Water-Supply Network Balancing (Hardy-Cross)

Iteratively balance loop flows until the head-loss closure in every loop tends to zero.

Inputs

Manning roughness n

Max iterations

Convergence Δq (L/s)

Economical velocity (m/s)

Auto-size pipe diameters to economical velocity

Pipe segments (one row per pipe per loop)

Loop	Pipe	Dir	L (m)	D (mm)	Q0 (L/s)

Results

Pipe	L (m)	D (mm)	Q0 (L/s)	Q (L/s)	V (m/s)	h (m)	S

Loop closure

Loop	Pipes	Residual Δh (m)

S = 10.29·n²·L/D^5.333, h = S·(Q/1000)², Δq = −Σh/(2·ΣS·Q). Repeated until |Δq| < tolerance in every loop.