## Solution

1. Head versus flow curves A, B, and C of Figure 11 are added together in parallel, giving curve (A + B + C). Curves (A + B + C), D, and E are added together in series, resulting in curve (A + B + C) + E + E. This latter curve indicates that 450 ft (137 m) total pump head is required at 3600 gpm (817 m3/h), point X. Curve (A + B + C) crosses point Y at 3600 gpm (817 m3/h) flow through the branches, and this condition requires 310 ft (94.5 m) total head, which is the head across branch points 1 and 2. From each individual component curve, the flow through branches A, B, and C can be read as 1250, 900, and 1450 gpm (284, 204, and 329 m3/h), respectively.

2. Because the total flow through components A, B, and C need be only 2500 gpm (800 + 700 + 1000) [568 m3/h (182 + 159 + 227)], the bypass should be designed to pass 1100 gpm (249 m3/h). Component B requires the maximum head, 200 ft (61 m) differential (point b) across points 1 and 2. Throttling valves are needed in components A and C and bypass F to increase the head in each branch to 200 ft (61 m) at the required flows. Branch A (point a) requires only 140 ft (42.7 m) total head to pass 800 gpm (182 m3/h); therefore the throttling valve must be designed for a 60-ft (42.7-m) head loss. Branch C (point c) requires only 150 ft (45.7 m) total head to pass 1000 gpm (227 m3/h), requiring a throttling valve for a 50-ft (15.3-m) head loss. The bypass control valve and piping should be designed to produce a 200-ft (61-m) head drop at 1100 gpm (249 m3/h).

At 3600 gpm (817 m3/h), the pump is now required to overcome 200 ft (61 m) total head across points 1 and 2, 40 ft (12.2 m) total head through component D, and 100 ft (30.1 m) total head through the system pipe and fittings, component E, for a total of 340 ft (103.3 m). The reduction in pumping head from 450 to 340 ft (137.1 to 103.6 m), a saving of 110 ft (33.5 m), or 24.4% water power, is the result of decreasing the branch head from 310 to 200 ft (94.5 to 61 m) by bypassing the excess flow.

## Renewable Energy Eco Friendly

Renewable energy is energy that is generated from sunlight, rain, tides, geothermal heat and wind. These sources are naturally and constantly replenished, which is why they are deemed as renewable.

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