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EXPRESSIONS
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Head loss, surge pressure

Friction losses

Volume inefficiency

Velocity jump shock

Nomogram Frequency vs. Pipe ID

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Allow for "overlap" of one displacement to the next. This is dependent on the volumetric efficiency, due to compressibility of your system liquid.
This may radically effect the level of flow fluctuation and pressure pulsation.

volumetric efficiency, due to compressibility

Inefficiency		 If in this example, the pump was a triplex then the flow would come to a complete halt between strokes. This is because a rotary driven reciprocating pump sucks & discharges for 180° of rotation and the next displacement begins after 120°. The overlap on triplex at 100% efficiency is therefore 60°. At 77.512% the calculation shows that the 60° has been lost, hence with no overlap the flow will come to a halt between displacements. It will be as "pulsatious" as a duplex.

By the same calculation as the example, if the efficiency was 85% then the lost angle would become 48°. With a "Quin" a new displacement should begin every 72 degrees (360/5), and as discussed above a triplex should displace every 120°. 120° minus 72°=48°. But at 85% efficiency, 48 has been lost, so a Quin can cause as much flow fluctuation as a perfect Triplex if the quin has low volumetric efficiency.

Therefore, A three headed diaphragm metering pump may produce flow fluctuations as bad as, or worse than, a duplex pump or double acting simplex pump. A quintuplex, or 5 plunger pump, may produce flow fluctuations as good as, or worse than, a good triplex pump, it all depends on volumetric efficiency. Consequently, where N2 is a divisor, you would have to treat a triplex N2 as 2x2=4, not 3x3=9.

 
1. Input Data VE – actual displacement divided by 100% volumetric displacement L – Connection rod length R – Crankshaft radius 2. Calculations VI – Volumetric inefficiency X – stroke before valve opening Parameter for calculation purposes Root
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Liquid Dynamics International provides pipeline and pump user problem analysis, diagnostics, prediction by software, pulsation analysis, piping system analysis, and piping system simulation. For water hammer and shock solutions pulsation dampening and shock alleviating devices can be obtained from our associate websites.

PulseGuard Inc., and Ltd. for further information about pulsation dampeners / pulsation dampers.
PulseGuard. USA: Pulsation Dampeners | Pulsation-Dampeners.com: Pulsation Dampeners
PulseGuard Limited: Pulsation Dampers | PulseGuard für Deutschland: Pulsationsdämpfer

Large pressure vessels, jumbo bladders, float separator / big bellows type pipeline surge attenuators and
expansion / contraction volume compensators, surge alleviators, and shock alleviators.
Shock-Guard. USA: Surge Alleviators | Water-Hammer.com: Water Hammer
ShockGuard.co.uk: Shock Alleviators | Suction-Stabilizers: Suction Stabilizers

Information about energy saving in pumping systems, standby emergency power, safety shutdown systems,
hydraulic accumulators, and hydropneumatic accumulators.
Accumulators-Hyd: Hydraulic Accumulators
Accumulators.co.uk: Hydropneumatic Accumulators | HydroTrole: Hydraulic and Control Engineering

Protection against excess flow. Protect against toxic spills when pipes burst, guard against gushers and fluid
loss when hoses split. Flow-Guard against excess flow floods with flow fuses and breather bags.
FlowGuard: Flow-Guard - Flow Fuses and Breather Bags

Fluid Flow Control Fluid-Flow-Control.com The Fluid Flow Control Source Pumps Accumulators Filters Dampers Heat Exchangers Valves Mixers P.I. / Pressure Indicators Controls Meters Vessels
HEAD 1 HEAD 3 HEAD 2 HEAD 1 DAMPER CHARACTERISTICS CONTROL CHOICE FLOW VELOCITY AND PRESSURE GO TO ZERO BETWEEN EVERY STROKE DEGREES ROTATION PRESSURE HEAD 1 HEAD 2 HEAD 1 PRESSURE ACTIVITY OF A 97% EFFICIENT DUPLEX PUMP FLOW VELOCITY AND PRESSURE GO TO ZERO BETWEEN EVERY STROKE DEGREES ROTATION PRESSURE This is "velocity jump" shock Here is a 77% efficient triplex pump pumping compressible liquid This case needs a Quintuplex pump PULSATION ACTIVITY (DEPENDS ON VOLUMETRIC EFFICIENCY)