HARDY CROSS METHOD

Condition :

• Friction Law In the Pipe

ℎ𝑓 = 𝑓.𝐿

𝐷

𝑈2

2𝑔= 𝑓.𝐿

𝐷

𝑄2

2𝑔𝐴2=8𝑓𝐿

𝑔𝜋2𝐷5𝑄2

ℎ𝑓 = 𝑘. 𝑄2

• Contnuity Law

𝑄𝑖 = 0

• Energy loss ℎ𝑓 = 0

STEPS

1. Select discharge distribution through pipe (Q0) using continuity law.

2. Calculate fricton loss each pipe using ℎ𝑓 = 𝑘. 𝑄2

3. Devide pipe network become several closed network, each pipe should exist at minimum in the one closed network.

4. Calculate total of friction loss at each closed network. ℎ𝑓 = 0 5. Calculate value 2𝑘𝑄 for each network

6. Calculate discharge correction, ∆𝑄 = 𝑘𝑄𝑜2

2𝑘𝑄𝑜

7. Corrected the discharge to balance energy loss in the network, 𝑄 = 𝑄0 + ∆𝑄

8. Repeat step 1 to 6 until ∆𝑄 ≈ 0

EXAMPLE

Closed networks

1st Iteration

1st closed network

2nd closed network

Discharge Correction

2nd Iterations

1st closed network

2nd closed network

3rd Iterations

1st closed network

2nd closed network

Result