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MÉTODO DE HARDY CROSS PARA EL BALANCE DE PÉRDIDAS ECUACIÓN DE HAZEN-WILLIAMS CHW N
150 para acero 1.851
Circuito I
Tramo 1-4 1-3 4-3
II
1-2 1-3 2-3
D (m) L (m) a 0.075 400 119302.54 0.050 300 644089.33 0.050 200 429392.89
0.075 0.050 0.050
ΔQ=-(∑_1^k▒(a_ij |Q 1) Q_ij ) )/(N∑_1^k▒ |^(N-1) ) )
a_ij=L_ij/(0.279C_Hij D_ij^2.63 )^N
400 119302.54 300 644089.33 200 429392.89
Q (m3/s) -0.00612 0.00612 -0.00122
H (m) -9.5483 51.5493 -1.7366 40.2644
a*|Q|^N-1 1560.1816 8423.0924 1423.4659 11406.7400
0.00612 -0.00612 0.00122
9.5483 -51.5493 1.7366 -40.2644
1560.1816 8423.0924 1423.4659 11406.7400
Circuito I
II
ΔQ=-(∑_1^k▒(a_ij |Q_ij |^(N1) Q_ij ) )/(N∑_1^k▒(a_ij |Q_ij |^(N-1) ) ) a*Q*|Q|^N-1 -9.5483 51.5493 -1.7366 40.2644
9.5483 -51.5493 1.7366 -40.2644
Tramo 1-4 1-3 4-3
H_ij=a_ij Q_ij^N
DQ (m) Otros Circuitos -0.0019 -0.0019 -0.0019 -0.0019 -0.0057
0.0019 0.0019 0.0019 0.0057
H (m) -13.4247 19.7654 -6.3455 -0.0047
0.0019
1 Q (m3/s) -0.0080 0.0023 -0.0031
0.0080 -0.0023 0.0031
a*|Q|^N-1 a*Q*|Q|^N-1 1824.7685 -13.4247 5420.8746 19.7654 2582.7170 -6.3455 9828.3601 -0.0047
H (m) a*|Q|^N-1 a*Q*|Q|^N-1 -15.7753 1965.2826 -15.7753 8.4643 3670.5907 8.4643 -9.9161 3171.1000 -9.9161 -17.2271 8806.9733 -17.2271
15.7753 -8.4643 9.9161 17.2271
1965.2826 3670.5907 3171.1000 8806.9733
15.7753 -8.4643 9.9161 17.2271
16 DQ (m) Otros Circuitos Q (m3/s) 0.0000 -0.0074 0.0000 0.0000 0.0036 0.0000 -0.0025 0.0000
1-2 1-3 2-3
13.4247 -19.7654 6.3455 0.0047
1824.7685 5420.8746 2582.7170 9828.3601
13.4247 -19.7654 6.3455 0.0047
0.0000 0.0000 0.0000 0.0000
0.0000
0.0074 -0.0036 0.0025
2 DQ (m) Otros Circuitos Q (m3/s) 0.0011 -0.0070 0.0011 0.0011 0.0044 0.0011 -0.0021 0.0032
-0.0011 -0.0011 -0.0011 -0.0032
-0.0011
0.0070 -0.0044 0.0021
H (m) a*|Q|^N-1 a*Q*|Q|^N-1 -12.1479 1742.8248 -12.1479 28.2185 6384.9821 28.2185 -4.6218 2232.4880 -4.6218 11.4488 10360.2949 11.4488
12.1479 1742.8248 -28.2185 6384.9821 4.6218 2232.4880 -11.4488 10360.2949
12.1479 -28.2185 4.6218 -11.4488
DQ (m) Otros Circuitos -0.0006 -0.0006 -0.0006 -0.0006 -0.0018
0.0006 0.0006 0.0006 0.0018
0.0006
3 Q (m3/s) -0.0076 0.0032 -0.0027
0.0076 -0.0032 0.0027
H (m) a*|Q|^N-1 a*Q*|Q|^N-1 -14.1437 1869.0727 -14.1437 15.7528 4883.8395 15.7528 -7.3875 2769.7181 -7.3875 -5.7785 9522.6302 -5.7785
14.1437 -15.7528 7.3875 5.7785
1869.0727 4883.8395 2769.7181 9522.6302
