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Head Losses - compressible fluid (ga

A) Calculation of Head losses , knowing the inlet condition and

Input data

piping

material cs

rugosity 5.00E-02

diameter D 219.70

length L 2000.00

loss friction ki 0.00

fittings

fluid viscosiy 0.01Molecular weight Mw 21.68

Compressibility Z 0.94

Temperature T 27.00

Pressure inlet P1 41000.00

process

flowrate inlet Qv1 1953.00

others perfect gas cte 8.31

output data

density (T1,P1) 1 37.903

G 5.424E+02

Re 10833244

B 1.01E+22

fdarcy 0.01422

velocity U1 14.31

head loss P 538790

5458

Pressure outlet P2 356121035612

density(T1,P2) 2 32.92

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B) Calculation of flow rate , knowing the inlet and outlet Press

Input data

piping

material SS

rugosity 1.00E-03

diameter D 800.00

length L 200.00


fittings

fluid viscosiy 0.01

Molecular weight Mw 44.00

Compressibility Z 1.00Temperature T 45.00


Pressure outlet P2 2402.00

process

estimate friction fvk (-2log10((/D)/3.7)))^-2

factor .Von karman


output data

density (T1,P1) 1 4.326

G 1.512E+02

Re 10998132

B 8.29E+23

fdarcy 0.00819

velocity U1 34.96

Volumetric flow Qv1 18


U2 38


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)

the piping arrangement

engineering SI energy balance to solve :

units units

*dP+G^2*ln( 1/2 ) + (f*L/D+ki)*

mm 5.00E-05 SI

mm 2.20E-01 SI after integration with T=cte

m 2.00E+03 SI

M/(Z*R*T)*(P2^2-P1^2)+2*G^2* Ln(P1

unitless 0.00 unitless or

to solve : F(p2) =0

with F'(p2)

cpo 1.10E-05 SI Newton Raphson : P2(n+1)=P2(g/mol 2.17E-02 SI

0.94

C 300.15 K P1 P2 (n) A B

mbars 4.10E+06 Pa 4.1000E+06 4.0590E+06 9.2446E-06 5.8840E+05

3.5919E+06 9.2446E-06 5.8840E+05

3.5613E+06 9.2446E-06 5.8840E+05

m3/h 5.43E-01 SI 3.5612E+06 9.2446E-06 5.8840E+05

3.5612E+06 9.2446E-06 5.8840E+05

SI 8.31E+00 SI 3.5612E+06 9.2446E-06 5.8840E+05

3.5612E+06 9.2446E-06 5.8840E+05

3.5612E+06 9.2446E-06 5.8840E+05

3.5612E+06 9.2446E-06 5.8840E+05

3.5612E+06 9.2446E-06 5.8840E+05

3.5612E+06 9.2446E-06 5.8840E+05

kg/m3

kg/s/m2

unitless

unitless

m/s

Pa

mbars

Pambars

kg/m3

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ure and the piping arrangement


units units

*dP+G^2*ln( 1/2 ) + (f*L/D+ki)*

mm 1.00E-06 SI

mm 8.00E-01 SI after integration with T=cte

m 2.00E+02 SI

M/(Z*R*T)*(P2^2-P1^2)+2*G^2* Ln(P1

unitless 5.00 unitless

or

G^2 =M/(Z*R*T) *(P1^2-P2^2)/ (2*ln(P1

cpo 1.10E-05 SI

g/mol 4.40E-02 SI

1.00 Iterative calculation :C 318.15 K Assume f(n) , calculate G,

mbars 2.60E+05 Pa

mbars 2.40E+05 Pa f(n) G Re

5.97E-03 5.9698E-03 1.5741E+02 1.1448E+07

8.1485E-03 1.5133E+02 1.1006E+07

SI 8.31E+00 SI 8.1887E-03 1.5123E+02 1.0998E+07

8.1894E-03 1.5122E+02 1.0998E+07

8.1894E-03 1.5122E+02 1.0998E+07

8.1894E-03 1.5122E+02 1.0998E+07

8.1894E-03 1.5122E+02 1.0998E+07

kg/m3

kg/s/m2

unitless

unitless

m/s

m3/s 63256.54 m3/h

kg/m3

m/s

m3/s 68470.86 m3/h

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^2/2 = 0

/P2) +(f*L/D +ki) *G^2=0

A*(P2^2-P1^2) +B*Ln(P1/P2) + C =0

A*2*P2-B/P2

) -F(p2)/F'(p2)

