Pump Discharge Pressure for Two Lines
A pump operator is supplying two 38 mm hose lines from a hydrant through the appliance pump. Line 1 is 90 m long and ends at a nozzle 5 m above the pump. The friction-loss table gives 30 kPa per 30 m of 38 mm line at the required flow, and the nozzle pressure must be 700 kPa. Line 2 is 60 m long and ends at a nozzle 10 m below the pump; its nozzle pressure must be 400 kPa. Elevation pressure is 10 kPa per metre of height. The pump has a rated discharge pressure of 1,000 kPa and a relief valve set at 900 kPa. The two lines leave separate discharge outlets. The operator intends to set one pump pressure for both lines and use the line 2 outlet valve to adjust if needed.
1. Calculate the pump discharge pressure required at each discharge outlet. Show the friction, elevation, and nozzle components.
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For line 1, friction loss is 30 kPa for each 30 m. The line is 90 m, so there are 90/30 = 3 sections: 3 × 30 = 90 kPa. The nozzle is 5 m above the pump, so elevation pressure is 5 × 10 = 50 kPa. Required outlet pressure = nozzle pressure + friction loss + elevation = 700 + 90 + 50 = 840 kPa. For line 2, the line is 60 m, so 60/30 = 2 sections: 2 × 30 = 60 kPa friction. The nozzle is 10 m below the pump, so elevation is -10 × 10 = -100 kPa, which assists the flow. Required outlet pressure = 400 + 60 - 100 = 360 kPa. The two outlets need different pressures: 840 kPa for line 1 and 360 kPa for line 2.
2. What single pump pressure should the operator set, and how should line 2 be managed? Explain why setting the pump to 360 kPa would be ineffective.
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The pump must be set to at least 840 kPa to satisfy line 1. Line 2 cannot simply be left on the same pressure: at 840 kPa its nozzle would receive far more than the required 360 kPa, creating excessive nozzle reaction, possible hose damage, and poor control. The line 2 outlet valve should be throttled to reduce the pressure to 360 kPa, or a pressure-reducing valve or separate discharge control should be used. Setting the pump to 360 kPa would be ineffective because line 1 would be underpressured by 840 - 360 = 480 kPa. The nozzle crew on line 1 would not receive the required 700 kPa at the nozzle, reducing reach and flow. The correct approach is to set the pump for the highest demand and control the lower-pressure line at its outlet.
3. Line 1 is extended by one 30 m length. Recalculate the required outlet pressure and assess it against the 900 kPa relief valve setting.
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With an extra 30 m, line 1 becomes 120 m, or 120/30 = 4 sections. Friction loss becomes 4 × 30 = 120 kPa. Elevation remains 5 × 10 = 50 kPa, and nozzle pressure remains 700 kPa. Required outlet pressure = 700 + 120 + 50 = 870 kPa. This is below the 900 kPa relief valve setting by 30 kPa, so the line can be supplied without the relief valve lifting under the stated conditions. However, the margin is small. If the nozzle is changed, the flow is increased, the elevation rises, or the hose has additional couplings, the required pressure could exceed 900 kPa. The operator should monitor the relief valve and consider a larger hose, a relay, or a lower-friction layout rather than relying on the 30 kPa margin.