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Friction loss
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16 2.2 1
20 1.9 2.8 2
25 2.3 3.5 3
32 1.8 2.9 4.4 4
40 1.8 2.3 3.7 5.5 5
50 1.8 2.0 2.9 4.6 6.9 6
63 1.8 2.0 2.5 3.6 5.8 8.6 7
75 1.9 2.3 2.9 4.3 6.8 10.3 8
90 2.2 2.8 3.5 5.1 8.2 12.3 9
110 2.7 3.4 4.2 6.3 10.0 15.1 10
125 3.1 3.9 4.8 7.1 11.4 17.1 11
140 3.5 4.3 5.4 8.0 12.7 19.2 12
160 4.0 4.9 6.2 9.1 14.6 21.9 13
180 4.4 5.5 6.9 10.2 16.4 24.6 14
200 4.9 6.2 7.7 11.4 18.2 27.4 15
225 5.5 6.9 8.6 12.8 20.5 30.8 16
250 6.2 7.7 9.6 14.2 22.7 34.2 17
280 6.9 8.6 10.7 15.9 25.4 38.3 18
315 7.7 9.7 12.1 17.9 28.6 43.1 19
355 8.7 10.9 13.6 20.1 32.2 48.5 20
400 9.8 12.3 15.3 22.7 36.3 54.7 21
450 11.0 13.8 17.2 25.5 40.9 61.5 22
500 12.3 15.3 19.1 28.4 45.4 68.3 23
560 13.7 17.2 21.4 31.7 50.8 24
630 15.4 19.3 24.1 35.7 57.2 25
710 17.4 21.8 27.2 40.2 64.5 26
800 19.6 24.5 30.6 45.3 27
900 22.0 27.6 34.4 51.0 28
1000 24.5 30.6 38.2 56.7 29
1100 26.9 33.7 42.0 62.4 30
1200 29.4 36.7 45.9 68.0 31
1400 34.4 42.9 53.5 32
1600 39.2 49.0 61.2 33
Dn [mm] 2 1/2 3.2 4 6 10 16Presiones nominales PN [bar]
HDPE PE80 DIN 8074 / ISO 4427Espesor [mm]
1 2 3 4 5 6 7
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
2
3 Pipe Thickness [mm], according ASME B36.10M4
5 ASME B36.10M SCHEDULE / IDENTIFICATION
6 Size 5 10 20 30 40 60 80 100 120 140 160 STD XS XXS
7 1/2 21.3 1.65 2.11 - 2.41 2.77 - 3.73 - 0 - 4.78 2.77 3.73 7.47
8 3/4 26.7 1.65 2.11 - 2.41 2.87 - 3.91 - 0 - 5.56 2.87 3.91 7.829 1 33.4 1.65 2.77 - 2.9 3.38 - 4.55 - 0 - 6.35 3.38 4.55 9.0910 1 1/4 42.2 1.65 2.77 2.97 3.56 4.85 6.35 3.56 4.85 9.7
11 1 1/2 48.3 1.65 2.77 - 3.18 3.68 - 5.08 - 0 - 7.14 3.68 5.08 10.15
12 2 60.3 1.65 2.77 - 3.18 3.91 - 5.54 - 0 - 8.74 3.91 5.54 11.0713 2 1/2 73 2.11 3.05 4.78 5.16 7.01 9.53 5.16 7.01 14.0214 3 88.9 2.11 3.05 - 4.78 5.49 - 7.62 - 0 - 11.13 5.49 7.62 15.2415 3 1/2 101.6 2.11 3.05 4.78 5.74 8.08 5.74 8.08
16 4 114.3 2.11 3.05 - 4.78 6.02 - 8.56 - 11.13 - 13.49 6.02 8.56 17.12
17 5 141.3 2.77 3.4 - - 6.55 - 9.53 - 12.7 - 15.88 6.55 9.53 19.05
18 6 168.3 2.77 3.4 - - 7.11 - 10.97 - 14.27 - 18.26 7.11 10.97 21.95
