changes in the system curve. The input power and hence
the efficiency as well as the NPSHr are dependent on the flow rate. The relationship of these
values is shown graphically in the pump characteristic curves, whose shape is influenced by
the specific speed nq and which document the performance of a centrifugal pump. [8]

Examples of characteristic curves for a pump. [8]

Pump head
The pump head is the head generated by a pump, given by the piezometric head difference
across the pump plus the difference in velocity heads between outlet and inlet. [1]
See Total dynamic head.
 The net head of a pump, H, is defined as the change
in Bernoulli head from inlet to outlet; for a liquid, this
is equivalent to the change in the energy grade line,
H = EGLout − EGLin [3]

Pump operating point

The operating point of a centrifugal pump, also called its duty point, is given by the
intersection of the pump characteristic curve with the system characteristic curve. The flow
rate and the developed head are both determined by the intersection. To change the operating
point either the system curve or the pump curve must be changed. [8]

Characteristic pump curves for centrifugal pumps, the system curve for a piping system, and the operating
point. [3]

Pump selection
The data required for selecting a pump size, i.e. the flow rate and the head of the desired
operating point are assumed to be known from the system characteristic curve; the electric
mains frequency is also given. With these values it is possible to choose the pump size, the
speed of rotation and, if necessary, the number of stages, from the selection chart in the sales
literature. [8]
 Selection chart for a volute casing pump series for n = 2900 rpm.
(First number = nominal diameter of the discharge nozzle, second number = nominal impeller
diameter). [8]

R
Relative roughness
The relative roughness e is the ratio of absolute roughness of the pipe wall to pipe inside
diameter in consistent units. [4]

k is the absolute roughness,

D is the internal diameter.
Resistance coefficient
Evaluation of the loss in valves and fittings involves the determination of the appropriate
resistance coefficient, which in turn defines the energy loss per unit mass of fluid:

e is the energy loss per unit mass of fluid,

K is the resistance coefficient,
V is the flow velocity upstream of the fitting or valve.
There are several ‘‘correlation’’ expressions for the resistance coefficient K:
K method (loss coefficient)
The K-method uses a single resistance coefficient zeta that is coupled to the velocity
pressure in the section in which the fitting or valve is present.
See xxx
Leq method (Equivalent Length)
The equivalent length method allows the user to describe the pressure loss through an
elbow or a fitting as a length of straight pipe.
See Equivalent length method
Crane method (Crane Technical Paper 410)
The Crane method which is an adaptation of the K method (see CRANE, Flow of Fluids
 Through Valves, Fittings and Pipe, Technical Paper No. 410M).
See xxx
2-K method (by B.W. Hooper 1981)
The 2K method is a technique developed by Hooper B.W. to predict head loss in an
elbow, valve, or tee. The 2K method improves the excess head method by
characterizing the change in pressure loss due to varying Reynolds number.
See xxx
3-K method (by Ron Darby in 1999)
The 3-K method (by Ron Darby in 1999) further improves the accuracy of the pressure
loss calculation by also characterizing the change in geometric proportions of a fitting
as its size changes.
See xxx
D.S. Miller method (1990)

See xxx
I.E. Idelchik method (2003)

See xxx
Donald C. Rennels method (2012)

See xxx
Resistance coefficient
The resistance coefficient K (also named z) is an empirical coefficient in the friction loss
equation for valves and fittings. It expresses the number of velocity heads lost by friction for
the particular valve or fitting. The coefficient is usually a function of the nominal diameter. [2]

xxxxxxxxxxxxxxxxxxx
DH is the head loss,
DP is the pressure loss,
g is the local acceleration due to gravity,
ρ is the fluid density,
V is the flow velocity.
Restrictive flow orifice
A Restrictive Flow Orifice (RFO) is a type of orifice plate. They are used to limit the potential
danger, damage, or wastage of an uncontrolled flow from (also called Restriction orifice).
[Wiki]
Reynolds number
The Reynolds number Re is a dimensionless number derived from the fluid velocity, the
internal diameter of the pipe and the kinematic viscosity of the fluid. [5]

V is the flow velocity,

D is the internal diameter,
n is the kinematic viscosity.
Roughness
See Absolute roughness and Relative Roughness.

