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IS 10189-2-2 (1993): Industrial process control valves,Part 2: Flow capacity, Section 2: Sizing equations forcompressible fluid flow under installed conditions [ETD 18:Industrial Process Measurement and Control]

IS 10189 (Part 2/Set 2 ) : 1993

w-;T9;

Indian Standard

INDUSTRIALPROCESSCONTROLVALVES PART 2 FLOW CAPACITY

Section 2 Sizing Equations for .compressible Fluid Flow

Under lnstalled,Conditions

UDC 621-646-2 : 6501156 : 621-5

Q BIS 1993

BUREAU OF INDIAN STANDARDS MANAK BHAVAN, 9 BAHADUR SHAH ZAFAR MARG

NEW DELHI 1 lQOO2

October 1993 Price Group 5

Industrial Process Measurement and Control Sectional Committee, ETD 18

FOREWORD

This Indian Standard ( Part 2/Set 2 ) was adopted by the Bureau ofIndian Standards, after the draft finalized by the Industrial Process Measurement and Control Sectional Committee had been approved by the Electrotechnical Drvision Council.

This series of Indian Standard on Tndustrial Process Control Valves is being printed in several parts. Following parts have so far been printed:

a) IS 10189 ( Part 1 ) : 1982 Industrial process control valves : Part 1 General requirements and tests;

b) IS 10189 ( Part 2/Set 1 ) : 1993 Industrial process control valves : Part 2 Flow capacity, Section 1 Sizing equations for incompressible fluid flow under installed conditions; and

c) IS 10189 ( Part 2/Set 2 ) : 1993 Industrial process control valves : Part 2 Flow capacity, Section 2 Sizing equations for compressible fluid flow under installed conditions.

This standard ( Part 2/Set 2 ) covers equations suitable for use in sizing industrial process control valves when the flowing media are compressible fluids. At very low ratios of pressure differential to absolute inlet pressure ( A p/p1 ), compressible fluids behave similar to incompressible fluids. Under such conditions the sizing equations presented in this section can be traced to the basic Bernoulli equation for Newtonian incompressible fluids. effects which require the basic equations

However, increasing values of A p/p~, result in compressibility to be modified by appropriate correction factors. The equations

presented are for use with gas or vapour and are not intended for use with multiphase streams such as gas-liquid, vapour-liquid or gas-solid mixtures.

While preparing this standard, blndustrial process control valves

assistance has been derived from IEC Publication 534-2-2 ( 1980 ) : Part 2 Flow capacity, Section 2 Sizing equations for compressible fluid

ljow under installed conditions’, issued by the International Electrotechnical Commission ( IEC ).

For the purpose of deciding whether a particular requirement of this standard is complied with, the final value, observed or calculated, expressing the result of a test or analysis, shall be rounded offin accordance with IS 2 : 1960 ‘Rules for rounding off numerical values ( revised)‘. The number of signifirant places retained in the rounded off value should be the same as that of the specified value in this standard.

IS 10189 ( Part 2 /Set 2 ) : 1993

Indian Standard

INDUSTRIAL PROCESS CONTROL VALVES

PART 2 FLOW CAPACITY

Section 2 Sizing Equations for Compressible Fluid Flow Under Installed Conditions

1 SCOPE 3 TERMINOLOGY

This standard (Part 2/Set 2) gives equations for use in For the purpose of this standard, definitions given in

sizing I.P.C. valves when the flowing media is compres- Part 1 of this standard shall apply with the addition of

sible fluid. the following.

3.1 Choked Flow 2 REFERENCES

The following Indian Standards are necessary adjuncts ro this standard:

IS No.

10189 (Part 1) :1982

me

Industrial process control valves : Part 1 General requirement and tests

10189 ( Part2/Sec 1 ): 1993

Industrial process control valves : Part 2 Flow capacity, Sectiou 1 Sizing equations for inconipres- sible fluid flow under installed conditions

A maximum limiting flow condition which compres- sible fluids can reach in passing through control valves.

NOTE - With fixed inlet (upstream) conditions, choked flow is evidenced by the failure of increasing pressure differential to produce further increase in the flow rate.

3.2 Critical Differential Pressure Ratio

The maximum ratio of differential pressure to inlet absolute pressure, that is, effective in all of the valve sizing equation. Choked flow occurs when this n~axinnm ratio has been reached.

