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Question: Fsolve, 20 ecuations, 20 unknows

Question:Fsolve, 20 ecuations, 20 unknows

Giulianot 25 Maple 2016
fsolve
September 07 2017
0

Hi, i wonder if there is a way to solve this 20×20 equations system for maple. Im trying fsolve but it doesn't work. aceitoso
 

nu := 6.1795*10^(-5)

0.6179500000e-4

 (1)

varepsilon := 0.46e-1

0.46e-1

 (2)

L__1 := 10.

10.

 (3)

L__2 := 15.

15.

 (4)

L__3 := 10.

10.

 (5)

L__4 := 5*sqrt(2.)

7.071067810

 (6)

L__5 := 6.

6.

 (7)

L__6 := 6.

6.

 (8)

L__7 := 20*sqrt(3.)*(1/3)

11.54700539

 (9)

L__8 := 15.

15.

 (10)

L__9 := 15.

15.

 (11)

L__10 := 20.

20.

 (12)

Re1 := 4*Q__1/(Pi*D__1*nu)

20604.24864*Q__1/D__1

 (13)

Re2 := 4*Q__2/(Pi*D__2*nu)

20604.24864*Q__2/D__2

 (14)

Re3 := 4*Q__3/(Pi*D__3*nu)

20604.24864*Q__3/D__3

 (15)

Re4 := 4*Q__4/(Pi*D__4*nu)

20604.24864*Q__4/D__4

 (16)

Re5 := 4*Q__5/(Pi*D__5*nu)

20604.24864*Q__5/D__5

 (17)

Re6 := 4*Q__6/(Pi*D__6*nu)

20604.24864*Q__6/D__6

 (18)

Re7 := 4*Q__7/(Pi*D__7*nu)

20604.24864*Q__7/D__7

 (19)

Re8 := 4*Q__8/(Pi*D__8*nu)

20604.24864*Q__8/D__8

 (20)

Re9 := 4*Q__9/(Pi*D__9*nu)

20604.24864*Q__9/D__9

 (21)

Re10 := 4*Q__10/(Pi*D__10*nu)

20604.24864*Q__10/D__10

 (22)

A__1 := (2.457*ln(1/((7/Re1)^.9+.27*varepsilon/D__1)))^16

1763934.700*ln(1/(0.7551394026e-3*(D__1/Q__1)^.9+0.1242e-1/D__1))^16

 (23)

A__2 := (2.457*ln(1/((7/Re2)^.9+.27*varepsilon/D__2)))^16

1763934.700*ln(1/(0.7551394026e-3*(D__2/Q__2)^.9+0.1242e-1/D__2))^16

 (24)

A__3 := (2.457*ln(1/((7/Re3)^.9+.27*varepsilon/D__3)))^16

1763934.700*ln(1/(0.7551394026e-3*(D__3/Q__3)^.9+0.1242e-1/D__3))^16

 (25)

A__4 := (2.457*ln(1/((7/Re4)^.9+.27*varepsilon/D__4)))^16

1763934.700*ln(1/(0.7551394026e-3*(D__4/Q__4)^.9+0.1242e-1/D__4))^16

 (26)

A__5 := (2.457*ln(1/((7/Re5)^.9+.27*varepsilon/D__5)))^16

1763934.700*ln(1/(0.7551394026e-3*(D__5/Q__5)^.9+0.1242e-1/D__5))^16

 (27)

A__6 := (2.457*ln(1/((7/Re6)^.9+.27*varepsilon/D__6)))^16

1763934.700*ln(1/(0.7551394026e-3*(D__6/Q__6)^.9+0.1242e-1/D__6))^16

 (28)

A__7 := (2.457*ln(1/((7/Re7)^.9+.27*varepsilon/D__7)))^16

1763934.700*ln(1/(0.7551394026e-3*(D__7/Q__7)^.9+0.1242e-1/D__7))^16

 (29)

A__8 := (2.457*ln(1/((7/Re8)^.9+.27*varepsilon/D__8)))^16

1763934.700*ln(1/(0.7551394026e-3*(D__8/Q__8)^.9+0.1242e-1/D__8))^16

 (30)