19 8 219.1 2.77 3.76 6.35 7.04 8.18 10.31 12.7 15.09 18.26 20.62 23.01 8.18 12.7 22.2320 10 273 3.4 4.19 6.35 7.8 9.27 12.7 15.09 18.26 21.44 25.4 28.58 9.27 12.7 25.421 12 323.8 3.96 4.57 6.35 8.38 10.31 14.27 17.48 21.44 25.4 28.58 33.32 9.53 12.7 25.422 14 355.6 3.96 6.35 7.92 9.53 11.13 15.09 19.05 23.83 27.79 31.75 35.71 9.53 12.7 - 23 16 406.4 4.19 6.35 7.92 9.53 12.7 16.66 21.44 26.19 30.96 36.53 40.49 9.53 12.7 - 24 18 457 4.19 6.35 7.92 11.13 14.27 19.05 23.83 29.36 34.93 39.67 45.24 9.53 12.7 - 25 20 508 4.78 6.35 9.53 12.7 15.09 20.62 26.19 32.54 38.1 44.45 50.01 9.53 12.7 - 26 22 559 4.78 6.35 9.53 12.7 - 22.23 28.58 34.93 41.28 47.63 53.98 9.53 12.7 - 27 24 610 5.54 6.35 9.53 14.27 17.48 24.61 30.96 38.89 46.02 52.37 59.54 9.53 12.7 - 28 26 660 - 7.92 12.7 15.88 - - - - - - - 9.53 12.7 - 29 28 711 - 7.92 12.7 - - - - - - - - 9.53 12.7 - 30 30 762 6.35 7.92 12.7 15.88 - - - - - - - 9.53 12.7 - 31 32 813 - 7.92 12.7 15.88 17.48 - - - - - - 9.53 12.7 - 32 34 864 - 7.92 12.7 15.88 17.48 - - - - - - 9.53 12.7 - 33 36 914 - 7.92 12.7 15.88 19.05 - - - - - - 9.53 12.7 - 34 38 965 - - - - - - - - - - - 9.53 12.7 - 35 40 1016 - - - - - - - - - - - 9.53 12.7 -
dext
36 42 1067 - - - - - - - - - - - 9.53 12.7 - 44 1118 - - - - - - - - - - - 9.53 12.7 - 46 1168 - - - - - - - - - - - 9.53 12.7 -
39 48 1219 - - - - - - - - - - - 9.53 12.7 -
Kv values as function of Cv values
Cv value are usually published in tables of this type
The Cv value is the water flow rate Q [GPM] that will pass through a valve
The reference water specific gravity is defined as SG = 1, for a temperature of 60 ºF.
For derivation, see sheet 1a.- Kv=f(Cv)
when the pressure across it is DP = 1 [psi].
Flow rate in m³/h Flow rate in m³/h Flow rate in gpmPressure in "Pascal" Pressure in "bar" Pressure in "psi"
Relationship Relationship Relationship
0.0027353 *Cv 0.864972 *Cv Cv direct from table
Example (SI, m3/h, Pa) Example (SI, m3/h, bar) Example (Imperial unitsValve: fully open Valve: fully open Datadn = 4 in dn = 4 in Valve:
50,000 Pa 0.50 Pa dn =SG = 1 SG = 1
From the table From the table SG =Cv = 1282 Cv = 1282
0.0027353 *Cv 0.864972 *Cv From the table
3.51 1,109 Cv =Q = Q = Q =Kv = 3.51 Kv = 1,109 Cv =
50,000 Pa 1 Pa DP =SG = 1 SG = 1 SG =Q = 784.1 m³/h Q = 784.1 m³/h Q =
Q =
Kvm3h,Pa = Kvm3h,bar =
DP = DP =DP =DP =
Kvm3h,Pa = Kvm3h,bar =
Kvm3h,Pa = Kvm3h,Pa =Kv * (DP/SG)^0.5 Kv * (DP/SG)^0.5
DP = DP =
Q(GPM )=Cv⋅√ ΔP( psi)
SGQ(m ³/h )=Kv(m³/ h ,Pa )⋅√ ΔP(Pa )
SGQ(m ³/h )=Kv(m³/ h ,bar )⋅√ ΔP(bar )
SG
Rev. 01.02.2014
Flow rate in gpmPressure in "psi"
Cv direct from table
Example (Imperial units
fully open4 in
50,000 Pa7.25 psi
1
From the table