3.3 Fitting

Any device such as a reducer, expander, elbow, T-piece, or band, which is attached directly to an end connection of a control valve.

.

4 NOMENCLATURE

Symbols Description

C Flow coefficient (A,&C,)

Nominal valve size (DN)

Internal diameter of the piping

Piping geometry facCor

Specific heat ratio factor

Molecular mass of flowing fluid

Nunierical constants

Inlet absolute pressure measured at the upstream pressure

tap

P2 Outlet absolute pressure measured at the downstream pressure tap

PC

P,

AP

Q

Absolute thermodynamic critical pressure

Reduced pressure ( pl/pc )

Pressure differential ( p1 - p2 ) between upstream and downstream pressure taps

Vnlunietric flow rate

Unit

Various (see Note 1)

111111

LllLll

Dimensionless

Dimensionless

Various

kPa or bar (see Note 2)

kPa or bar

kPa or bar

Dimensionless

kPa or bar

m”/h (see Note 3)

1

IS 10189 (Part 2/Set 2) : 1993

S~ytnOols Description Unit

Y z

Y

Pl

5

Inlet absolute temperature (“C + 273)

Absolute thermodynaniic critical temperature

Reduced temperature~( T,/T, )

Absolute reference temperature for standard cubic metrc

Mass flow rate

Ratio of pressure differential to inlet absolute pressure

@p/m)

Pressure differential ratio factor of a control valve without attached fittings

Pressure differential ratio factor of a control valve with attached fittings

Expansion factor

Conipressihility factor - ratio of ideal to actual inlet specific mass (function of y,, T,)

Specific heat ratio

Density (specific mass) of fluid at p, and Tl

Head loss coefficient ofa reducer, expander or other fitting attached to a control valve

K

K

Dimensionsless

K (see Note 3)

kg/h

Dimensionless

Dimensionless

Dituensionless

Dimensionless

Dinmlsionless

Dimensionless

kg/‘&

Dimensionless

NC W&S

I See Part I of this standard.

2 1(,5 Pa = 102 kPa = 1 bar.

3 Volumetric flow rates in cubic metrcs per hour, identified by the symbol 8, refer to standard conditions. The standard cubic metre is taken at 1 013.25 mbar and either 273 K or 288.5 K.

5 INSTALLATION

5.1 In many industrial applications, control valves are installed using a variety of piping fittings attached to the upstream and downstream connections ou the valve. These fittings usually have a significant reducing effect ou the iustalled valve sizing coefficient. A correctiou factor is introduced to account for these effect?.

5.2 In sizing control valves, using the relationships presented herein, the tlow coefficients calculated in- clude all head losses between pressure taps located as shown in Fig.1. It should be noted that the locations 01 the upstream and downstrea 111 pressure taps ha\gc IWW

fixed at the outer limits. (See Part 1 of this standard) These calculated flow coefficients will normally be compared with rated flow coefficients listed in valve manufacturers literature. Rated coefficients also iuclude all head losses front two pipe diameters upstream through six pipe diameters downstream but where the rnutrol valve has been installed without fittings attached.

6 SIZING EQtJATIONS

6.1 The equations listed below identify the relation- ships between flow rates, flow coefficients, related installation factors aud prrtinent service conditions for

UPSTREAM PRESSURE I--

4 2 DOWNSTREAM @-j PRESSURE

TAP i(

TAP

& 9-

4 p2

CONTROL VALVE OR CONTROL VALVE WITH ATTACHED FITTINGS

FIG. I PKJZSSURE TAP LOCATIONS

2

IS 10189 ( Part 2 /Set 2 ) : 1993

control valves handling compressible fluids. Flow rates for compressible fluids may be encountered in either

mass or volume units and thus equations are necessary to handle both situations. Flow rales may be calculated using the appropriate equation selected from the following:

W=N,.F,.C.Ym (1)

W=N,.F,,.C.y,.Y

When the flow rale is kunwu and the valve sizing coefficient C is to be detcnuined, the following respec- tive rearrangenmits of the above equations shall be used:

c= W N,.F,.Yh.p,.p, (4)

c=

% = (6)

NOTES

1 I;i, is unity when the umtml valve is installedwithout fittings. Refer IO (7) foorF~> values with other installation contigmtions.