A__9 := (2.457*ln(1/((7/Re9)^.9+.27*varepsilon/D__9)))^16

1763934.700*ln(1/(0.7551394026e-3*(D__9/Q__9)^.9+0.1242e-1/D__9))^16

 (31)

A__10 := (2.457*ln(1/((7/Re10)^.9+.27*varepsilon/D__10)))^16

1763934.700*ln(1/(0.7551394026e-3*(D__10/Q__10)^.9+0.1242e-1/D__10))^16

 (32)

B__1 := (37530/Re1)^16

14680.75929*D__1^16/Q__1^16

 (33)

B__2 := (37530/Re2)^16

14680.75929*D__2^16/Q__2^16

 (34)

B__3 := (37530/Re3)^16

14680.75929*D__3^16/Q__3^16

 (35)

B__4 := (37530/Re4)^16

14680.75929*D__4^16/Q__4^16

 (36)

B__5 := (37530/Re5)^16

14680.75929*D__5^16/Q__5^16

 (37)

B__6 := (37530/Re6)^16

14680.75929*D__6^16/Q__6^16

 (38)

B__7 := (37530/Re7)^16

14680.75929*D__7^16/Q__7^16

 (39)

B__8 := (37530/Re8)^16

14680.75929*D__8^16/Q__8^16

 (40)

B__9 := (37530/Re9)^16

14680.75929*D__9^16/Q__9^16

 (41)

B__10 := (37530/Re10)^16

14680.75929*D__10^16/Q__10^16

 (42)

f__1 := 8*((8/Re1)^12+1/(A__1+B__1)^1.5)^(1/12)

8*(0.1173811769e-40*D__1^12/Q__1^12+1/(1763934.700*ln(1/(0.7551394026e-3*(D__1/Q__1)^.9+0.1242e-1/D__1))^16+14680.75929*D__1^16/Q__1^16)^1.5)^(1/12)

 (43)

f__2 := 8*((8/Re2)^12+1/(A__2+B__2)^1.5)^(1/12)

8*(0.1173811769e-40*D__2^12/Q__2^12+1/(1763934.700*ln(1/(0.7551394026e-3*(D__2/Q__2)^.9+0.1242e-1/D__2))^16+14680.75929*D__2^16/Q__2^16)^1.5)^(1/12)

 (44)

f__3 := 8*((8/Re3)^12+1/(A__3+B__3)^1.5)^(1/12)

8*(0.1173811769e-40*D__3^12/Q__3^12+1/(1763934.700*ln(1/(0.7551394026e-3*(D__3/Q__3)^.9+0.1242e-1/D__3))^16+14680.75929*D__3^16/Q__3^16)^1.5)^(1/12)

 (45)

f__4 := 8*((8/Re4)^12+1/(A__4+B__4)^1.5)^(1/12)

8*(0.1173811769e-40*D__4^12/Q__4^12+1/(1763934.700*ln(1/(0.7551394026e-3*(D__4/Q__4)^.9+0.1242e-1/D__4))^16+14680.75929*D__4^16/Q__4^16)^1.5)^(1/12)

 (46)

f__5 := 8*((8/Re5)^12+1/(A__5+B__5)^1.5)^(1/12)

8*(0.1173811769e-40*D__5^12/Q__5^12+1/(1763934.700*ln(1/(0.7551394026e-3*(D__5/Q__5)^.9+0.1242e-1/D__5))^16+14680.75929*D__5^16/Q__5^16)^1.5)^(1/12)

 (47)

f__6 := 8*((8/Re6)^12+1/(A__6+B__6)^1.5)^(1/12)

8*(0.1173811769e-40*D__6^12/Q__6^12+1/(1763934.700*ln(1/(0.7551394026e-3*(D__6/Q__6)^.9+0.1242e-1/D__6))^16+14680.75929*D__6^16/Q__6^16)^1.5)^(1/12)

 (48)

f__7 := 8*((8/Re7)^12+1/(A__7+B__7)^1.5)^(1/12)