1282
1,282 -7.25 psi
1 -3,452 gpm
784.11 m³/h
Cv * (DP/SG)^0.5
Q(GPM )=Cv⋅√ ΔP( psi)
SG
K values as function of Cv valuesExample
The singular pressure drop coefficient "K" is defined Fluid: waterin the Darcy-Weisbach equation as Q = 784.1
K * (f / L) * hv 3452where "hv" is the velocity pressure dn = 4
hv = [Pa] For a "sure" ball valve, Ref 1
Cv = 1282"v" is the liquid velocity [m/s] SG = 1
Q = 3452
Examples, for a Bray Series 20/21 Butterfly lined valve SG * Q^2/Cv^2Sg = 1Q = 3452Cv = 1282
7.25
Cv value are usually published in tables of this type 50,000
DP =
(r / 2) * v^2
"r" is the liquid density [kg/m³]
DP =
DP =
DP =
Pressure drop in SI (m3/h,Pa) Singular pressure drop coefficient "K"
m³/h Flow velocitygpm dn = 4in sch = STD
For a "sure" ball valve, Ref 1 #VALUE! mm
- #VALUE! m - A = (pi()/4)*d^2gpm A = #VALUE! m²
SG * Q^2/Cv^2 Q = 784.1 m³/h - Q = 0.218 m³/sgpm v = Q / A
Q = 0.218 m³/s
psi A = #VALUE! m²
Pa v = #VALUE! m/s
Kv-valueVelocity pressure
hv =
1000 kg/m³
0.0027353 * Cv hv =Cv = 1282 - SG = 1
3.51 1000 kg/m³v = #VALUE!
SG * ( Q / Kv )^2 hv = #VALUE! PaSG = 1Q = 784.1 m³/h Singular pressure drop coefficient
Kv = 3.51 K =
50,000 Pa 50000.0 Pahv = #VALUE! PaK = #VALUE! -
Flow rate in m³/h Flow rate in m³/h Flow rate in gpmPressure in "Pascal" Pressure in "bar" Pressure in "psi"
Relationship Relationship Relationship
di =
di =
r / 2 * v^2
r = SG * rwater
rwater =
Kvm3h,Pa = SG * rwater / 2 * v^2
Kvm3h,Pa = rwater =
DP =
DP / hv
DP = DP =
Kvm3h ,Pa=0 .0027353⋅Cv
Q(m ³/ h)=Kv(m³/ h ,Pa )⋅√ΔP(Pa )
SG
Q(m ³/ h)
Kv(m³/ h ,Pa )=√ΔP(Pa )
SG
[Q(m ³/ h)
Kv(m³/ h ,Pa ) ]2
=ΔP(Pa )
SG
ΔP(Pa )=SG⋅[Q(m ³/ h)
Kv (m³/ h ,Pa ) ]2
0 *Cv 0.86 *Cv Cv direct from table
Example (SI, m3/h, Pa) Example (SI, m3/h, bar) Example (Imperial unitsValve: fully open Valve: fully open Datadn = 4 in dn = 4 in Valve:
### Pa 0.50 Pa dn =SG = 1 SG = 1
From the table From the table SG =Cv = ### Cv = ###
0 *Cv 0.86 *Cv From the table
3.51 ### Cv =Q = Q = Q =Kv = 3.51 Kv = ### Cv =
### Pa 1 Pa DP =SG = 1 SG = 1 SG =Q = ### m³/h Q = ### m³/h Q =
Q =
Kvm3h,Pa = Kvm3h,bar =
DP = DP =DP =DP =
Kvm3h,Pa = Kvm3h,bar =
Kvm3h,Pa = Kvm3h,Pa =Kv * (DP/SG)^0.5 Kv * (DP/SG)^0.5
DP = DP =
Q(GPM )=Cv⋅√ ΔP( psi)
SGQ(m ³/h )=Kv(m³/ h ,Pa )⋅√ ΔP(Pa )
SGQ(m ³/h )=Kv(m³/ h ,bar )⋅√ ΔP(bar )
SG
Rev. 01.02.2014
Singular pressure drop coefficient calculated as a function of the pipediameter and Kv value.