S
Sonic velocity (Choked flow)
The maximum velocity that a gas or gas-liquid mixture can attain in a conduit at a given
upstream pressure (except in certain converging-diverging nozzles), no matter how low the
 discharge pressure is. For gases this maximum velocity is equal to the speed of sound at the
local conditions. [2]
See Speed of sound
Specific gravity
The specific gravity SG of a fluid is the ratio of the specific weight of a given fluid to the
specific weight of water at the standard reference temperature 4°C. The specific gravity is
also the ratio of the density of a given fluid to that of water at standard conditions [11]

gfluid is the specific weight of a given fluid,

gwater is the specific weight of water at 4°C,
rfluid is the density of a given fluid,
rwater is the density of water at 4°C.
Specific weight
The specific weight g is the weight per unit volume of a substance. [3]

ρ is the density of the fluid,

g is the local acceleration due to gravity.
Speed of flow
See flow velocity
Speed of sound
The speed of sound of a fluid (also called acoustic velocity or sonic velocity) is the rate of
propagation of small disturbance pressure pulses (“sound waves”) through the fluid. [12]
For fluids in general, the speed of sound c is given by the Newton–Laplace equation:

Ks is a coefficient of stiffness, the isentropic bulk modulus (or the modulus of bulk
elasticity for gases),
ρ is the density of the fluid.
Static head
The static head is the potential energy of a liquid expressed in head form. [4]
Static pressure
The static pressure is another term for pressure, used in context with the Bernoulli equation to
distinguish it from dynamic pressure. [3]
Swamee–Jain equation
The Swamee–Jain equation is used to solve directly for the Darcy–Weisbach friction factor f
for a full-flowing circular pipe. It is an approximation of the implicit Colebrook–White
equation. [Wiki]

Re is the Reynolds number,

ε is the pipe's absolute roughness height,
Dh the pipe hydraulic diameter,
log function is understood to be base-10.
Static pressure head
xxx. [x]
Steady flow
A flow in which all fluid variables (velocity, pressure, density, temperature, etc.) at all fixed
points in the flow are constant in time (but generally vary from place to place). [3]
System characteristic curve
The system characteristic curve plots the head Hsys required by the system as a function of
the flow rate Q. It is composed of the so-called “static” and “dynamic” components. The static
component consists of the geodetic head Hgeo and the pressure head difference between the
inlet and outlet tanks, which are independent of the flow rate. The pressure head difference is
zero when both tanks are open to the atmosphere. [8]

System characteristic curve Hsys with static and dynamic components. [8]

T
Torricelli’s law
Torricelli’s law may be derived from Bernoulli’s principle and relates the velocity of fluid
leaving an orifice in a fluid filled container to the height of the fluid above the orifice. This
equation is a simplification which will generally hold for simple hole geometries, where
pressure losses may be essentially ignored. [neutrium.net]

g : Gravitational acceleration (m/s²)

p : Pressure of the fluid (Pa)
v : Velocity of the fluid (m/s)
z : Fluid height (m)
ρ : Density of the fluid (kg/m³)
Total dynamic head
The total dynamic head TDH is the total equivalent height that a fluid is to be pumped, taking
into account friction losses in the pipe (also called pump head, System head). [wiki]
 Illustration of the system

Application of the extended Bernoulli equation for a real fluid

where:

is the total static head, this is the difference in height between the liquid level
on the inlet and discharge sides (geodetic head).

is the static pressure head, this is the pressure head difference between the
inlet and outlet tank.
In the case of open boxes at atmospheric pressure, the pressures P0 and
P3 are equal and the static pressure head is zero.

is the dynamic head, this is the dynamic height due to the vertical speed
difference in the two tanks.
In general, the liquid surface flow velocities v0 and v3 of tanks are very
low and the dynamic head is considered to be zero (negligible).

is the pressure loss head, this is the sum of all the head losses of the
installation, suction and discharge piping.
(= resistance to flow in the pipes, valves, strainer, piping inlet and outlet,
etc.).
Total head
The total head is the sum of the pressure head, velocity head, and elevation head along a
streamline is constant during steady flow when compressibility and frictional effects are
negligible. [3]
Total head equation
The total head equation H is. [x] xxx

(An alternative form of the Bernoulli equation expressed in terms of

heads)
 P/ρ.g is the pressure head; it represents the height of a fluid column that produces the
static pressure P,
V²/2g is the velocity head; it represents the elevation needed for a fluid to reach the velocity
V during frictionless free fall,
z is the elevation head; it represents the potential energy of the fluid.
Total head loss
The total head loss consist of major head losses, which are due to frictional effects in fully
developed flow in constant area tubes, and minor head losses, which occur at entrances,
sudden area changes, bends, elbows, fittings, valves, contraction and diffusers, etc.. . [Wiki]
The total head equation Hloss is expressed as:

Total pressure equation

The total pressure equation Ptotal is. [x] xxx

(An alternative form of the Bernoulli equation expressed in

terms of pressures)
P is the static pressure,
V is the velocity head,
z is the elevation.
Total pressure loss
The total pressure loss consist of major pressure losses, which are due to frictional effects in
fully developed flow in constant area tubes, and minor pressure losses, which occur at
entrances, sudden area changes, bends, elbows, fittings, valves, contraction and diffusers,
etc.. . [Wiki]
The total pressure equation Ploss is expressed as:

Total static head

The total static head is the difference between the discharge and suction static head of a
pump including the difference between the surface pressure of the discharge and suction
tanks . [6]
Transition flow
The transition flow is the flow regime between laminar and turbulent flow (2000 < Reynolds
number < 4000). Velocity fluctuations may be present and impossible to predict. [4]
Turbulent flow
The turbulent flow is the flow regime characterized by fluctuating motion and erratic path
above Reynolds numbers of 4000. Flow occurs when inertial forces predominate resulting in
macroscopic mixing of the fluid. [4]

U
Uniform flow
Uniform flow is a flow in which all fluid properties, such as velocity, pressure, temperature,
etc., do not vary with position. [3]
Units
The units are specific systems to quantify numerically the dimensions of a physical quantity.
The most common systems of units are SI (kg, N, m, s), English (lbm, lbf, ft, s), BGS (slug, lb, ft,
s), and CGS (g, dyne, cm, s). [3]
Unsteady flow
A flow in which at least one variable at a fixed point in the flow changes with time. [3]
V
Valve flow coefficient
The xxx. [x]
Vapor pressure
The Vapor pressure is the absolute pressure at which a liquid will start to evaporate. [5]
Velocity
See Flow velocity
Velocity head
Velocity head VH is the kinetic energy of a fluid expressed in head form (also called dynamic
head). [4]

V is the flow velocity,

g is the local acceleration due to gravity.
Velocity head difference
The velocity head difference is the difference in velocity head between the outlet and inlet of
the system. [6]
Velocity pressure
Velocity pressure VP is the Kinetic energy of a fluid expressed in pressure form (also called
dynamic pressure). [1]

ρ is the density of the fluid,

V is the flow velocity.
Venturi meter
A venturi meter is a device used to measure flowrate by the pressure drop through a tapered
section of tube or pipe. [4]
Volumetric flowrate
The volumetric flowrate is the volume of fluid which passes per unit time (also known as
volume flowrate, or volume velocity). [wikipedia.org]
The volumetric flow rate Q in a pipe line is the ratio of the mass flowrate to density of the fluid.

m is the mass flowrate,

ρ is the density of the fluid.

W
Water Hammer
Water hammer is the dynamic pressure surge that results from the sudden transformation of
the kinetic energy in a flowing fluid into pressure when the flow is suddenly stopped. The
sudden closing of a valve can cause a water hammer. [2]
Work
The work is the energy required to drive the fluid through the system. [6]

X
Y

Nomenclature

Symbol Definition Unit S.I.

Av Flow Coefficient m²

Cv Flow Coefficient USG/min

D Diameter m

dH Head loss m

dP Pressure loss Pa = N/m²

e Absolute roughness m

f, l Friction factor

fD Darcy friction factor

fF Fanning friction factor

g Gravity acceleration m/s²

H Height m

k Pressure loss coefficient

Kv Flow Coefficient m³/h

L Length m

n Kinematic viscosity m²/s

P Pressure Pa

Qm Mass flowrate kg/s

Qv Volume flowrate m³/s

r density of the fluid kg/m³

Re Reynolds number

A Cross section area m²

V Flow velocity m/s

Wh Hydraulic power W
Energy and work J = N.m
Dynamic viscosity

g Specific weight N/m3

Dh
Pompes en parallèle et en série avec courbes

K en parallèle et en série
References of the test cases presented
Sources

[1] Internal Flow System - Second Edition - D.S. Miller (1990)

[2] Piping Fluid Flow Material - Selection and Line Sizing - KLM Technology Group (2013)
[3] Fluid Mechanics - Fundamentals and Applications - Cengel Cimbala - 4th Ed. (2018)
[4] Fluid Mechanics - Worked Examples - Carl Schaschke (1998)
[5] Pipe Flow Expert Help - Version 7.40
[6] Pump System Analysis and Sizing - Jacques Chaurette - 5th Ed (2003)
[7] A Practical Guide to Accurate Flow Measurement – Upp LaNasa - 2nd Ed. (2002)
[8] Selecting centrifugal pumps - KSB (2005)
[9] Orifice Plates and Venturi Tubes - Michael Reader-Harris (2015)
[10] The Measurement Instrumentation and Sensors Handbook (1999)
[11] Engineering Fluid Mechanics - Clayton T. Crowe - 9th Ed (2009)
[12] Fluid Mechanics - 8th Ed - Frank M White (2016)
[13] Chemical Engineering - Fluid Mechanics - 3rd Ed. - Ron Darby (2017)

HydrauCalc Edition: June 2022

© François Corre 2022