14.1437 -15.7528 7.3875 5.7785
4 DQ (m) Otros Circuitos Q (m3/s) 0.0003 -0.0072 0.0003 0.0003 0.0039 0.0003 -0.0023 0.0010
-0.0003 -0.0003 -0.0003 -0.0010
-0.0003
0.0072 -0.0039 0.0023
H (m) -13.0305 22.1878 -5.7953 3.3620
13.0305 -22.1878 5.7953 -3.3620
a*|Q|^N-1 a*Q*|Q|^N-1 1799.9386 -13.0305 5716.7885 22.1878 2477.2289 -5.7953 9993.9560 3.3620
1799.9386 5716.7885 2477.2289 9993.9560
13.0305 -22.1878 5.7953 -3.3620
5 DQ (m) Otros Circuitos Q (m3/s) -0.0002 -0.0074 -0.0002 -0.0002 0.0035 -0.0002 -0.0025 -0.0005
0.0002 0.0002 0.0002 0.0005
0.0002
0.0074 -0.0035 0.0025
H (m) a*|Q|^N-1 a*Q*|Q|^N-1 -13.6425 1838.3205 -13.6425 18.4955 5257.8734 18.4955 -6.6561 2640.0787 -6.6561 -1.8030 9736.2726 -1.8030
13.6425 -18.4955 6.6561 1.8030
1838.3205 5257.8734 2640.0787 9736.2726
13.6425 -18.4955 6.6561 1.8030
6 DQ (m) Otros Circuitos Q (m3/s) 0.0001 -0.0073 0.0001 0.0001 0.0037 0.0001 -0.0024 0.0003
-0.0001 -0.0001 -0.0001 -0.0003
-0.0001
0.0073 -0.0037 0.0024
H (m) a*|Q|^N-1 a*Q*|Q|^N-1 -13.3040 1817.2090 -13.3040 20.4899 5511.3340 20.4899 -6.1754 2550.6555 -6.1754 1.0105 9879.1985 1.0105
13.3040 -20.4899 6.1754 -1.0105
1817.2090 5511.3340 2550.6555 9879.1985
13.3040 -20.4899 6.1754 -1.0105
DQ (m) Otros Circuitos -0.0001 -0.0001 -0.0001 -0.0001 -0.0002
0.0001 0.0001 0.0001 0.0002
0.0001
7 Q (m3/s) -0.0074 0.0036 -0.0025
0.0074 -0.0036 0.0025
H (m) a*|Q|^N-1 a*Q*|Q|^N-1 -13.4905 1828.8745 -13.4905 19.3767 5371.6016 19.3767 -6.4388 2600.1123 -6.4388 -0.5526 9800.5884 -0.5526
13.4905 -19.3767 6.4388 0.5526
1828.8745 5371.6016 2600.1123 9800.5884
13.4905 -19.3767 6.4388 0.5526
8 DQ (m) Otros Circuitos Q (m3/s) 0.0000 -0.0073 0.0000 0.0000 0.0037 0.0000 -0.0024 0.0001
0.0000 0.0000 0.0000 -0.0001
0.0000
0.0073 -0.0037 0.0024
H (m) -13.3875 19.9868 -6.2930 0.3062
13.3875 -19.9868 6.2930 -0.3062
a*|Q|^N-1 a*Q*|Q|^N-1 1822.4459 -13.3875 5448.7026 19.9868 2572.8713 -6.2930 9844.0198 0.3062
1822.4459 5448.7026 2572.8713 9844.0198
13.3875 -19.9868 6.2930 -0.3062
9 DQ (m) Otros Circuitos Q (m3/s) 0.0000 -0.0074 0.0000 0.0000 0.0036 0.0000 -0.0025 -0.0001
0.0000 0.0000 0.0000 0.0001
0.0000
0.0074 -0.0036 0.0025
H (m) a*|Q|^N-1 a*Q*|Q|^N-1 -13.4443 1825.9937 -13.4443 19.6491 5406.1823 19.6491 -6.3733 2587.9090 -6.3733 -0.1685 9820.0850 -0.1685
13.4443 -19.6491 6.3733 0.1685
1825.9937 5406.1823 2587.9090 9820.0850
13.4443 -19.6491 6.3733 0.1685