C F(P2) F'(P2) P2(n+1)

3.8077E+07 3.4990E+07 7.4903E+01 3.5919E+06 -4.6714E+05

3.8077E+07 2.0216E+06 6.6247E+01 3.5613E+06 -3.0516E+04

3.8077E+07 8.6303E+03 6.5681E+01 3.5612E+06 -1.3140E+02

3.8077E+07 1.6001E-01 6.5679E+01 3.5612E+06 -2.4362E-03

3.8077E+07 0.0000E+00 6.5679E+01 3.5612E+06 0.0000E+00

3.8077E+07 0.0000E+00 6.5679E+01 3.5612E+06 0.0000E+00

3.8077E+07 0.0000E+00 6.5679E+01 3.5612E+06 0.0000E+00

3.8077E+07 0.0000E+00 6.5679E+01 3.5612E+06 0.0000E+00

3.8077E+07 0.0000E+00 6.5679E+01 3.5612E+06 0.0000E+00

3.8077E+07 0.0000E+00 6.5679E+01 3.5612E+06 0.0000E+00

3.8077E+07 0.0000E+00 6.5679E+01 3.5612E+06 0.0000E+00

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^2/2 = 0

/P2) +(f*L/D +ki) *G^2=0

/P2)+f*L/D+ki)

alculate Re , calculate f(n+1) , compare f(n+1) vs f(n)

B f(n+1)

8.63E+23 8.1485E-03 2.1787E-03

8.30E+23 8.1887E-03 4.0218E-05

8.29E+23 8.1894E-03 7.1761E-07

8.29E+23 8.1894E-03 1.2797E-08

8.29E+23 8.1894E-03 2.2819E-10

8.29E+23 8.1894E-03 4.0690E-12

8.29E+23 8.1894E-03 7.2548E-14

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Head Losses - compressible fluid (gas

A) Calculation of Head losses , knowing the inlet condition and

Input data

piping

material SS

rugosity 1.00E-03

diameter D 800.00

length L 200.00


fittings

CP/CV k 1.40

fluid viscosiy 0.01



Temperature inlet T1 45.00


(k-1)/k

(k+1)/k

process flowrate Qv 63621.00


output data

density (T1,P1) 1 4.326

G 1.521E+02

Re 11061499

B 8.34E+23

fdarcy 0.00818

velocity U 35.16

head loss P 19675

199

Pressure outlet P2 240325

2403

Temperature outlet T2 311


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B) Calculation of flow rate , knowing the inlet and outlet Press

Input data

pipingmaterial SS

rugosity 1.00E-03

diameter D 800.00

length L 200.00


fittings

CP/CV k 1.40

fluid viscosiy 0.01



Temperature inlet T1 45.00


Pressure outlet P2 2403.00

(k-1)/k

(k+1)/k

process estimate friction

factor .Von karman fvk (-2log10((/D)/3.7)))^-2


output data

density (T1,P1) 1 4.326

G 1.522E+02

Re 11068364

B 8.35E+23

fdarcy 0.00818

velocity U1 35.18



U2 37


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)

the piping arrangement


units units

*dP+G^2*ln( 1/2 ) + (f*L/D+ki)*

mm 1.00E-06 SI

mm 8.00E-01 SI after integration with P/^k=cte

m 2.00E+02 SI

M/(Z*R*T1)*[k/(k+1)]*p1^[(k-1)/k]*(P

unitless 5.00 unitless or

to solve : F(p2) =0

with F'(p2)


cpo 1.10E-05 SI Newton Raphson : P2(n+1)=P2(

g/mol 4.40E-02 SI

1.00

C 318.15 K P1 P2 (n) A' B'

