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FLUID FLOW IN PIPE 1
CONTENT
Chapter Description Page
I Purpose 2
II Pressure, Velocity and Pressure Drop 2
III Friction coefficient and Flow resistance 3
IV. Gas 6
V. Symbols and Units 10
VI. Unit Conversion 10
VII. Standard Pipe Dimension 12
VIII. Properties of Fluids 13
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I. PURPOSE
This manual is purposed for pressure drop calculation along pipe and their valves and fittings.
II. PRESSURE, VELOCITY AND PRESSURE LOSSES
Velocity profile of fluid flow inside pipe is shown as the following figure.
Figure 1. Velocity profile of fluid flow in pipe
Velocity is almost zero at inside pipe wall and maximum at the centre of pipe. In this manual,
velocity of fluid is defined as average velocity.
Pressure definition of moving fluid inside pipe is shown in figure 2 below.
Figure 2. Pressure definition of moving fluid inside pipe.
Fluid potential energy expressed in pressure is PTOT,
PTOT = Pst + .g.h (1)
Local downstream static pressure, P
P = PTOT – PLOSS – 0.5 V 2 (2)
Or
FLUID FLOW IN PIPE 3
2
)(63.353
D
QV
P = Pst + .g.h - PLOSS – 0.5 V 2 (3)
Pst is equipment pressure,is fluid density, g gravitation, h liquid level which is =0 for gas, V fluid
velocity. Converted in MKS appropriate units become,
P = Pst + 0.1 SG.h - PLOSS – 0.0051 SG.V2 in kg/cm2 A (4)
Pst in kg/cm2, h in meter, V in m/s
m/s (5)
Q fluid flowrate in m3/hr, D in mm
This manual will examines pressure drop or PLOSS .
PLOSS = 0.0051 f . (L/D).SGV 2 or PLOSS = 5.1 f .(L/D)..V2. 10-6 kg/cm2 (6)
f is friction coefficient, L is pipe length or equivalent length if piping accessories is expressed in
length. Unit for L is converted in mm when D in mm. Local losses of short component is also
calculated in other method,
PLOSS = 0.0051 K.SG.V 2 or PLOSS = 5.1 K.V 2 .10-6 kg/cm2 (7)
K is flow resistance. Addition of equation (6) and (7) become,
PLOSS = 0.0051 SG.V2 [ Ki + f.(L/D)i ] or PLOSS =5.1.V2 [ Ki + f.(L/D)i ].10-6 kg/cm2 (8)
III. FRICTION COEFFICIENT AND REISTANCE COEFFICIENT
In laminar and transition region, friction coefficient f is function of Re, and D,
f = F (Re, /D) (9)
Re is Reynold number, is roughness of pipe, D is inside diameter of pipe.
Re = .V.D/ (10)
in kg/m3
or
310...Re
DVSG (11)
V in m/s, D is inside diameter of pipe in mm and is fluid viscosity in cP (Centipoise).
Friction factor, f is provided from Moody diagram. In laminar region, where Re < 2 x 103,
f = 64/Re. For Re < 1000, corrected (L/D)= 0.001 Re.(L/D) (12)
In fully turbulence region, where f is only depending to /D,
f = 0.014122 + 3.032764 (/D) – 44.06676 (/D)2 (13)
or
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f = {1.14 – 2 log (/D)} -2 for Re > 3500/(/D) (14)
Figure 3. Moody diagram
Example 1. Liquid with m = 0.08 cP, SG = 1, capacity Q = 100 m3/hr flows in commercial steel
pipe, length L=100 m = 100,000 mm, D = 100 mm. = 0.045, /D = 0.00045. With equation (12),
Re = 1.77 x 106 in fully turbuence zone. From Moody diagram f = 0.017. Equation (5) V = 3.536
m/s. Equation (6) PLOSS = 1.084 kg/cm2.
Table 1 presents equivalent length (L/D)EQ and flow resistance (K).
Example 2. Liquid data is as example 1. Number of glove valve =1, number of LR elbows = 6 ,
number of tee in straight flow = 3 and sudden enlargement to vessel = 1. (L/D)eq =
100,000/100 + 1x340 + 6x20 + 3x20 = 1520 and K=1x1=1. Equation (8),
PLOSS = 0.0051 x 1 x 3.5362 x {1 + 0.04 x 1520} = 1.711 kg/cm2
Incompressible and compressible fluids.
Incompressible fluids could not be reduced their volume by any force. Liquids are
incompressible fluid. Compressible fluids could be reduced their volume by force. Gasses and
vapors are compressible fluid.