10 DQ (m) Otros Circuitos Q (m3/s) 0.0000 -0.0074 0.0000 0.0000 0.0037 0.0000 -0.0025 0.0000
0.0000 0.0000 0.0000 0.0000
0.0000
0.0074 -0.0037 0.0025
H (m) a*|Q|^N-1 a*Q*|Q|^N-1 -13.4130 1824.0373 -13.4130 19.8350 5429.6382 19.8350 -6.3290 2579.6180 -6.3290 0.0931 9833.2936 0.0931
13.4130 -19.8350 6.3290 -0.0931
1824.0373 5429.6382 2579.6180 9833.2936
13.4130 -19.8350 6.3290 -0.0931
DQ (m) Otros Circuitos 0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000
0.0000
11 Q (m3/s) -0.0074 0.0036 -0.0025
0.0074 -0.0036 0.0025
H (m) a*|Q|^N-1 a*Q*|Q|^N-1 -13.4302 1825.1166 -13.4302 19.7323 5416.7010 19.7323 -6.3534 2584.1923 -6.3534 -0.0513 9826.0099 -0.0513
13.4302 -19.7323 6.3534 0.0513
1825.1166 5416.7010 2584.1923 9826.0099
13.4302 -19.7323 6.3534 0.0513
12 DQ (m) Otros Circuitos Q (m3/s) 0.0000 -0.0074 0.0000 0.0000 0.0036 0.0000 -0.0025 0.0000
0.0000 0.0000 0.0000 0.0000
0.0000
0.0074 -0.0036 0.0025
H (m) -13.4207 19.7889 -6.3399 0.0283
13.4207 -19.7889 6.3399 -0.0283
a*|Q|^N-1 a*Q*|Q|^N-1 1824.5213 -13.4207 5423.8372 19.7889 2581.6696 -6.3399 9830.0280 0.0283
1824.5213 5423.8372 2581.6696 9830.0280
13.4207 -19.7889 6.3399 -0.0283
13 DQ (m) Otros Circuitos Q (m3/s) 0.0000 -0.0074 0.0000 0.0000 0.0036 0.0000 -0.0025 0.0000
0.0000 0.0000 0.0000 0.0000
0.0000
0.0074 -0.0036 0.0025
H (m) a*|Q|^N-1 a*Q*|Q|^N-1 -13.4260 1824.8497 -13.4260 19.7577 5419.9010 19.7577 -6.3474 2583.0612 -6.3474 -0.0156 9827.8119 -0.0156
13.4260 -19.7577 6.3474 0.0156
1824.8497 5419.9010 2583.0612 9827.8119
13.4260 -19.7577 6.3474 0.0156
14 DQ (m) Otros Circuitos Q (m3/s) 0.0000 -0.0074 0.0000 0.0000 0.0036 0.0000 -0.0025 0.0000
0.0000 0.0000 0.0000 0.0000
0.0000
0.0074 -0.0036 0.0025
H (m) a*|Q|^N-1 a*Q*|Q|^N-1 -13.4231 1824.6686 -13.4231 19.7749 5422.0722 19.7749 -6.3433 2582.2936 -6.3433 0.0086 9829.0343 0.0086
13.4231 -19.7749 6.3433 -0.0086
1824.6686 5422.0722 2582.2936 9829.0343
13.4231 -19.7749 6.3433 -0.0086
DQ (m) Otros Circuitos 0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000
0.0000
15 Q (m3/s) -0.0074 0.0036 -0.0025
0.0074 -0.0036 0.0025
H (m) a*|Q|^N-1 a*Q*|Q|^N-1 -13.4247 1824.7685 -13.4247 19.7654 5420.8746 19.7654 -6.3455 2582.7170 -6.3455 -0.0047 9828.3601 -0.0047
13.4247 -19.7654 6.3455 0.0047
1824.7685 5420.8746 2582.7170 9828.3601
13.4247 -19.7654 6.3455 0.0047
16 DQ (m) Otros Circuitos Q (m3/s) 0.0000 -0.0074 0.0000 0.0000 0.0036 0.0000 -0.0025 0.0000
0.0000 0.0000 0.0000 0.0000