2 Refer to (8) for dctnils of lhe expansion faclor Y

.1 &,I+$& N9 xc numerical constants, thevaluesofwhich account for the necessary conversion of measurement units used in the equations and also for the specific tlow coelticient desired. Flow coefficient included are Av, Kv alld C’v and values of the constants may he

obtained from Table 1.

6.2 In some cases, volumetric valve sizing equations for compressible fluids ront;:iu the term G. This term defines the relative density of the flowing fluid to air when both are at standard conditions. The relatioltship

reduces to the following :

where

M = molecular mass of flowing fluid, and

Ma = molecular nms of air = 28.97

6.3 Several other equations for sizing control valves for compressible fluids are in conuuon -world-wide usage. Some of these equations are given in Annex A.

7 PIPING GEOMEI’RY FACTOR Fp

7.1 The piping geometry l’artor F,, modifies ~Ihe flow coefficienl for reducers, expanders or other fittings allached to the valve body. F, is the ratio of the flow coefficient for a valve with fittings attached to its inlet and/or to the rated flow coefficient.

To meet the n~aximuu permissible tolerance of *5 percent, the F,, factor shall be determined by test.

When calculated values are permissible, the following equation nlay be used:

F,, =

$_ l+z C 2 Nz d2 0

NOTE - Values for N2 are given in Table I.

7.2 In the above equation, the factorZc is the algebraic sum of all the effective velocity head coefficients of reducers, expanders or other fittings attached to the conlrol valve. The velocity head coefficient of the control valve itselt is not included.

x1; = <I + 5, + Gn, - i;B? (8)

where

‘Q = upstreani resistance coefficient,

<2 = downstream resistance coefficient,

‘CSI = inlet Bernoulli coefficient, and

‘Q=Q = outlet Bernoulli coefficient.

‘I‘able 1 Numerical (lo&ants N

( CkUrse h. 1 )

N8 3.95 x lo” 1.10 9.48 x lo- kg/h - kpa - K -

3.95 x lo6 1.10 x IO2 9.48 x IfI” kg/h - bar - K -

Ns(T3 = ‘73 K) 8.S5 x 11+ ‘7.46 x 10’ L.l’xlO’ - m ‘III kl’a - K -

8.SS x Nl' L4h x 10’ 2.17xx103 - m~lh IlilT - K -

NC> (I’s = “8S.S K) 9.35 x lo5 “A0 x IO’ 2.25 x 10’ - m3/l, kl’a - K -

9.35 x ICI7 1.60 x to.7 2.25 x 103 - m3/h bar - K -

3

IS 10189 (Part 2/Set 2) : 1993

Wheu inlet and outlet fittings are identical, CR1 = <B;sz

and therefore, drop out of the equation.

III those cases where the piping diameters approaching and leaving the control valve are different, values of

Ll and &2 may be calculated using the following

relationship:

d4 i;Blor~B2= l- yj 0

If the inlet and outlet fittings are’short-length couuuer- cially available concentric reducers or expanders, the 5 terms may be approximated using the following expressions:

- reducer only:

- expander only:

‘s2 = 1.0 1 - ; i 01

- reducer and expander of equal size:

(II)

2 2

Cl + I& = 1.5 I 1 - 01 5 (12)

When the inlet and outlbt f&&s ire different from those describe. above, the resistance coefficients cl and

c2 have not been tabulated and thus the value ofF,, shall

be obtained by test.

8 EXPANSION FACTOR Y

8.1 The expansiou factor Y accounts for the change in density as the fluid passes from the valve inlet to the “vena contracta” (the location just downstream of the orifice where the jet stream area is a minimum). It also accounts for the change in “vena contracta” area as the pressure differential is varied.

Theoretically, Y is affected by all of the following:

a) ratio of port area to body inlet area,

b) shape of the flow path,

c) pressure differential ratio x,

d) Reynolds number, and

e) specific heat ratio y.

The influences of Items (a), (b) and (c) are accounted for by the pressure differential ratio factor x, which may br established by air test.

8.2 The Reynolds number is the ratio of inertial to viscous limrs at the control valve orifice. In the case of conllmssible Bow, its value is beyond the range of influence since turbulent flow almost always exists.

The value of the ratio of specific heats of the fluid affects the pressure differential ratio factor+

Y may be calculated using equation (13) or the equation given in Annex B:

y= ] _x 3 FY’T

;!3)

In the above equation, the value inserted forx inay not exceed the product of FY and xT even though the actual

value of x is greater, See 9 and 10 for information on x, xT and FY.