(For derivation, see sheet "2a.- K=f(Kv,d)"
K coefficient
K =d = #VALUE! m
Kv = 3.51 -K = #VALUE! -
Pressure drop
K * hvK = #VALUE!hv = #VALUE! Pa
#VALUE! Pa
p^2*1620*d^4/kv^2
DP =
DP =
K=π2⋅1620⋅d4
Kv2
Microsoft Editor de ecuaciones 3.0
Cv direct from table
Example (Imperial units
fully open4 in
50,000 Pa7.25 psi
1
1282
1,282 -7.25 psi
1 -3,452 gpm
784.11 m³/h
Cv * (DP/SG)^0.5
Q(GPM )=Cv⋅√ ΔP( psi)
SG
[2] http://www.valvias.com/discharge-coefficient.php
Coeficiente de descarga "C" en función del coeficiente de flujo "Kv"Discharge coefficient "C" as a function of flow coefficient "Kv"(Valid for liquids)Ecuación de descarga de una válvulaEquation of a discharge though a valve
The discharge coefficient is non dimensional and for a givenvalve model its value is practically constant for any diameter.Usually, the published values are for the totaly open valves.
Fixed cone valves, are discharge valves. For this reason they arecaracterized by means of the discharge coefficient "C" instead ofthe flow coefficient Cv or KvFor this type of valves, the dischaarge coefficient is of the orderof C = 0.75 to C = 0.85
Q =C ⋅ A ⋅√2 ⋅ g ⋅Δh
The discharge coefficient is non dimensional and for a givenvalve model its value is practically constant for any diameter.Usually, the published values are for the totaly open valves.
Fixed cone valves, are discharge valves. For this reason they arecaracterized by means of the discharge coefficient "C" instead ofthe flow coefficient Cv or KvFor this type of valves, the dischaarge coefficient is of the orderof C = 0.75 to C = 0.85
Application of CV and Kv coeficients, for gases
[3]Critical pressure ratio and choked flow
Q = Kv * 18.9 * (DP * (2 * Pin - DP) / SG * (293/(273+tout)) )^0.5Kv = 1.8DP = 0.5 barPin = 4 bar
If the downstream pressure falls below Sg = 1the critical value, the flow become choked. tout = 20 °C
Q = 65.9 m³/h
For air
k = 1.4
Pcrit/Pin = (2 / (k+1) )^(k/(k-1) )Pcrit/Pin = 0.528Pcrit = 0.528 * Pin
The minimum ratio between the upstreampressure to the downstream pressure required for choked flow of air is(Pup/Pdw)min 1.893
Pcrit
Pin
=( 2k+1 )
kk−1
Q=Kv⋅18 . 9⋅√ ΔP⋅(2⋅P in−ΔP )SG
⋅293.15273+tout
Joukomatic. [3]Liquids and gases
[4]Cv for gasesSub-critical flow
Kv * 18.9 * (DP * (2 * Pin - DP) / SG * (293/(273+tout)) )^0.5
SCFH
psia
paiaT: absolute temperature °RSG: Gas specific gravity
Where the reference density is airat 70°F and 14.7 psia
[4] Q =Cv for gases Kv =Critical flow DP =
Pin =Sg =tout =Q =
[3]http://detector-gas-systems.web.cern.ch/detector-gas-systems/downloads/kv_calc_doc.pdf
JoucomaticEngineering informationFlow data Flow factor and orifice size
QG: Gas flow rate
P1: Inlet pressure
P2: Oulet pressure
SG = rG / rAir
Q=Kv⋅18 . 9⋅√ ΔP⋅(2⋅P in−ΔP )SG
⋅293.15273+tout
Cv=QG
962⋅√SG⋅TP1
2−P22
QG=962⋅Cv⋅√P12−P2
2
SG⋅T
Cv=QG
816⋅P1