8*(0.1173811769e-40*D__7^12/Q__7^12+1/(1763934.700*ln(1/(0.7551394026e-3*(D__7/Q__7)^.9+0.1242e-1/D__7))^16+14680.75929*D__7^16/Q__7^16)^1.5)^(1/12)

 (49)

f__8 := 8*((8/Re8)^12+1/(A__8+B__8)^1.5)^(1/12)

8*(0.1173811769e-40*D__8^12/Q__8^12+1/(1763934.700*ln(1/(0.7551394026e-3*(D__8/Q__8)^.9+0.1242e-1/D__8))^16+14680.75929*D__8^16/Q__8^16)^1.5)^(1/12)

 (50)

f__9 := 8*((8/Re9)^12+1/(A__9+B__9)^1.5)^(1/12)

8*(0.1173811769e-40*D__9^12/Q__9^12+1/(1763934.700*ln(1/(0.7551394026e-3*(D__9/Q__9)^.9+0.1242e-1/D__9))^16+14680.75929*D__9^16/Q__9^16)^1.5)^(1/12)

 (51)

f__10 := 8*((8/Re10)^12+1/(A__10+B__10)^1.5)^(1/12)

8*(0.1173811769e-40*D__10^12/Q__10^12+1/(1763934.700*ln(1/(0.7551394026e-3*(D__10/Q__10)^.9+0.1242e-1/D__10))^16+14680.75929*D__10^16/Q__10^16)^1.5)^(1/12)

 (52)

H__1 := piecewise(Q__1 > 0, 8000*10^6*f__1*L__1*Q__1^2/((9.8*(Pi^2))*D__1^5), -8000*10^6*f__1*L__1*Q__1^2/((9.8*(Pi^2))*D__1^5))

piecewise(0 < `#msub(mi("Q"),mi("1"))`, 6.616893624*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("1"))`^12/`#msub(mi("Q"),mi("1"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("1"))`/`#msub(mi("Q"),mi("1"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("1"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("1"))`^16/`#msub(mi("Q"),mi("1"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("1"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("1"))`^5, -6.616893624*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("1"))`^12/`#msub(mi("Q"),mi("1"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("1"))`/`#msub(mi("Q"),mi("1"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("1"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("1"))`^16/`#msub(mi("Q"),mi("1"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("1"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("1"))`^5)

 (53)

H__2 := piecewise(Q__2 > 0, 8000*10^6*f__2*L__2*Q__2^2/((9.8*(Pi^2))*D__2^5), -8000*10^6*f__2*L__2*Q__2^2/((9.8*(Pi^2))*D__2^5))

piecewise(0 < `#msub(mi("Q"),mi("2"))`, 9.925340436*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("2"))`^12/`#msub(mi("Q"),mi("2"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("2"))`/`#msub(mi("Q"),mi("2"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("2"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("2"))`^16/`#msub(mi("Q"),mi("2"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("2"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("2"))`^5, -9.925340436*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("2"))`^12/`#msub(mi("Q"),mi("2"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("2"))`/`#msub(mi("Q"),mi("2"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("2"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("2"))`^16/`#msub(mi("Q"),mi("2"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("2"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("2"))`^5)

 (54)

H__3 := piecewise(Q__3 > 0, 8000*10^6*f__3*L__3*Q__3^2/((9.8*(Pi^2))*D__3^5), -8000*10^6*f__3*L__3*Q__3^2/((9.8*(Pi^2))*D__3^5))

piecewise(0 < `#msub(mi("Q"),mi("3"))`, 6.616893624*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("3"))`^12/`#msub(mi("Q"),mi("3"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("3"))`/`#msub(mi("Q"),mi("3"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("3"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("3"))`^16/`#msub(mi("Q"),mi("3"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("3"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("3"))`^5, -6.616893624*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("3"))`^12/`#msub(mi("Q"),mi("3"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("3"))`/`#msub(mi("Q"),mi("3"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("3"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("3"))`^16/`#msub(mi("Q"),mi("3"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("3"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("3"))`^5)

 (55)