0.0000
0.0074 -0.0036 0.0025
150 para acero 1.851
Circuito I
Tramo 1-4 1-3 4-3
II
1-2 1-3 2-3
D (m) L (m) a 0.075 400 119302.54 0.050 300 644089.33 0.050 200 429392.89
0.075 0.050 0.050
ΔQ=-(∑_1^k▒(a_ij |Q 1) Q_ij ) )/(N∑_1^k▒ |^(N-1) ) )
a_ij=L_ij/(0.279C_Hij D_ij^2.63 )^N
400 119302.54 300 644089.33 200 429392.89
Q (m3/s) -0.00612 0.00612 -0.00122
H (m) -9.5483 51.5493 -1.7366 40.2644
a*|Q|^N-1 1560.1816 8423.0924 1423.4659 11406.7400
0.00612 -0.00612 0.00122
9.5483 -51.5493 1.7366 -40.2644
1560.1816 8423.0924 1423.4659 11406.7400
Circuito I
II
ΔQ=-(∑_1^k▒(a_ij |Q_ij |^(N1) Q_ij ) )/(N∑_1^k▒(a_ij |Q_ij |^(N-1) ) ) a*Q*|Q|^N-1 -9.5483 51.5493 -1.7366 40.2644
9.5483 -51.5493 1.7366 -40.2644
Tramo 1-4 1-3 4-3
H_ij=a_ij Q_ij^N
DQ (m) Otros Circuitos -0.0019 -0.0019 -0.0019 -0.0019 -0.0057
0.0019 0.0019 0.0019 0.0057
H (m) -13.4247 19.7654 -6.3455 -0.0047
0.0019
1 Q (m3/s) -0.0080 0.0023 -0.0031
0.0080 -0.0023 0.0031
a*|Q|^N-1 a*Q*|Q|^N-1 1824.7685 -13.4247 5420.8746 19.7654 2582.7170 -6.3455 9828.3601 -0.0047
H (m) a*|Q|^N-1 a*Q*|Q|^N-1 -15.7753 1965.2826 -15.7753 8.4643 3670.5907 8.4643 -9.9161 3171.1000 -9.9161 -17.2271 8806.9733 -17.2271
15.7753 -8.4643 9.9161 17.2271
1965.2826 3670.5907 3171.1000 8806.9733
15.7753 -8.4643 9.9161 17.2271
16 DQ (m) Otros Circuitos Q (m3/s) 0.0000 -0.0074 0.0000 0.0000 0.0036 0.0000 -0.0025 0.0000
1-2 1-3 2-3
13.4247 -19.7654 6.3455 0.0047
1824.7685 5420.8746 2582.7170 9828.3601
13.4247 -19.7654 6.3455 0.0047
0.0000 0.0000 0.0000 0.0000
0.0000
0.0074 -0.0036 0.0025
2 DQ (m) Otros Circuitos Q (m3/s) 0.0011 -0.0070 0.0011 0.0011 0.0044 0.0011 -0.0021 0.0032
-0.0011 -0.0011 -0.0011 -0.0032
-0.0011
0.0070 -0.0044 0.0021
H (m) a*|Q|^N-1 a*Q*|Q|^N-1 -12.1479 1742.8248 -12.1479 28.2185 6384.9821 28.2185 -4.6218 2232.4880 -4.6218 11.4488 10360.2949 11.4488
12.1479 1742.8248 -28.2185 6384.9821 4.6218 2232.4880 -11.4488 10360.2949
12.1479 -28.2185 4.6218 -11.4488
DQ (m) Otros Circuitos -0.0006 -0.0006 -0.0006 -0.0006 -0.0018
0.0006 0.0006 0.0006 0.0018
0.0006
3 Q (m3/s) -0.0076 0.0032 -0.0027
0.0076 -0.0032 0.0027
H (m) a*|Q|^N-1 a*Q*|Q|^N-1 -14.1437 1869.0727 -14.1437 15.7528 4883.8395 15.7528 -7.3875 2769.7181 -7.3875 -5.7785 9522.6302 -5.7785
14.1437 -15.7528 7.3875 5.7785
1869.0727 4883.8395 2769.7181 9522.6302
14.1437 -15.7528 7.3875 5.7785
4 DQ (m) Otros Circuitos Q (m3/s) 0.0003 -0.0072 0.0003 0.0003 0.0039 0.0003 -0.0023 0.0010
