Problemas de Mecanica de Fluidos en Polymath

FACULTAD DE INGENIERÍA QUÍMICA-UNT

Problema 11.1

POLYMATH Results09-24-2010, Rev5.1.225

NLE Solution

Variable Value f(x) Ini Guessfr 0.016662 8.625E-10 0.02e 1.5E-06d 0.09797A 0.007538viscin 1.3E-06Q 0.015L 80.5g 9.81k 1pe 9.81z2 -12ft 0.017Leq 30v2 1.9899178Re 1.5E+05h3 0.2018233h1 2.7631214h2 0.3087896hL 3.2737343p2 83.62478

NLE Report (safenewt)

Nonlinear equations[1] f(fr) = 1/sqrt(fr)+2*log(e/(3.7*d)+2.51/(Re*sqrt(fr))) = 0

Explicit equations[1] e = 1.5e-6[2] d = 0.09797

Mecánica de Fluidos-Profesor: Dr. Ing. Guillermo Evangelista B. Página 1


[3] A = 7.538e-3[4] viscin = 1.3e-6[5] Q = 1.5e-2[6] L = 80.5[7] g = 9.81[8] k = 1[9] pe = 9.81[10] z2 = -12[11] ft = 0.017[12] Leq = 30[13] v2 = Q/A[14] Re = d*v2/viscin[15] h3 = k*v2^2/(2*g)[16] h1 = fr*L*v2^2/(2*g*d)[17] h2 = 3*ft*Leq*v2^2/(2*g)[18] hL = h1+h2+h3[19] p2 = pe*(-hL-z2-v2^2/(2*g))

SettingsMax iterations = 150Tolerance F = 0.0000001Tolerance X= 0.0000001Tolerance min = 0.0000001

GeneralSearch range: .018 > fr > .015number of implicit equations: 1number of explicit equations: 19



POLYMATH Results 09-24-2010, Rev5.1.225

NLE Solution

Variable Value f(x) Ini Guess fr 0.0165599 0 0.02 e 1.5E-06 d 0.09797 A 0.007538 viscin 1.3E-06 Q 0.015 L 80.5 g 9.81 k 1 pe 9.81 z2 -12 ft 0.017 Leq 30 v2 1.9899178 Re 1.5E+05 h3 0.2018233 h1 2.7462012 h2 0.3087896 hL 3.2568141 p2 83.790768


Nonlinear equations [1] f(fr) = fr-0.25/(log(e/(3.7*d)+5.74/Re^0.9))^2 = 0

Explicit equations [1] e = 1.5e-6 [2] d = 0.09797 [3] A = 7.538e-3 [4] viscin = 1.3e-6 [5] Q = 1.5e-2 [6] L = 80.5 [7] g = 9.81



[8] k = 1 [9] pe = 9.81 [10] z2 = -12 [11] ft = 0.017 [12] Leq = 30 [13] v2 = Q/A [14] Re = d*v2/viscin [15] h3 = k*v2^2/(2*g) [16] h1 = fr*L*v2^2/(2*g*d) [17] h2 = 3*ft*Leq*v2^2/(2*g) [18] hL = h1+h2+h3 [19] p2 = pe*(-hL-z2-v2^2/(2*g))

Settings Max iterations = 150 Tolerance F = 0.0000001 Tolerance X = 0.0000001 Tolerance min = 0.0000001

General Search range: .018 > fr > .015 number of implicit equations: 1 number of explicit equations: 19



Problema 11.2


NLE Solution

Variable Value f(x) Ini Guess fr 0.0220647 2.814E-09 0.02 e 4.6E-05 d 0.0525 A 0.002168 sg 0.82 rho 1000 peagua 9.81 visdin 0.00165 pe 8.0442 dens 820 Q 0.00725 v 3.3440959 Re 8.725E+04 zb 4.5 k 1 Leve 100 Leva 150 Lec 30 L 38 g 9.81 h1 0.5699785 h6 0.5699785 ft 0.019 h2 1.0829591 h3 1.6244387 h4 0.3248877 h5 9.1029313 hL 13.275174 pa 142.98705




Nonlinear equations [1] f(fr) = 1/sqrt(fr)+2*log(e/(3.7*d)+2.51/(Re*sqrt(fr))) = 0

Explicit equations [1] e = 4.6e-5 [2] d = 0.0525 [3] A = 2.168e-3 [4] sg = 0.82 [5] rho = 1000 [6] peagua = 9.81 [7] visdin = 1.65e-3 [8] pe = sg*peagua [9] dens = sg*rho [10] Q = 435/60000 [11] v = Q/A [12] Re = v*dens*d/visdin [13] zb = 4.5 [14] k = 1 [15] Leve = 100 [16] Leva = 150 [17] Lec = 30 [18] L = 38 [19] g = 9.81 [20] h1 = k*v^2/(2*g) [21] h6 = v^2/(2*g) [22] ft = 0.019 [23] h2 = ft*Leve*v^2/(2*g) [24] h3 = ft*Leva*v^2/(2*g) [25] h4 = ft*Lec*v^2/(2*g) [26] h5 = fr*L*v^2/(2*d*g) [27] hL = h1+h2+h3+h4+h5+h6 [28] pa = pe*(hL+zb)


