3ee126b2-32d7-45ee-b6a2-1b40e1965d4f 98 5 7 decimal

Following is a MathCad example done in SMath

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All SMath inputs highlighted

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Parameters

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A

B

C

Elevation

Z.A 100 ft * :

Z.B 90 ft * :

Z.C 30 ft * :

Length

L.A 500 ft * :

L.B 1500 ft * :

L.C 2000 ft * :

Diameter

d.A 8 in * :

d.B 10 in * :

d.C 12 in * :

Friction factor

f.A 0.02 :

f.B 0.01 :

f.C 0.04 :

f L d Q h.L f L d / * Q π d 2^4 / * / (2^* 12 g.e * / * :

MathCAD Solve Block

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F 1 el Z.A E.P Q.A Q.A abs / f.A L.A d.A Q.A h.L * + ≡ (:

F 2 el Z.B E.P Q.B Q.B abs / f.B L.B d.B Q.B h.L * + ≡ (:

F 3 el Z.C E.P Q.C Q.C abs / f.C L.C d.C Q.C h.L * + ≡ (:

F 4 el Q.A Q.B + Q.C + 0 ≡ (:

where Z.B ft 90

guess Z.B 333 gal min / * 666 gal min / * 999 gal min / * 41 mat :

F Unknowns E.P Q.A Q.B Q.C 41 mat

Using Maxima F guess FindRoot Maxima 25.8102 m * 0.0801 m 3^s / * 0.0674 m 3^s / * 0.1475 m 3^s / * - 41 mat

F F guess FindRoot : 25.8102 m * 0.0801 m 3^s / * 0.0674 m 3^s / * 0.1475 m 3^s / * - 41 mat

Negative value inicates that

flow is in opposite direction

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MathCAD Result

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Result

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E.P F 1 el : ft 84.679

Q.A F 2 el : gal min / 1270

Q.B F 3 el : gal min / 1068

Q.C F 4 el : gal min / 2338 -

Headloss

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MathCAD Calculation

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Q.A Q.A abs / f.A L.A d.A Q.A h.L * ft 15.321

In pipe A

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Q.B Q.B abs / f.B L.B d.B Q.B h.L * ft 5.321

In pipe B

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Q.C Q.C abs / f.C L.C d.C Q.C h.L * ft 54.679 -

In pipe C

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Energy Balance between

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Z.A E.P Q.A Q.A abs / f.A L.A d.A Q.A h.L * + (- ft 0

Resrvoir A & P

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OK

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Z.B E.P Q.B Q.B abs / f.B L.B d.B Q.B h.L * + (- ft 0

Resrvoir B & P

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OK

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Z.C E.P Q.C Q.C abs / f.C L.C d.C Q.C h.L * + (- ft 0

Resrvoir C & P

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OK

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Continuity at P

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Q.A Q.B + Q.C + 0

OK

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