-0.0003 -0.0003 -0.0003 -0.0010
-0.0003
0.0072 -0.0039 0.0023
H (m) -13.0305 22.1878 -5.7953 3.3620
13.0305 -22.1878 5.7953 -3.3620
a*|Q|^N-1 a*Q*|Q|^N-1 1799.9386 -13.0305 5716.7885 22.1878 2477.2289 -5.7953 9993.9560 3.3620
1799.9386 5716.7885 2477.2289 9993.9560
13.0305 -22.1878 5.7953 -3.3620
5 DQ (m) Otros Circuitos Q (m3/s) -0.0002 -0.0074 -0.0002 -0.0002 0.0035 -0.0002 -0.0025 -0.0005
0.0002 0.0002 0.0002 0.0005
0.0002
0.0074 -0.0035 0.0025
H (m) a*|Q|^N-1 a*Q*|Q|^N-1 -13.6425 1838.3205 -13.6425 18.4955 5257.8734 18.4955 -6.6561 2640.0787 -6.6561 -1.8030 9736.2726 -1.8030
13.6425 -18.4955 6.6561 1.8030
1838.3205 5257.8734 2640.0787 9736.2726
13.6425 -18.4955 6.6561 1.8030
6 DQ (m) Otros Circuitos Q (m3/s) 0.0001 -0.0073 0.0001 0.0001 0.0037 0.0001 -0.0024 0.0003
-0.0001 -0.0001 -0.0001 -0.0003
-0.0001
0.0073 -0.0037 0.0024
H (m) a*|Q|^N-1 a*Q*|Q|^N-1 -13.3040 1817.2090 -13.3040 20.4899 5511.3340 20.4899 -6.1754 2550.6555 -6.1754 1.0105 9879.1985 1.0105
13.3040 -20.4899 6.1754 -1.0105
1817.2090 5511.3340 2550.6555 9879.1985
13.3040 -20.4899 6.1754 -1.0105
DQ (m) Otros Circuitos -0.0001 -0.0001 -0.0001 -0.0001 -0.0002
0.0001 0.0001 0.0001 0.0002
0.0001
7 Q (m3/s) -0.0074 0.0036 -0.0025
0.0074 -0.0036 0.0025
H (m) a*|Q|^N-1 a*Q*|Q|^N-1 -13.4905 1828.8745 -13.4905 19.3767 5371.6016 19.3767 -6.4388 2600.1123 -6.4388 -0.5526 9800.5884 -0.5526
13.4905 -19.3767 6.4388 0.5526
1828.8745 5371.6016 2600.1123 9800.5884
13.4905 -19.3767 6.4388 0.5526
8 DQ (m) Otros Circuitos Q (m3/s) 0.0000 -0.0073 0.0000 0.0000 0.0037 0.0000 -0.0024 0.0001
0.0000 0.0000 0.0000 -0.0001
0.0000
0.0073 -0.0037 0.0024
H (m) -13.3875 19.9868 -6.2930 0.3062
13.3875 -19.9868 6.2930 -0.3062
a*|Q|^N-1 a*Q*|Q|^N-1 1822.4459 -13.3875 5448.7026 19.9868 2572.8713 -6.2930 9844.0198 0.3062
1822.4459 5448.7026 2572.8713 9844.0198
13.3875 -19.9868 6.2930 -0.3062
9 DQ (m) Otros Circuitos Q (m3/s) 0.0000 -0.0074 0.0000 0.0000 0.0036 0.0000 -0.0025 -0.0001
0.0000 0.0000 0.0000 0.0001
0.0000
0.0074 -0.0036 0.0025
H (m) a*|Q|^N-1 a*Q*|Q|^N-1 -13.4443 1825.9937 -13.4443 19.6491 5406.1823 19.6491 -6.3733 2587.9090 -6.3733 -0.1685 9820.0850 -0.1685
13.4443 -19.6491 6.3733 0.1685
1825.9937 5406.1823 2587.9090 9820.0850
13.4443 -19.6491 6.3733 0.1685
10 DQ (m) Otros Circuitos Q (m3/s) 0.0000 -0.0074 0.0000 0.0000 0.0037 0.0000 -0.0025 0.0000
0.0000 0.0000 0.0000 0.0000
