Deluge Manifold Hydraulics

What is modelled

A pump lifts water from a reservoir through a header to banks of identical open nozzles. The flow settles where the head the pump delivers equals the head the system demands: the lift to the nozzles, the pressure the nozzles need at that flow and the friction in the header.

Equations

• Nozzle flow q = K √p, so the total for n open nozzles is Q = n K √p and the nozzle head is hn = 10.197 p metres for p in bar.
• Pump curve H = H0 − k Q² + zsuction.
• Header friction (Darcy-Weisbach) hf = f (L / D) v² / 2g, with f from the Colebrook-White equation.
• Operating point H(Q) = z + hn + hf, power P = ρ g Q H / η, drain time t = V / Q, integrated with RK4 as the level falls.

Checks run in the page

• The pump and demand heads cross at the operating flow.
• Colebrook-White against the Swamee-Jain approximation.
• Reservoir mass balance with RK4 against a finer Euler integration.
• The pump affinity law with no static lift.

Honest simplifications

Every open nozzle sees the same pressure, so header pressure drop along the bank, the transient fill of the pipes, water hammer, valve opening time and pump start-up are ignored. Values are illustrative for a generic water deluge for noise and heat control and are not design data for any real installation.

• Close banks one at a time and see the operating flow fall while the nozzle pressure rises.
• Choose Undersized header: the friction head grows and the flow drops.
• Choose Weak pump: the curves cross earlier and the reservoir lasts longer.