FLUID FLOW IN PIPE 1 - Design and selection · PDF fileFLUID FLOW IN PIPE 1 ... Velocity...

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


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


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


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


Table 1. Equivalent length and flow resistance


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


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


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


Figure 9. Net expansion factor, Y for nozzle, orifice and infinite enlargement .


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


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


VII. STANDARD PIPE DIMENSION (TABLE FOR INSIDE DIAMETER)


VIII. PROPERTIES OF FLUIDS


PROPERTIES OF SOME GASSES


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


See “Steam Table” in Turbine page of this blog for other steam properties.


COMPRESSIBILITY FACTOR OF GAS

FLUID FLOW IN PIPE 1 - Design and selection · PDF fileFLUID FLOW IN PIPE 1 ... Velocity...

Documents

Transcript of FLUID FLOW IN PIPE 1 - Design and selection · PDF fileFLUID FLOW IN PIPE 1 ... Velocity...