9 PRESSURE DIFFERENTIAL RATIO FACTOR

9.1 Pressure Differential Ratio Factor Without Reducers or Other Fittings XT

9.1.1 xT is the pressure differential ratio factor of a control valve installed without reducers or other fit- tings. If the inlet p~ssure pi is held constant and the outlet pressure p2 is progressively lowered, the mass

flow rate through a valve will increase to a maxinnm limit, a condition referred 10 as choked flow. Further reductions inp?will produce no further increase in flow

rate. This limit is reached when the pressure differential ratio r reaches a value of FYX,~. The limiting value of x is defined as the critical differential pressure ratio. The value ofx used in any of the sizing equations (1) to (6) and in the relationship for Y [equation (13)] must be held to this limit even though the actual pressure dif- ferential ratio is greater. Thus, the numerical value of Y may range from 0.667, when x = Fyq-, to 1 .O for very low differential pressures.

9.1.2 The value of XT-may be established by air~test.

The test procedure for this determination is covered in Part 4 of this standard (in preparation). However, X,

may be approximated from F, ‘, the liquid pressure

recovery factor of a control valve without attached fittings. Equation (A-S) shows this relationship.

NOTE - FI_ is defined in Part 2/Secl of this standard for sizing equations for incompressible tluid tlow under installed conditions.

9.1.3 Representative values of XT for several types of

control valves with full size trim and at full rated openings are giveu in Table 2. Caution should be exer- cised in the use of this information. When precise values are required they shall be obtained by test.

9.2 Pressure Ditrereutial Ratio Factor With Reducers or Other Fittings _+,,

9.2.1 If a control valve is installed with reducers or other fittings, the value ofxT will bc affected.

To meet the specified tolerance limitatiou of 25 percent, the valve and attached fittings shall be tested as a unit. When estimated values are permissible, the following equation may be used:

In the above relationship, xT is the pressure differential

ratio factor for a control valve installed without reducers or other fitiings. < is Ihe sum of the inlet velocity head coefficients (<, + &) of the reducer or

other fitting attached to the inlet face of Ihe valve.

4

IS 10189 ( Part 2 /See 2 ) : 1993

conditions. Instead, the density is inferred from the inlet pressure and temperature based on the laws of ideal gases. Under some conditions, real gas behaviour can deviate markedly from the ideal. In these cases, the compressibility factorZsha11 be introduced to compen- sate for the discrepancy. Z is a function of both reduced pressure and temperature. For use in this section, reduced pressurep, is defined as the ratio of the actual inlet absolute pressure to the absolute thermodynamic critical pressure for the fluid in question. The reduced temperature T, is defined similarly. That is:

9.2.2 If the inlet Citting is a short-length commercially available concentric reducer the value of 5 may be estimated using equation (10). For other types of fit- tings, cl and Fp shall be obtained by test.

NOTE - Values of N5 in equation (14) are listed in Table 1.

10 SPECIFIC: HEAT RATIO FACTOR F.,

10.1 The factor xT is based on air near atmospheric pressure as tht-flowing fluid. At temperatures not ex- ceeding 37O*C, the specific heat ratio y for air is 1.40. If the specific heat ratio for the flowing fluid is not 1.40, the factor F., is used to adjust x,. Use the following

equation to calculate the specific heat ratio factor:

F,-J- ” 1.40 (15)

11 COMPRESSIBILITY FACTOR Z

11.1 Sizing equations (2), (3), (5) and (6) do not contain a term for the actual density of the fluid at upstream

pr=: c

T, =;

c (17)

Absolute thermodynamic critical pressures and temperatures for most fluids and curves from which Z may be determined can be found in numerous reference handbooks of physical data.

Table 2 Representative xT Values for Full Size ‘Ikim at Full Rated Opening

(Clause 9.1.3)

Valve Qpe

Globe : Single port

Double port

Angle

Ball

Butterfly

n-h lLPe

Ported Plug

Contoured plug

Characterized cage

Ported plug

Contoured plug

Contoured plug

Characterized cage

Venturi

Characrerized segmental

Conventional (port dia. : 0.8 d)

(60” open)

(900 open)

Either

Flow-to-close

Flow-to-open

Flow-to-close

NOTE- Values in this table are approximate only and do not apply to all valves of a type. If accuratevalues are needed they shall be determined by test.