⋅√SG⋅T
QG=Cv⋅816⋅P1
√ SG⋅T
Liquids
Q [m3
h ]=Kv⋅√ΔP [bar ]SG
SGwater=1______________Gases
Q [Nm3
h ]=Kv⋅18 .9⋅√ΔP⋅(2⋅Pin−ΔP )[bar ]SG
and with temperature correction
Q=Kv⋅18 .9⋅√ΔP⋅(2⋅Pin−ΔP )SG
⋅293.15273+tout
SGair=1 (1 bar absolute and 15 ° C )
Joukomatic. [3]Liquids and gases
Kv * 18.9 * (DP * (2 * Pin - DP) / SG * (293/(273+tout)) )^0.51.80.5 bar4 bar1
20 °C65.9 m³/h
http://detector-gas-systems.web.cern.ch/detector-gas-systems/downloads/kv_calc_doc.pdf
Engineering information
Flow factor and orifice size
Microsoft Editor de ecuaciones 3.0
Liquids
Q [m3
h ]=Kv⋅√ΔP [bar ]SG
SGwater=1______________Gases
Q [Nm3
h ]=Kv⋅18 .9⋅√ΔP⋅(2⋅Pin−ΔP )[bar ]SG
and with temperature correction
Q=Kv⋅18 .9⋅√ΔP⋅(2⋅Pin−ΔP )SG
⋅293.15273+tout
SGair=1 (1 bar absolute and 15 ° C )
Cv Coeficiente de caudal para válvulas de mariposaTabla Cv Coeficiente de caudal para válvulas de mariposa en función de la posición de oberturaTamaño Cv [gpm] [psi]NPS DN Apertura - posición del disco
(inches) (mm) 90º80º 70º 60º 50º
Abierta1 25 61 56 36 21 11
1 1/2 40 147 129 87 50 262 50 244 172 123 73 45
2 1/2 65 439 310 201 115 713 80 691 488 290 165 1024 100 1282 906 515 294 1825 125 2070 1416 805 459 2846 150 2786 1873 1065 607 3768 200 5191 3402 1935 1147 714
10 250 8238 5385 3062 1815 113012 300 12102 7820 4448 2636 164214 350 15210 9829 5590 3313 206416 400 19940 12885 7328 4343 270618 450 26150 16898 9610 5695 354920 500 32690 21124 12014 7120 4436
(*) Datos según catálogo: Bray Series 20/21 Butterfly lined valve
http://www.valvias.com/coeficiente-de-caudal-valvula-de-mariposa.php
Tabla Cv Coeficiente de caudal para válvulas de mariposa en función de la posición de obertura From table in sheet "Bray"Cv [gpm] [psi] dn =Apertura - posición del disco Cv =
40º 30º 20º 10º
5.6 2.7 0.97 0.0712.8 5.9 1.7 0.2527 16 7 0.8943 25 11 1.462 35 16 2
110 63 28 3.6172 98 44 6227 130 59 7427 244 106 13675 387 168 21981 562 245 31
1234 706 307 401617 925 403 522121 1213 528 682651 1517 660 85
From table in sheet "Bray"20 in
32690
Size Cv [gpm] [psi]
90º 80º 70º 60º 50º 40º 30º 20º 10º
NPS (Iinch)
ND (mm)
Opening - disc position
Pressure loss coefficient "K" for gas flow
a =
b =b =
Fluid airSG =
c =
a =b =c =
From Sheet Air blown linehv =
Pressure loss coefficient
K =
hv =K =
a * DP^2 + b *
Pin =
C = (SG*Qm3h^2) / (Kv
Qm3h =
tout =
Kvm3h,bar =
DP =
DP =DP =
DP =
DP =
Microsoft Editor de ecuaciones 3.0
c=SG⋅Qm3h
2
Kvm3h ,bar2 ⋅18 .92
⋅273+ tout293 . 15
ΔPbar2 −2⋅P inbar
⋅ΔPbar+c=0Gases
Q [Nm3
h ]=Kv⋅18 . 9⋅√ΔP⋅(2⋅Pin−ΔP )[bar ]SG
and with temperature correction
Q=Kv⋅18 . 9⋅√ΔP⋅(2⋅Pin−ΔP )SG
⋅293.15273+tout
Qm3 h=Kvm 3h,bar⋅18 .9⋅√ ΔPbar⋅(2⋅Pinbar−ΔPbar )
SG⋅293 . 15273+ tout
Qm3 h
Kvm3h ,bar⋅18 .9=√ΔPbar⋅(2⋅Pinbar
−ΔPbar )
SG⋅293 .15273+tout
SG⋅Qm3 h2
Kvm3h ,bar2 ⋅18 .92
⋅273+tout293 .15
=ΔPbar⋅(2⋅Pinbar−ΔPbar )
c=SG⋅Qm3h
2
