e5a4ddb5-add8-4fc0-b3bd-dbeee2b0ae4d 6 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

L.1 200 m * :

L.2 100 m * :

L.3 200 m * :

L.4 100 m * :

D.1 0.25 m * :

D.2 0.25 m * :

D.3 0.25 m * :

D.4 0.25 m * :

Density of Water γ 62.4 lb ft 3^/ * :

Nodal Supply & Demands - known

QJ.1 0.32 m 3^s / * :

QJ.2 0.28 m 3^s / * :

QJ.3 0.14 m 3^s / * :

QJ.4 0.10 m 3^s / * :

node:1

QJ.1 Q.1 - Q.4 - 0 ≡

node:2

Q.1 Q.2 + QJ.2 - 0 ≡

node:3

Q.3 Q.2 - QJ.3 - 0 ≡

K.1 Q.1 n^* K.2 Q.2 n^* - K.3 Q.3 n^* - K.4 Q.4 n^* - 0 ≡

g.e 9.8066 m s 2^/ *

h.f f L * V 2^* 2 g.e * D * / ≡

V 2^1 π 4 / D 2^* / (2^Q 2^* ≡

h.f f L * 2 g.e * D * / 16 π 2^D 4^* / * Q 2^* ≡ 8 f * L * g.e D 5^* π 2^* / Q 2^* ≡

Hence K 8 f * L * g.e D 5^* n 2^* / ≡

f 0.02 :

D 0.25 0.25 0.25 0.25 41 mat m * :

L 20010020010041 mat m * :

j 1 D rows range KK j el 8 f * L j el * g.e D j el (5^* π 2^* / : for

KK s 2^m 5^/ 338.5552 169.2776 338.5552 169.2776 41 mat

K.1 KK 1 el : 338.555 s 2^m 5^/ *

K.2 KK 2 el : 169.278 s 2^m 5^/ *

K.3 KK 3 el : 338.555 s 2^m 5^/ *

K.4 KK 4 el : 169.278 s 2^m 5^/ *

Governing Equations

F 1 el QJ.1 Q.1 - Q.4 - 0 ≡ (:

F 2 el Q.1 Q.2 + QJ.2 - (:

F 3 el Q.3 Q.2 - QJ.3 - 0 ≡ (:

F 4 el K.1 Q.1 * Q.1 abs * K.2 Q.2 * Q.2 abs * - K.3 Q.3 * Q.3 abs * - K.4 Q.4 * Q.4 abs * - 0 ≡ (:

Initial guess for 
each variable g_var .2 .2 .2 .2 41 mat m 3^s / * :

F Uknown QJ.1 Q.1 - Q.4 - 0 ≡ Q.1 Q.2 + QJ.2 - Q.3 Q.2 - QJ.3 - 0 ≡ K.1 Q.1 * Q.1 abs * K.2 Q.2 * Q.2 abs * - K.3 Q.3 * Q.3 abs * - K.4 Q.4 * Q.4 abs * - 0 ≡ 41 mat :

F F g_var FindRoot eval : m 3^s / 0.218 0.062 0.202 0.102 41 mat

Q.1 F 1 el : m 3^s / 0.218

Q.2 F 2 el : m 3^s / 0.062

Q.3 F 3 el : m 3^s / 0.202

Q.4 F 4 el : m 3^s / 0.102

Node 1 QJ.1 Q.1 - Q.4 - 0 m 3^s / *

hf1 K.1 Q.1 * Q.1 abs * 16.14887 m *

Node 2 Q.1 Q.2 + QJ.2 - 0 m 3^s / *

hf2 K.2 Q.2 * Q.2 abs * - 0.64229 m * -

Node 3 Q.3 Q.2 - QJ.3 - 0 m 3^s / *

hf3 K.3 Q.3 * Q.3 abs * - 13.7594 m * -

hf4 K.4 Q.4 * Q.4 abs * - 1.74728 m * -

Hence K.1 Q.1 * Q.1 abs * K.2 Q.2 * Q.2 abs * - K.3 Q.3 * Q.3 abs * - K.4 Q.4 * Q.4 abs * - 0 m *

Additional check
at Node 4 QJ.4 Q.4 + Q.3 - 0 m 3^s / *