5

IS 10189 (Part 2Bec 2) : 1993

ANNEXA

(Clause 6.3) OTHER SIZING EQUATIONS

A-l In addition to the control valve sizing equations presented in 6 there are other sizing equations for compressible flow which have achieved significant worldwide usage. Two such equations, which have been widely used and which may be expected to con- tinue in usage for the forseeable future, are presented and briefly described in this Annex. These equations are not preferred and their use should be discontinued in the interest of uniformity of practice.

One well-recognized relationship is:

where

Qa = choked air flow rate, in standard cubic metres per hour at Ts = 288.5 K;

Pl = inlet absolute pressure, in bars;

QbV= non-choked water flow rate, in cubic metres per hour; and

A, = pressure differential, in bars.

A-3 Contol valves exhibiting high pressure recovery capabilities will have low values of C, and vice versa.

The normal range of this coefficient is approximately 14 to 38. Within testing tolerances, C, is related to the pressure differential ratio factor xT by:

All variables in this equation have been defined in~the main body of this section except C,. The constant NLO and all other constants in this Annexare to~be found in Table 3.

A-2 The magnitude of the coefficient C, is a measure

of the pressure recovery characteristic of the control valve in question. Its determination entails flow testing with both compressible and incompressible fluids. In the test with a compressible medium the pressure differential across the valve shall be sufficient to produce choked flow, whereas for the test with an incompressible fluid no choking is permitted. If air and water at 288.5 K are used for the tests, C, may be computed from the fnllowing relationship:

QJP, ‘1 = 2*106 Qw/,,@

c, -40%

The bracketed expression in equation (A-l) is an in- dication of the fraction of choked flow which exists for the value of Apip used in the computation. Choked flow is indicated when the bracketed value is equal to, or greater than, 90°. Thus the bracketed value shall be limited to 90°.

,

Results obtained with equations (3) and (A-l) agree within measurement tolerances.

A-4 Another form of equation (A-l) is given by ~the following expression where the flow rate is in mass units rather than volumetric units:

Table 3 Numerical Constants N

(Clause A-l)

Flow Coeftkieot C Formula Units

A, & C” W Q P. rip P T

NIO (Ts - 273 K) 1.66 x IO’ 4.62 x 1O-3 4.00 x 1O-3 - m3/h Wa K

1.66 x lo4 4.62 x 10-l 4.00 x 10-I - m3/h bar K

Nlo (Ts - ‘l&L5 K) 1.71 x loz 4.75 x 1o-3 4.11 x IO” - m3/h kFJa K

1.71 x 104 4.75 x 10-l 4.11 x 10-l - m3/h bar K

NII 1.91 x 103 5.30x lo-’ 4.58 x IO-’ kg/h - kPa KS/m3 1.91 x lo4 5.30 x 10-l 4.58 x 10-l k/h bar Kg/m3 -

Ntz (Ts - 273 K) 1.01 x IO5 2.79 2.41 m3/h kPa K

l.OI~X 10’ 2.79x 10’ 2.41 x IO2 - m3/h bar K

NE (Ts - 288.5 K) 1.06 x 16 2.95 2.55 m3/h kPa K

1.06 x 10’ 2.95 x 102 2.55x lo2 - m’/h bar K

N13 7.67 x 10” 2.13 x 10-l 1.84 x 10-l k@ kkl

7.67 - x 105 2.13 x 101 1.84 x IO’ k0 bar

6

IS 10189 ( Part 2 /Set 2 ) : 1993

A-5 Another easily identifiable relationship is:

Q=NIGi (y-0.148y”)

where

pvc = “vena contracta” pressure

A-8 Equation (A-5) is based on the proposition that, within testing tolerances:

A-6 Wifh fhe exception ofy and C, the variables in the

above expression are as previously defined in this section. The variable y is defined as follows: C,= XT

II- 0.84

I/-

c’,- may be determined by testing with eitherwaterorair 1.63 4 y=_ under choked flow conditions. It is taken to be

C, Pl equivalent to the liquid pressure-recovery factor FL as

A-7 Values of y are limited to 1.5, since at this value defined in Part 2/Set 1 of this standard.

the expression 0, - 0.148 .?) has a value of 1.0 which A-Y With flow rate in utitss uuits equation (A-S) has is an indication that choked flow conditions exist. the form:

Cf is a coefficient that indicates pressure recovery W-N,, c c,y, q 0, - 0.1489) characteristics and is defined by:

111 this relationship, the variable G, is defined as the

ratio of the density of the flowing fluid to the density of air when both are al inlet pressure and temperature.