Kvm3h ,bar2 ⋅18 .92
⋅273+ tout293 . 15
ΔPbar⋅(2⋅P inbar−ΔPbar )=c
2⋅Pinbar⋅ΔPbar−ΔPbar
2 −c=0
ΔPbar2 −2⋅P inbar
⋅ΔPbar+c=0
Rev. 01.02.2014
Singular coefficient for a valve with gasSolution using the VBA function
K = K_Gas_PinBar_SG_QNm3h_HvPascal_Cv_toutCelcius
Pin = 1.44 bar1 SG = 1 -
1.44 bar Q = 74,760 Nm³/h
Hv = 170.1 Pa-2.88 Cv = 126,000
tout = 128.6 ªCK = #VALUE! -
Pressur lossK * hv
K = #VALUE! -1 - hv = 170.1 Pa
74,760 Nm³/h #VALUE! Pa
128.6 ºC
109,112 (Annex A) Check of flow rate0.0018
(- b - (b^2 - 4 * a * c)^0.5 ) / (2 * a)1 Q = Kv * 18.9 * (DP*(2*Pin-DP)/SG*293.15/(273 ))^0.5
-2.88 Kv = 109,1120.00180 DP = 0.000626 bar0.0006 bar Pin = 1.44 bar
62.6 Pa SG = 1
128.6 ºCFrom Sheet Air blown line Q = 74,760 Nm³/h
170.1 Pa
Pressure loss coefficientK * hv
63 Pa170.12 Pa0.3677
a * DP^2 + b * DP + c = 0
-2 * Pin
C = (SG*Qm3h^2) / (Kvm3h,bar^2*18.9^2) * (273+tout)/293.15 DP =
DP =
tout =
DP / hv
c=SG⋅Qm3h
2
Kvm3h ,bar2 ⋅18 .92
⋅273+ tout293 . 15
ΔPbar2 −2⋅P inbar
⋅ΔPbar+c=0
Qm3 h=Kvm 3h,bar⋅18 .9⋅√ ΔPbar⋅(2⋅Pinbar−ΔPbar )
SG⋅293 . 15273+ tout
Rev. 01.02.2014
Annex A
Pipe nominal diameter (CS)dn = 36 in
Valve: Norris butterfly From table, for 200 psi valvesFully open valve value(Shhet Norris. B.V.)
Cv = 126,000
Kv value
0.865972 * CvCv = 126,000
109,112
Kvm3h,bar =
Kvm3h,bar =
[2a] Norris butterfly valveshttp://www.norriseal.com/files/comm_id_47/BV_HowTo_Brochure_120811.pdf
Valve diameter (Air blown line)dn = 36 in
From table, for 200 psi valvesFully open valve value
Cv = 126,000
Kv-valueRelation Kv - Cv
0.865972 * CvCv = 126,000
109112.5
Kvm3h,bar =
Kvm3h,bar =
Kvm3h ,bar=0. 864972⋅Cv
[1]
[2] Coeficiente de descarga
[3] http://detector-gas-systems.web.cern.ch/detector-gas-systems/downloads/kv_calc_doc.pdf
JoucomaticEngineering informationFlow data Flow factor and orifice size
[4] http://www.fnwvalve.com/FNWValve/assets/images/PDFs/FNW/tech_AboutCv.pdfFNWAbout CV.(Flow coefficients)
[5] Ideal valveFlow calculation for gaseshttp://www.idealvalve.com/pdf/Flow-Calculation-for-Gases.pdf
[6] Spiraxsarcohttp://www.spiraxsarco.com/resources/steam-engineering-tutorials/control-hardware-el-pn-actuation/control-valve-sizing-for-steam-systems.asp
[7] Intellsitesuitehttp://help.intellisitesuite.com/Hydrocarbon/papers/6110.pdf
[8]
[9] Joucomatichttp://detector-gas-systems.web.cern.ch/detector-gas-systems/downloads/kv_calc_doc.pdf
Engineering informationFlow data Flow factor and orifice size
http://www.valvias.com/coeficiente-de-caudal-valvula-de-bola.php
http://www.valvias.com/ecuaciones-de-fluidos-coeficiente-de-descarga-c.php#c-K
http://detector-gas-systems.web.cern.ch/detector-gas-systems/downloads/kv_calc_doc.pdf
http://www.spiraxsarco.com/resources/steam-engineering-tutorials/control-hardware-el-pn-actuation/control-valve-sizing-for-steam-systems.asp
Microsoft Editor de ecuaciones 3.0