H__4 := piecewise(Q__4 > 0, 8000*10^6*f__4*L__4*Q__4^2/((9.8*(Pi^2))*D__4^5), -8000*10^6*f__4*L__4*Q__4^2/((9.8*(Pi^2))*D__4^5))

piecewise(0 < `#msub(mi("Q"),mi("4"))`, 4.678850351*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("4"))`^12/`#msub(mi("Q"),mi("4"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("4"))`/`#msub(mi("Q"),mi("4"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("4"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("4"))`^16/`#msub(mi("Q"),mi("4"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("4"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("4"))`^5, -4.678850351*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("4"))`^12/`#msub(mi("Q"),mi("4"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("4"))`/`#msub(mi("Q"),mi("4"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("4"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("4"))`^16/`#msub(mi("Q"),mi("4"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("4"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("4"))`^5)

 (56)

H__5 := piecewise(Q__5 > 0, 8000*10^6*f__5*L__5*Q__5^2/((9.8*(Pi^2))*D__5^5), -8000*10^6*f__5*L__5*Q__5^2/((9.8*(Pi^2))*D__5^5))

piecewise(0 < `#msub(mi("Q"),mi("5"))`, 3.970136174*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("5"))`^12/`#msub(mi("Q"),mi("5"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("5"))`/`#msub(mi("Q"),mi("5"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("5"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("5"))`^16/`#msub(mi("Q"),mi("5"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("5"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("5"))`^5, -3.970136174*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("5"))`^12/`#msub(mi("Q"),mi("5"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("5"))`/`#msub(mi("Q"),mi("5"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("5"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("5"))`^16/`#msub(mi("Q"),mi("5"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("5"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("5"))`^5)

 (57)

H__6 := piecewise(Q__6 > 0, 8000*10^6*f__6*L__6*Q__6^2/((9.8*(Pi^2))*D__6^5), -8000*10^6*f__6*L__6*Q__6^2/((9.8*(Pi^2))*D__6^5))

piecewise(0 < `#msub(mi("Q"),mi("6"))`, 3.970136174*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("6"))`^12/`#msub(mi("Q"),mi("6"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("6"))`/`#msub(mi("Q"),mi("6"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("6"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("6"))`^16/`#msub(mi("Q"),mi("6"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("6"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("6"))`^5, -3.970136174*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("6"))`^12/`#msub(mi("Q"),mi("6"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("6"))`/`#msub(mi("Q"),mi("6"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("6"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("6"))`^16/`#msub(mi("Q"),mi("6"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("6"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("6"))`^5)

 (58)

H__7 := piecewise(Q__7 > 0, 8000*10^6*f__7*L__7*Q__7^2/((9.8*(Pi^2))*D__7^5), -8000*10^6*f__7*L__7*Q__7^2/((9.8*(Pi^2))*D__7^5))

piecewise(0 < `#msub(mi("Q"),mi("7"))`, 7.640530634*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("7"))`^12/`#msub(mi("Q"),mi("7"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("7"))`/`#msub(mi("Q"),mi("7"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("7"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("7"))`^16/`#msub(mi("Q"),mi("7"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("7"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("7"))`^5, -7.640530634*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("7"))`^12/`#msub(mi("Q"),mi("7"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("7"))`/`#msub(mi("Q"),mi("7"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("7"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("7"))`^16/`#msub(mi("Q"),mi("7"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("7"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("7"))`^5)

 (59)

H__8 := piecewise(Q__8 > 0, 8000*10^6*f__8*L__8*Q__8^2/((9.8*(Pi^2))*D__8^5), -8000*10^6*f__8*L__8*Q__8^2/((9.8*(Pi^2))*D__8^5))

piecewise(0 < `#msub(mi("Q"),mi("8"))`, 9.925340436*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("8"))`^12/`#msub(mi("Q"),mi("8"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("8"))`/`#msub(mi("Q"),mi("8"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("8"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("8"))`^16/`#msub(mi("Q"),mi("8"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("8"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("8"))`^5, -9.925340436*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("8"))`^12/`#msub(mi("Q"),mi("8"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("8"))`/`#msub(mi("Q"),mi("8"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("8"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("8"))`^16/`#msub(mi("Q"),mi("8"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("8"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("8"))`^5)