General



Search range: .018 > fr > .015 number of implicit equations: 1 number of explicit equations: 28


NLE Solution

Variable Value f(x) Ini Guess fr 0.0222163 0 0.02 e 4.6E-05 d 0.0525 A 0.002168 sg 0.82 rho 1000 peagua 9.81 visdin 0.00165 pe 8.0442 dens 820 Q 0.00725 v 3.3440959 Re 8.725E+04 zb 4.5 k 1 Leve 100 Leva 150 Lec 30 L 38 g 9.81 h1 0.5699785 h6 0.5699785 ft 0.019 h2 1.0829591



h3 1.6244387 h4 0.3248877 h5 9.1654617 hL 13.337704 pa 143.49006



Explicit equations [1] e = 4.6e-5 [2] d = 0.0525 [3] A = 2.168e-3 [4] sg = 0.82 [5] rho = 1000 [6] peagua = 9.81 [7] visdin = 1.65e-3 [8] pe = sg*peagua [9] dens = sg*rho [10] Q = 435/60000 [11] v = Q/A [12] Re = v*dens*d/visdin [13] zb = 4.5 [14] k = 1 [15] Leve = 100 [16] Leva = 150 [17] Lec = 30 [18] L = 38 [19] g = 9.81 [20] h1 = k*v^2/(2*g) [21] h6 = v^2/(2*g) [22] ft = 0.019 [23] h2 = ft*Leve*v^2/(2*g) [24] h3 = ft*Leva*v^2/(2*g) [25] h4 = ft*Lec*v^2/(2*g) [26] h5 = fr*L*v^2/(2*d*g) [27] hL = h1+h2+h3+h4+h5+h6 [28] pa = pe*(hL+zb)





Problema 11.3


NLE Solution

Variable Value f(x) Ini Guess fr 0.0094063 2.47E-11 0.02 e 1.5E-04 A 0.02333 d 0.1723 sg 0.9 rho 1.94 visdin 6.0E-05 Q 0.1336303 p2 2.88E+04 z2 25 peagua 62.4 L 50 g 32.2 K 6.5 ft 0.019 Leq 30



v 5.7278307 pe 56.16 h2 3.3113709 h1 1.3905853 h3 0.5807635 Re 2.872E+04 hL 5.2827197 p1 211.81026


Nonlinear equations [1] f(fr) = 1/sqrt(fr)+2*log(e/3.7*d)+2.51/(Re*sqrt(fr)) = 0

Explicit equations [1] e = 1.5e-4 [2] A = 0.02333 [3] d = 0.1723 [4] sg = 0.9 [5] rho = 1.94 [6] visdin = 6e-5 [7] Q = 60/449 [8] p2 = 200*144 [9] z2 = 25 [10] peagua = 62.4 [11] L = 50 [12] g = 32.2 [13] K = 6.5 [14] ft = 0.019 [15] Leq = 30 [16] v = Q/A [17] pe = sg*peagua [18] h2 = K*v^2/(2*g) [19] h1 = fr*L*v^2/(2*g*d) [20] h3 = 2*ft*Leq*v^2/(2*g) [21] Re = d*v*sg*rho/visdin [22] hL = h1+h2+h3 [23] p1 = (p2+pe*(hL+z2))/144

Settings



Max iterations = 150 Tolerance F = 0.0000001 Tolerance X = 0.0000001 Tolerance min = 0.0000001



NLE Solution

Variable Value f(x) Ini Guess fr 0.0260042 0 0.02 e 1.5E-04 A 0.02333 d 0.1723 sg 0.9 rho 1.94 visdin 6.0E-05 Q 0.1336303 p2 2.88E+04 z2 25 peagua 62.4 L 50 g 32.2 K 6.5 ft 0.019 Leq 30 v 5.7278307 pe 56.16 h2 3.3113709 h1 3.8443435 h3 0.5807635



Re 2.872E+04 hL 7.7364779 p1 212.76723



Explicit equations [1] e = 1.5e-4 [2] A = 0.02333 [3] d = 0.1723 [4] sg = 0.9 [5] rho = 1.94 [6] visdin = 6e-5 [7] Q = 60/449 [8] p2 = 200*144 [9] z2 = 25 [10] peagua = 62.4 [11] L = 50 [12] g = 32.2 [13] K = 6.5 [14] ft = 0.019 [15] Leq = 30 [16] v = Q/A [17] pe = sg*peagua [18] h2 = K*v^2/(2*g) [19] h1 = fr*L*v^2/(2*g*d) [20] h3 = 2*ft*Leq*v^2/(2*g) [21] Re = d*v*sg*rho/visdin [22] hL = h1+h2+h3 [23] p1 = (p2+pe*(hL+z2))/144







Problema 11.8


NLES Solution

Variable Value f(x) Ini Guess fr 0.0168385 0 0.02 v 38.250804 -9.486E-13 5 g 32.2 e 1.5E-04 d 0.3188 A 0.07986 viscin 6.55E-06 Re 1.862E+06 L 25 h1 30 hL 30 Q 3.0547092