mbars 2.60E+05 Pa 2.6000E+05 2.5740E+05 3.4211E-04 1.652E+04

2.86E-01 2.4075E+05 3.4211E-04 1.652E+04

1.71 2.4033E+05 3.4211E-04 1.652E+04

m3/h 1.77E+01 SI 2.4033E+05 3.4211E-04 1.652E+04

2.4033E+05 3.4211E-04 1.652E+04

SI 8.31E+00 SI 2.4033E+05 3.4211E-04 1.652E+042.4033E+05 3.4211E-04 1.652E+04

2.4033E+05 3.4211E-04 1.652E+04

2.4033E+05 3.4211E-04 1.652E+04

2.4033E+05 3.4211E-04 1.652E+04

2.4033E+05 3.4211E-04 1.652E+04

kg/m3

kg/s/m2

unitless

unitless

m/s

Pa

mbars

Pa

mbars

K 37.93 C

kg/m3

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ure and the piping arrangement

energy balance to solve :

engineering SI

units units *dP+G^2*ln( 1/2 ) + (f*L/D+ki)*

mm 1.00E-06 SI after integration with P/^k=cte

mm 8.00E-01 SI

m 2.00E+02 SI M/(Z*R*T1)*[k/(k+1)]*p1^[(k-1)/k]*(P

or


G^2 =2*M/(Z*R*T1) *k/(k+1)*P1^(k-1)/


cpo 1.10E-05 SI

g/mol 4.40E-02 SI Iterative calculation :

1.00 Assume f(n) , calculate G,

C 318.15 K

mbars 2.60E+05 Pa f(n) G Re

mbars 2.40E+05 Pa

2.86E-01 5.9698E-03 1.5844E+02 1.1523E+07

1.71 8.1419E-03 1.5230E+02 1.1076E+07

8.1822E-03 1.5219E+02 1.1069E+07

5.97E-03 8.1829E-03 1.5219E+02 1.1068E+07

8.1829E-03 1.5219E+02 1.1068E+07

SI 8.31E+00 SI 8.1829E-03 1.5219E+02 1.1068E+078.1829E-03 1.5219E+02 1.1068E+07

kg/m3

kg/s/m2

unitless

unitless

m/s

m3/s 63660.48 m3/h

kg/m3

m/s

m3/s 67346.10 m3/h

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^2/2 = 0

^ [(k+1)/k)]-P1^[(k+1)/k)]+G^2*1/k* Ln(P1/P2) +(f*L/D +ki) *G^2/2=0

A'*(P2^x-P1^x) +B'*Ln(P1/P2) + C' =0

A'*x*P2^x-1-B'/P2

) -F(p2)/F'(p2)

C' F(P2) F'(P2) P2(n+1)

8.1496E+04 7.0455E+04 4.2309E+00 2.4075E+05 -1.6653E+04

8.1496E+04 1.6991E+03 4.0261E+00 2.4033E+05 -4.2204E+02

8.1496E+04 1.1075E+00 4.0208E+00 2.4033E+05 -2.7545E-01

8.1496E+04 4.7221E-07 4.0208E+00 2.4033E+05 -1.1743E-07

8.1496E+04 -4.6566E-10 4.0208E+00 2.4033E+05 0.0000E+00

8.1496E+04 -4.8021E-10 4.0208E+00 2.4033E+05 0.0000E+008.1496E+04 1.5571E-09 4.0208E+00 2.4033E+05 -3.7835E-10

8.1496E+04 -4.6566E-10 4.0208E+00 2.4033E+05 0.0000E+00

8.1496E+04 -4.6566E-10 4.0208E+00 2.4033E+05 0.0000E+00

8.1496E+04 -4.8021E-10 4.0208E+00 2.4033E+05 0.0000E+00

8.1496E+04 -4.8021E-10 4.0208E+00 2.4033E+05 0.0000E+00

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^2/2 = 0

^ [(k+1)/k)]-P1^[(k+1)/k)]+G^2*1/k* Ln(P1/P2) +(f*L/D +ki) *G^2/2=0

k*(P1^(k+1)/k-P2^(k+1)/k) /(2/k*ln(P1/P2)+f*L/D+ki)

alculate Re , calculate f(n+1) , compare f(n+1) vs f(n)

B f(n+1)

8.69E+23 8.1419E-03 2.1721E-03

8.35E+23 8.1822E-03 4.0293E-05

8.35E+23 8.1829E-03 7.2238E-07

8.35E+23 8.1829E-03 1.2943E-08

8.35E+23 8.1829E-03 2.3190E-10

8.35E+23 8.1829E-03 4.1550E-128.35E+23 8.1829E-03 7.4444E-14

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