0.0000
0.0074 -0.0037 0.0025
H (m) a*|Q|^N-1 a*Q*|Q|^N-1 -13.4130 1824.0373 -13.4130 19.8350 5429.6382 19.8350 -6.3290 2579.6180 -6.3290 0.0931 9833.2936 0.0931
13.4130 -19.8350 6.3290 -0.0931
1824.0373 5429.6382 2579.6180 9833.2936
13.4130 -19.8350 6.3290 -0.0931
DQ (m) Otros Circuitos 0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000
0.0000
11 Q (m3/s) -0.0074 0.0036 -0.0025
0.0074 -0.0036 0.0025
H (m) a*|Q|^N-1 a*Q*|Q|^N-1 -13.4302 1825.1166 -13.4302 19.7323 5416.7010 19.7323 -6.3534 2584.1923 -6.3534 -0.0513 9826.0099 -0.0513
13.4302 -19.7323 6.3534 0.0513
1825.1166 5416.7010 2584.1923 9826.0099
13.4302 -19.7323 6.3534 0.0513
12 DQ (m) Otros Circuitos Q (m3/s) 0.0000 -0.0074 0.0000 0.0000 0.0036 0.0000 -0.0025 0.0000
0.0000 0.0000 0.0000 0.0000
0.0000
0.0074 -0.0036 0.0025
H (m) -13.4207 19.7889 -6.3399 0.0283
13.4207 -19.7889 6.3399 -0.0283
a*|Q|^N-1 a*Q*|Q|^N-1 1824.5213 -13.4207 5423.8372 19.7889 2581.6696 -6.3399 9830.0280 0.0283
1824.5213 5423.8372 2581.6696 9830.0280
13.4207 -19.7889 6.3399 -0.0283
13 DQ (m) Otros Circuitos Q (m3/s) 0.0000 -0.0074 0.0000 0.0000 0.0036 0.0000 -0.0025 0.0000
0.0000 0.0000 0.0000 0.0000
0.0000
0.0074 -0.0036 0.0025
H (m) a*|Q|^N-1 a*Q*|Q|^N-1 -13.4260 1824.8497 -13.4260 19.7577 5419.9010 19.7577 -6.3474 2583.0612 -6.3474 -0.0156 9827.8119 -0.0156
13.4260 -19.7577 6.3474 0.0156
1824.8497 5419.9010 2583.0612 9827.8119
13.4260 -19.7577 6.3474 0.0156
14 DQ (m) Otros Circuitos Q (m3/s) 0.0000 -0.0074 0.0000 0.0000 0.0036 0.0000 -0.0025 0.0000
0.0000 0.0000 0.0000 0.0000
0.0000
0.0074 -0.0036 0.0025
H (m) a*|Q|^N-1 a*Q*|Q|^N-1 -13.4231 1824.6686 -13.4231 19.7749 5422.0722 19.7749 -6.3433 2582.2936 -6.3433 0.0086 9829.0343 0.0086
13.4231 -19.7749 6.3433 -0.0086
1824.6686 5422.0722 2582.2936 9829.0343
13.4231 -19.7749 6.3433 -0.0086
DQ (m) Otros Circuitos 0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000
0.0000
15 Q (m3/s) -0.0074 0.0036 -0.0025
0.0074 -0.0036 0.0025
H (m) a*|Q|^N-1 a*Q*|Q|^N-1 -13.4247 1824.7685 -13.4247 19.7654 5420.8746 19.7654 -6.3455 2582.7170 -6.3455 -0.0047 9828.3601 -0.0047
13.4247 -19.7654 6.3455 0.0047
1824.7685 5420.8746 2582.7170 9828.3601
13.4247 -19.7654 6.3455 0.0047
16 DQ (m) Otros Circuitos Q (m3/s) 0.0000 -0.0074 0.0000 0.0000 0.0036 0.0000 -0.0025 0.0000
0.0000 0.0000 0.0000 0.0000
0.0000
0.0074 -0.0036 0.0025
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