NLES Report (safenewt)

Nonlinear equations [1] f(fr) = fr-0.25/(log(e/(3.7*d)+5.74/Re^0.9))^2 = 0 [2] f(v) = hL-h1 = 0

Explicit equations [1] g = 32.2 [2] e = 1.5e-4 [3] d = 0.3188 [4] A = 0.07986 [5] viscin = 6.55e-6 [6] Re = v*d/viscin [7] L = 25 [8] h1 = fr*L*v^2/(2*d*g) [9] hL = 30



[10] Q = v*A


General number of implicit equations: 2 number of explicit equations: 10

Problema 11.9


NLES Solution

Variable Value f(x) Ini Guess fr 0.0244849 1.708E-08 0.02 v 3.0955499 -1.194E-08 2 e 4.6E-05 d 0.04658 A 0.001704 visdin 0.003 sg 0.9 rho 900 pe 8.829 Re 4.326E+04 P 68 hL 7.7018915 L 30 g 9.81 h1 7.7018915 Q 0.0052748




Nonlinear equations [1] f(fr) = 1/sqrt(fr)+2*log(e/(3.7*d)+2.51/(Re*sqrt(fr))) = 0 [2] f(v) = hL-h1 = 0

Explicit equations [1] e = 4.6e-5 [2] d = 0.04658 [3] A = 1.704e-3 [4] visdin = 3e-3 [5] sg = 0.90 [6] rho = sg*1000 [7] pe = sg*9.81 [8] Re = v*rho*d/visdin [9] P = 68 [10] hL = P/pe [11] L = 30 [12] g = 9.81 [13] h1 = fr*L*v^2/(2*g*d) [14] Q = v*A





Problema 11.10


NLES Solution

Variable Value f(x) Ini Guess fr 0.0268305 7.105E-15 0.018 v 7.0499802 7.39E-13 5 e 4.0E-04 d 0.512 A 0.20589 pe 68.47 viscin 1.59E-04 Re 2.27E+04 p1 3.6E+04 p2 2.592E+04 z2 -55 L 5000 hL 202.21776 g 32.2 h1 202.21775 Q 1.4515204


Nonlinear equations [1] f(fr) = 1/sqrt(fr)+2*log(e/(3.7*d)+2.51/(Re*sqrt(fr))) = 0 [2] f(v) = hL-h1 = 0

Explicit equations [1] e = 4e-4 [2] d = 0.512 [3] A = 0.20589 [4] pe = 68.47 [5] viscin = 1.59e-4 [6] Re = v*d/viscin [7] p1 = 250*144 [8] p2 = 180*144



[9] z2 = -55 [10] L = 5000 [11] hL = ((p1-p2)/pe)-z2 [12] g = 32.2 [13] h1 = fr*L*v^2/(2*g*d) [14] Q = v*A





Problema 11.17


NLES Solution

Variable Value f(x) Ini Guess fr 0.0114089 6.217E-14 0.02 d 0.3137736 -2.645E-11 0.2 e 1.5E-04 Q 0.5 viscin 4.38E-06 pe 61 P12 1440 hL 23.606557 pi 3.1416 g 32.2 L 1000 v 6.4661593 Re 4.632E+05 h1 23.606557


Nonlinear equations [1] f(fr) = 1/sqrt(fr)+2.5*log(e/(3.7*d)+2.51/(Re*sqrt(fr))) = 0 [2] f(d) = hL-h1 = 0

Explicit equations [1] e = 1.5e-4 [2] Q = 0.5 [3] viscin = 4.38e-6 [4] pe = 61 [5] P12 = 10*144



[6] hL = (P12)/pe [7] pi = 3.1416 [8] g = 32.2 [9] L = 1000 [10] v = 4*Q/(pi*d^2) [11] Re = v*d/viscin [12] h1 = fr*L*v^2/(2*g*d)



Problema 11.18


NLES Solution

Variable Value f(x) Ini Guess fr 0.0070049 1.981E-11 0.018 d 0.0831361 -1.938E-08 0.004 e 1.5E-06 pi 3.1416 viscin 3.6E-07 Q 0.06 v 11.05301 Re 2.553E+06 pe 9.53 p 150 hL 15.739769 g 9.81 L 30 h1 15.739769




Nonlinear equations [1] f(fr) = 1/sqrt(fr)+2.5*log(e/(3.7*d)+2.51/(Re*sqrt(fr))) = 0 [2] f(d) = hL-h1 = 0

Explicit equations [1] e = 1.5e-6 [2] pi = 3.1416 [3] viscin = 3.6e-7 [4] Q = 0.06 [5] v = 4*Q/(pi*d^2) [6] Re = d*v/viscin [7] pe = 9.53 [8] p = 150 [9] hL = p/pe [10] g = 9.81 [11] L = 30 [12] h1 = fr*L*v^2/(2*g*d)





Nota:

Los problemas resueltos son del libro de Mecánica de Fluidos, Robert Mott. 6ta edición.

El resto de problemas, queda como trabajo para ustedes. cualquier duda o afianzamiento para los no desarrollados,

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Problemas de Mecanica de Fluidos en Polymath