ANNEXB (Clause 8.2)

RIGOROUS EXPRESSION FOR THE EXPANSION FACTOR Y

B-l A different formula is given in this Annexure sion factor Y. This equation can be simplified with a which iutroduces a rigorous expression for the expan- good approximation to a linear relationship:

FIG. 2 Extmsrc 1s F,\c I( JK \‘b PK MI ‘KIT DROP RATIO I-I II< WIDELY D~S+XRIN(; VALUES OF Fs (FOR y = 1.4, AIR)

7

IS 10189 (Part 2/Set 2) : 1993

in which the value inserted forx is set equal tax, when

its actual value is greater thanx,.

B-2 The factors used in the above equation are:

Al EL.! 1 2 y-1

au = i-i 2 y+l

this is dependent on thd specific heat ratio y only.

B-3 In practice, the value of Us can be obtained from Table 3 below or deduced from a graph as a function of y. On the other hand the following simpler foumula can be used.

‘Jy = 0.310 + 0.122 y

which gives an error smaller than 1 percent (y being in the normal range of the values for gases).

B-4 Fg is the pressure recovery factor of the valve at

rated travel. For any valve, its value must be considered as a known quantity, which is experimentally obtained as outlined in the standard on testing~procedures.

Through Fg the value ofX, is calculated by:

2 *t

xcr = 1 - - ( 1 Y+l

this is the value nf x corresponding to ihe choked flow.

B-5 This value can be deduced from a graph as a function of Fg, y being a fixed parameter. When Fg is in the range 0.7 to 1.1; a simpler formula can bc. used, which is (for air):

-% = 0.684 F, - 0.210

which gives an error smaller than 1 percent in respect to the equation (A-4).

B-5.1 In practice, instead of calculating Y by means of the above equations, it is possible to use a simple graph, similar to that of Figure 2. In this graph Y is drawn for an assigned ga,s (air) as a function of x, the factor Fg being assumed as a parameter. By this means the value of Y can be obtained immediately and used directly in equations (1) to (6) inclusive.

B-6 The relatiomhip (A-l) bc~wecn Y and x is linear, as is equation (13) of the main text. It h;ls 10 be noted, howcvcr,

Table 4 Values ofy aud u.,

(Clause B-8)

Gas ur Vapour Symbol y = (I,, ( ; 0,

Acaylene C2H2 1.30 0.472 Air - 1.40 0.484 Ammonia NH3 1.32 0.474

Argon A 1.67 0.5 14

N-Butane C4H10 1.11 0.446

(.‘arbon dioxide CO2 1.30 0.472

Carbon monoxide CO I .40 0.484 Etbane (:2H6 I.“‘2 0.461 Ethylene C2H4 1.X C.461

Freon (F-12) CCI?F? 1.13 0.449 (dichlorodifluoromethane)

Helium He 1.66 0.513

Hydrogen H: 1.41 0.485

Methane CH4 1.32 0.473 Natural gas ‘) 1.27*) 0.468’) Neon Ne 1.64 0.511

Nitric oxide NO 1.40 0.484

Nitrogen N2 1.41 0.485 Octane CRHIS 1.66 0.5 13 Oxygen 02 1.40 0.484 Pentane CsH12 1.06 0.438 Propane C:3H8 1.15 0.452

Propylene C3H6 1.14 0.450 Saturated Sleam 1.25-1.32” 0.465-0.4742)

Sulphur dioxide so2 1.26 0.467 Superheated steam 1.315 0.474

‘) Representative values : exact characteristics require knowledge of exact constituents.

2, For water vapour, y is not constant but varies with thevalues of the initial quality and initial pressure.

that the critical value X, is very different from the terminal value xT of equation (13). Nevertheless, the

nuttterical results of equations (13) and (B-l) differ slightly (less than 1 petcent for air, in the normal range of FJ if the

pmper correlation fnmmla between .Q and Ft: is used.

This correlation formula gives:

.rT = 2.25 c7., F, 2 = 0.527 F, * for air

B-7 It has to be remarked that the method described in this Annex takes into account more ac.curately the in- fluence of the various physical quantities, in particular that of Fgand y. Moreover, since the theory is not based on the ideal gas law, equations (1) and (4) with the use of formula (A-l) are valid also for real gases and va~pouts (by assuming the value of p, corresponding

to the values of pt and T,).