Pressure drop of gasses can be approached as incompressible fluid if,
- Low velocity, low pressure drop
- No significant temperature exchange
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Table 1. Equivalent length and flow resistance
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IV. GAS
Properties of gas is sensitive by temperature and pressure changes. When gas is approached
as ideal gas, properties of gas has the following relation,
Gas constant,
R = kJ/kg.K (15)
MW is molecular weight of gas. Gas constant pressure specific heat,
Cp = kJ/kg.K (16)
Gas density of perfect gas,
= kg/m3 (17)
P absolute pressure in kg/cm2 A, R in kJ/kg.oK and T is temperature in oK
In significant differences of pressure or temperature, gas properties are corrected by
compressibility factor Z (see Attachment),
= kg/m3 (18)
Z is provided from gas compressibility chart.
Gas flows through orifice and nozzle.
In special case for orifice and nozzle, equation (7) can be expressed in the following equation.
PLOSS = kg/cm2 (19)
V1 is fluid velocity at orifice hole or nozzle neck (=V/). Flow factor, C is defined as C 2 = 1/K.2
is ratio (D1/D), D1 orifice or nozzle neck diameter and D or Do is inside pipe diameter.
For compressible fluid, C factor in equation (19) shall be corrected by net expansion factor Y.
PLOSS = kg/cm2 (20)
C is given in figure 5, 6, 7 and 8. For figure 7 and 8, Re is based on pipe diameter.
Gas velocity is limited at sound velocity a.
a = (1000 . k . T . Z . R)0.5 m/s (21)
k is adiabatic exponent (Cp/Cv), T temperature in K. The following figures show values of C
and Y for nozzle and orifice.
MW
314.8
1
.
k
kR
TR
P
.
.1.98
ZTR
P
..
.1.98
2
62 10.1.1.5
C
V
22
62
.
10.1.1.5
YC
V
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Figure 4. Orifice and Nozzle
Figure 5. Flow coefficient of Flange Taps Nozzle for Re > 1.5 x 105
Figure 6. Flow coefficient of Flange Taps Orifice for Re > 1.5 x 105
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Figure 7. Flow coefficient Cd of Elliptical Nozzle (Do- Do/2 Taps) for Re ≤ 2 x 105
Figure 8. Flow coefficient of square edge flange taps orifice for Re < 1 x 104 , where C = Cd.(1-
4 )-0.5
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Figure 9. Net expansion factor, Y for nozzle, orifice and infinite enlargement .
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V. SYMBOLS AND UNITS
Unless otherwise noted, the following symbols and units are used in this manual.
Symbol Description Unit
Diameter ratio of nozzle or orifice
C Flow coefficient
D or Do Inside pipe diameter mm
D1 Orifice or nozzle diameter mm
Surface roughness mm
f Friction factor
g Gravity 9.81 m/s2
h Head m
K Flow resistance
L Pipe length m
L/D Equivalent length
Viscosity cP (centipoise)
P Pressure kg/cm2A
P Differential pressure kg/cm2
Q Volume flow m3/hr
Fluid density kg/m3
Re Reynold Number
R Gas constant kJ/kg.K
SG Specific gravity
T Absolute temperature 0 K
V Fluid velocity m/s
Y Gas net expansion factor
VI. UNIT CONVERSION
Designation Unit to be converted Factor Unit to be used
Length ft 304.8 mm
inch 25.4 mm
Pressure psi 0.06897 bar
kg/cm2 (at.) 0.981 bar atm. 1.013 bar
Pa (Pascal) 10-5 bar
Temperature F (Fahrenheit) (t-32) x (5/9) C
K (Kelvin) T - 273 C
R (Rankin) (5/9) K
Velocity ft/s 0.3048 m/s
ft/min (fpm) 0.00508 m/s
Volume flow GPM (US) 0.227 m3/hr
CFM 1.699 m3/hr
Mass lb 0.4536 kg
Power HP 0.7457 kW
Head ft 0.3048 m
Enthalpy kcal/kg 4.1868 kJ/kg
BTU/lb 2.326 kJ/kg
Gas constant kcal/kg.K 4.1868 kJ/kg.K
Specific heat BTU/lb.R 4.1868 kJ/kg.K
& Entropy
Specific mass lb/ft3 16.0185 kg/m3
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or density
Specific volume ft3 /lb 0.06243 m3/kg
Viscosity N.s/m2 1000 cP
lbf.s/ft2 47880.3 cP
Note : American Standard State condition is condition where pressure at 1.013 bar A and
temperature at 15.5 C. In volume, is common written as SCF. Normal condition is at 1.0132 bar
A and 0 C. In volume, is common written as Nm3
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VII. STANDARD PIPE DIMENSION (TABLE FOR INSIDE DIAMETER)
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VIII. PROPERTIES OF FLUIDS
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PROPERTIES OF SOME GASSES
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Extrapolation or use following equation for other temperature,
5.1
To
T
CT
CToo
is viscosity at any temperature T . o is known viscosity at known To (T and To in Kelvin). C is
Sutherland’s constant:
Gas Approx. C Gas Approx. C
O2 127 NH3 370
Air 120 H2 72
N2 111
CO2 240
CO 118
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See “Steam Table” in Turbine page of this blog for other steam properties.
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COMPRESSIBILITY FACTOR OF GAS
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