 (60)

H__9 := piecewise(Q__9 > 0, 8000*10^6*f__9*L__9*Q__9^2/((9.8*(Pi^2))*D__9^5), -8000*10^6*f__9*L__9*Q__9^2/((9.8*(Pi^2))*D__9^5))

piecewise(0 < `#msub(mi("Q"),mi("9"))`, 9.925340436*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("9"))`^12/`#msub(mi("Q"),mi("9"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("9"))`/`#msub(mi("Q"),mi("9"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("9"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("9"))`^16/`#msub(mi("Q"),mi("9"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("9"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("9"))`^5, -9.925340436*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("9"))`^12/`#msub(mi("Q"),mi("9"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("9"))`/`#msub(mi("Q"),mi("9"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("9"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("9"))`^16/`#msub(mi("Q"),mi("9"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("9"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("9"))`^5)

 (61)

H__10 := piecewise(Q__10 > 0, 8000*10^6*f__10*L__10*Q__10^2/((9.8*(Pi^2))*D__10^5), -8000*10^6*f__10*L__10*Q__10^2/((9.8*(Pi^2))*D__10^5))

piecewise(0 < `#msub(mi("Q"),mi("10"))`, 1.323378725*10^10*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("10"))`^12/`#msub(mi("Q"),mi("10"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("10"))`/`#msub(mi("Q"),mi("10"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("10"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("10"))`^16/`#msub(mi("Q"),mi("10"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("10"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("10"))`^5, -1.323378725*10^10*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("10"))`^12/`#msub(mi("Q"),mi("10"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("10"))`/`#msub(mi("Q"),mi("10"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("10"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("10"))`^16/`#msub(mi("Q"),mi("10"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("10"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("10"))`^5)

 (62)

NULL

fsolve({Q__1 = Q__4, Q__3 = Q__7, 4*Q__1/(Pi*D__1^2) = 3.5, 4*Q__10/(Pi*D__10^2) = 3.5, 4*Q__2/(Pi*D__2^2) = 3.5, 4*Q__3/(Pi*D__3^2) = 3.5, 4*Q__4/(Pi*D__4^2) = 3.5, 4*Q__5/(Pi*D__5^2) = 3.5, 4*Q__6/(Pi*D__6^2) = 3.5, 4*Q__7/(Pi*D__7^2) = 3.5, 4*Q__8/(Pi*D__8^2) = 3.5, 4*Q__9/(Pi*D__9^2) = 3.5, H__1+H__4 = H__5+H__8, H__3+H__7 = H__6+H__10, Q__1+Q__5 = Q__2, Q__4+Q__8 = 980*(1/60), Q__5+Q__9 = Q__8+17, Q__7+Q__10 = 950*(1/60), Q__2+Q__3+Q__6 = 4000*(1/60), Q__9+Q__10+17.5 = Q__6}, {D__1 = 30, D__10 = 30, D__2 = 30, D__3 = 30, D__4 = 30, D__5 = 30, D__6 = 30, D__7 = 30, D__8 = 30, D__9 = 30, Q__1 = 20, Q__10 = 5, Q__2 = 40, Q__3 = 20, Q__4 = 20, Q__5 = 20, Q__6 = 20, Q__7 = 20, Q__8 = 5, Q__9 = 5})