However, to avoid the use of tables to infer the value of p,, prnclical relationshipbetweenp, and p1 canbe used. In

this way the following fortttulae for steam ate obtained:

IS 10189 ( Fart 2 /Set 2 ) : 1993

saturated dry steattt (initial quality = 1) :

W = 0.72. N6. C .pl . Y fi

B-8 By setting y = 1.14 there results Us= 0.450,

x, = (0.539 - 0.118 Fi) Fpz; hence Y can be

calculated or deduced frottt a graph drawn for y = 1.14. In the same way, a similar formula can be obtaitted for waler vapour having a quality smaller than 1, by using the proper value ofy, as reported in the hattdbook mentioned under Able 4.

superheated steam:

W= 0.72.N,.C.p,

1 + 0.001 2G At yG

where At is the degree of superheat in degrees Celsius.

By setting y = 1.3 15 there results u? = 0.474,

X, = (0.596 - 0.139 FL: *)F$ hence Yran be calculated

or deduced from a graph drawn for y = 1.3 15.

Standard Mark

The use of the Standard Mark is governed by the provisions of the Bureau of Indian Standards Act, 1986 and the Rules and Regulations made thereunder. The Standard Mark on products covered by an Indian Standard conveys the assurance that they have been produced to comply with the requirements of that standard under a well defined system of inspection, testing and quality control which is devised and supervised by BIS and operated by the producer. Standard marked products are also continuously checked by BIS for con- formity to that standard as a further safeguard. Details of conditions under which a licence for the use of the Standard Mark may be granted to manufacturers or producers may be obtained from the Bureau of Indian Standards.

Brreau of Indian Standards

BIS is a statutory institution established under the Bureau of In&an S#dr& Act, 1986 to promote harmonious development of the activities of standardization, marking and quality certification of goods and attending to connected matters in the country.

Copyright

BIS has the copyright of all its publications. No part of these publications may be reproduced in any form without the prior permission in writing of BIS. This does not preclude the free use, in the course of implementing the standard. of necessary details, such as symbols and sizes, type or grade designations. Enquiries relating to copyright be addressed to the Director ( Publications ), BIS.

Review of Indian Standards

Amendments are issued to standards as the need arises on the basis of comments. Standards are also reviewed periodically; a standard along with amendments is reaffirmed when such review indicates that no changes are needed; if the review indicates that changes are needed, it is taken up for revision. Users of Indian Standards should ascertain that they are-in possession of the latest amendments or edition by referring to the latest issue of ‘BIS Handbook’ and ‘Standards Monthly Additions’. Comments on this Indian Standard may be sent to BIS giving the following reference:

Dot No. ETD 18 ( 3105 )

Amendments Issued Since Publication

Amend No. Date of Issue Text Affected

BUREAU OF 1NDIAN STANDARDS

Headquarters:

Manak Bhavan, 9 Bahadur Shah Zafar Marg, New Delhi 110002 Telegrams : Manaksanstha Telephones : 331 0~1 31, 331 13 75 ( Common to all 05ces )

Regional Ofices t Telephone

Central : Manak Bhavan, 9 Bahadur Shah Zafar Marg NEW DELHI 110002 I

331 01 31 331 13 75

Eastern : l/14 C. I. T. Scheme VII M, V. I. P. Road, Maniktola CALCUTTA 700054 I

37 84 99, 37 85 61 37 86 26, 37 86 62

Northern 8 SC0 445-446, Sector 35-C, CHANDIGARH 160036

Southern : C. I. T. Campus, IV Cross Road, MADRAS 600113

Western 1 Manakalaya, E9 MIDC, Marol, Andheri ( East ) BOMBAY 400093

I

53 38 43, 53 16 40 53 23 84

1

235 02 16, 235 04 42 235 15 19, 235 23 15

I

632 92 95, 632 78 58 632 78 91, 632 78 92

Branch-es : AHMADABAD. BANGALORE. BHOPAL. BHUBANESHWAR. COIMBATORE. FARIDABAD. GHAZIABAD. GUWAHATI. HYDERABAD. JAIPUR. KANPUR. LUCKNOW. PATNA. THIRUVANANTHAPURAM.

Printed at New India Printing Prew. Khurla. India

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