fsolve({`#msub(mi("Q"),mi("1"))` = `#msub(mi("Q"),mi("4"))`, `#msub(mi("Q"),mi("3"))` = `#msub(mi("Q"),mi("7"))`, 4*`#msub(mi("Q"),mi("1"))`/(Pi*`#msub(mi("D",fontstyle = "normal"),mi("1"))`^2) = 3.5, 4*`#msub(mi("Q"),mi("10"))`/(Pi*`#msub(mi("D",fontstyle = "normal"),mi("10"))`^2) = 3.5, 4*`#msub(mi("Q"),mi("2"))`/(Pi*`#msub(mi("D",fontstyle = "normal"),mi("2"))`^2) = 3.5, 4*`#msub(mi("Q"),mi("3"))`/(Pi*`#msub(mi("D",fontstyle = "normal"),mi("3"))`^2) = 3.5, 4*`#msub(mi("Q"),mi("4"))`/(Pi*`#msub(mi("D",fontstyle = "normal"),mi("4"))`^2) = 3.5, 4*`#msub(mi("Q"),mi("5"))`/(Pi*`#msub(mi("D",fontstyle = "normal"),mi("5"))`^2) = 3.5, 4*`#msub(mi("Q"),mi("6"))`/(Pi*`#msub(mi("D",fontstyle = "normal"),mi("6"))`^2) = 3.5, 4*`#msub(mi("Q"),mi("7"))`/(Pi*`#msub(mi("D",fontstyle = "normal"),mi("7"))`^2) = 3.5, 4*`#msub(mi("Q"),mi("8"))`/(Pi*`#msub(mi("D",fontstyle = "normal"),mi("8"))`^2) = 3.5, 4*`#msub(mi("Q"),mi("9"))`/(Pi*`#msub(mi("D",fontstyle = "normal"),mi("9"))`^2) = 3.5, `#msub(mi("Q"),mi("1"))`+`#msub(mi("Q"),mi("5"))` = `#msub(mi("Q"),mi("2"))`, `#msub(mi("Q"),mi("4"))`+`#msub(mi("Q"),mi("8"))` = 49/3, `#msub(mi("Q"),mi("5"))`+`#msub(mi("Q"),mi("9"))` = `#msub(mi("Q"),mi("8"))`+17, `#msub(mi("Q"),mi("7"))`+`#msub(mi("Q"),mi("10"))` = 95/6, piecewise(0 < `#msub(mi("Q"),mi("1"))`, 6.616893624*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("1"))`^12/`#msub(mi("Q"),mi("1"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("1"))`/`#msub(mi("Q"),mi("1"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("1"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("1"))`^16/`#msub(mi("Q"),mi("1"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("1"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("1"))`^5, -6.616893624*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("1"))`^12/`#msub(mi("Q"),mi("1"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("1"))`/`#msub(mi("Q"),mi("1"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("1"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("1"))`^16/`#msub(mi("Q"),mi("1"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("1"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("1"))`^5)+piecewise(0 < `#msub(mi("Q"),mi("4"))`, 4.678850351*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("4"))`^12/`#msub(mi("Q"),mi("4"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("4"))`/`#msub(mi("Q"),mi("4"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("4"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("4"))`^16/`#msub(mi("Q"),mi("4"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("4"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("4"))`^5, -4.678850351*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("4"))`^12/`#msub(mi("Q"),mi("4"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("4"))`/`#msub(mi("Q"),mi("4"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("4"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("4"))`^16/`#msub(mi("Q"),mi("4"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("4"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("4"))`^5) = piecewise(0 < `#msub(mi("Q"),mi("5"))`, 3.970136174*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("5"))`^12/`#msub(mi("Q"),mi("5"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("5"))`/`#msub(mi("Q"),mi("5"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("5"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("5"))`^16/`#msub(mi("Q"),mi("5"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("5"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("5"))`^5, -3.970136174*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("5"))`^12/`#msub(mi("Q"),mi("5"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("5"))`/`#msub(mi("Q"),mi("5"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("5"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("5"))`^16/`#msub(mi("Q"),mi("5"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("5"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("5"))`^5)+piecewise(0 < `#msub(mi("Q"),mi("8"))`, 9.925340436*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("8"))`^12/`#msub(mi("Q"),mi("8"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("8"))`/`#msub(mi("Q"),mi("8"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("8"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("8"))`^16/`#msub(mi("Q"),mi("8"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("8"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("8"))`^5, -9.925340436*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("8"))`^12/`#msub(mi("Q"),mi("8"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("8"))`/`#msub(mi("Q"),mi("8"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("8"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("8"))`^16/`#msub(mi("Q"),mi("8"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("8"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("8"))`^5), piecewise(0 < `#msub(mi("Q"),mi("3"))`, 6.616893624*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("3"))`^12/`#msub(mi("Q"),mi("3"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("3"))`/`#msub(mi("Q"),mi("3"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("3"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("3"))`^16/`#msub(mi("Q"),mi("3"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("3"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("3"))`^5, -6.616893624*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("3"))`^12/`#msub(mi("Q"),mi("3"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("3"))`/`#msub(mi("Q"),mi("3"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("3"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("3"))`^16/`#msub(mi("Q"),mi("3"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("3"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("3"))`^5)+piecewise(0 < `#msub(mi("Q"),mi("7"))`, 7.640530634*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("7"))`^12/`#msub(mi("Q"),mi("7"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("7"))`/`#msub(mi("Q"),mi("7"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("7"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("7"))`^16/`#msub(mi("Q"),mi("7"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("7"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("7"))`^5, -7.640530634*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("7"))`^12/`#msub(mi("Q"),mi("7"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("7"))`/`#msub(mi("Q"),mi("7"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("7"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("7"))`^16/`#msub(mi("Q"),mi("7"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("7"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("7"))`^5) = piecewise(0 < `#msub(mi("Q"),mi("6"))`, 3.970136174*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("6"))`^12/`#msub(mi("Q"),mi("6"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("6"))`/`#msub(mi("Q"),mi("6"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("6"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("6"))`^16/`#msub(mi("Q"),mi("6"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("6"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("6"))`^5, -3.970136174*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("6"))`^12/`#msub(mi("Q"),mi("6"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("6"))`/`#msub(mi("Q"),mi("6"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("6"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("6"))`^16/`#msub(mi("Q"),mi("6"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("6"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("6"))`^5)+piecewise(0 < `#msub(mi("Q"),mi("10"))`, 1.323378725*10^10*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("10"))`^12/`#msub(mi("Q"),mi("10"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("10"))`/`#msub(mi("Q"),mi("10"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("10"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("10"))`^16/`#msub(mi("Q"),mi("10"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("10"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("10"))`^5, -1.323378725*10^10*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("10"))`^12/`#msub(mi("Q"),mi("10"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("10"))`/`#msub(mi("Q"),mi("10"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("10"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("10"))`^16/`#msub(mi("Q"),mi("10"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("10"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("10"))`^5), `#msub(mi("Q"),mi("2"))`+`#msub(mi("Q"),mi("3"))`+`#msub(mi("Q"),mi("6"))` = 200/3, `#msub(mi("Q"),mi("9"))`+`#msub(mi("Q"),mi("10"))`+17.5 = `#msub(mi("Q"),mi("6"))`}, {`#msub(mi("Q"),mi("1"))` = 20, `#msub(mi("Q"),mi("10"))` = 5, `#msub(mi("Q"),mi("2"))` = 40, `#msub(mi("Q"),mi("3"))` = 20, `#msub(mi("Q"),mi("4"))` = 20, `#msub(mi("Q"),mi("5"))` = 20, `#msub(mi("Q"),mi("6"))` = 20, `#msub(mi("Q"),mi("7"))` = 20, `#msub(mi("Q"),mi("8"))` = 5, `#msub(mi("Q"),mi("9"))` = 5, `#msub(mi("D",fontstyle = "normal"),mi("1"))` = 30, `#msub(mi("D",fontstyle = "normal"),mi("10"))` = 30, `#msub(mi("D",fontstyle = "normal"),mi("2"))` = 30, `#msub(mi("D",fontstyle = "normal"),mi("3"))` = 30, `#msub(mi("D",fontstyle = "normal"),mi("4"))` = 30, `#msub(mi("D",fontstyle = "normal"),mi("5"))` = 30, `#msub(mi("D",fontstyle = "normal"),mi("6"))` = 30, `#msub(mi("D",fontstyle = "normal"),mi("7"))` = 30, `#msub(mi("D",fontstyle = "normal"),mi("8"))` = 30, `#msub(mi("D",fontstyle = "normal"),mi("9"))` = 30})

 (63)

NULL


 

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