Homework Assignment 3 At Edmonston Pumping Plant

Home Work Assignment 3ad Edmonston Pumping Plantthe

The assignment involves calculating the maximum power demand in kilowatts (kW) of the Edmonston Pumping Plant when operating at full flow capacity, considering the efficiencies and energy losses in the system. The plant lifts water 2,000 feet using fourteen pumps, with a maximum flow rate of 10,000 acre-feet per day. The assessment incorporates fluid mechanics principles, including the energy equation, pump efficiencies, and friction losses in the piping system.

Paper For Above instruction

The Edmonston Pumping Plant is a critical infrastructure component in California's water distribution system, responsible for lifting vast quantities of water over significant elevation differences. A comprehensive understanding of the plant’s power requirements necessitates applying fluid mechanics principles, notably the Bernoulli energy equation, and accounting for energy losses due to system inefficiencies and friction.

To determine the maximum power demand at full capacity, we first convert all parameters into consistent units and analyze the system's energy dynamics. The energy equation provided guides this analysis, emphasizing the need to include all relevant energy terms, such as pressure, velocity, elevation head, pump head, and energy losses.

Parameters and Conversions

• Flow rate: 10,000 acre-feet/day
• Elevation head: 2000 feet
• Number of pumps: 14
• Efficiency of pump/motor: 65%
• Friction loss: 2% of the total energy
• Gravity: g = 32.2 ft/sec²

Converting flow rate to volumetric flow rate in consistent units:

1 acre-foot = 43,560 cubic feet. Therefore:

10,000 acre-feet/day = 10,000 × 43,560 ft³ / 86400 sec ≈ 5,048.33 ft³/sec

Step 1: Calculate the energy per unit weight (head) required to lift water

The head due to elevation is given as 2000 ft. Since the water is lifted to this height, the potential energy term per unit weight (h) is 2000 ft.

Step 2: Incorporate the energy losses due to friction:

Friction loss (h_L) = 2% of the total energy head = 0.02 × 2000 ft = 40 ft

Step 3: Determine the specific energy (head) needed for the pump:

Effective head (H_effective) = Head to lift + friction loss = 2000 ft + 40 ft = 2040 ft

Step 4: Calculate the total power required (hydraulic power) using the energy equation:

Hydraulic power (P_hydraulic) = (ρ × g × Q × H_effective) / 550 ft·lb/sec (conversion factor to horsepower)

Where:

- ρ (density of water) ≈ 62.4 lb/ft³

- g = 32.2 ft/sec²

- Q = volumetric flow rate in ft³/sec

- H_effective = head in feet

Substituting the known values:

P_hydraulic

= (62.4 lb/ft³ × 32.2 ft/sec² × 5,048.33 ft³/sec × 2040 ft) / 550

Calculating numerator:

62.4 × 32.2 ≈ 2009.28 lb·ft/sec² per ft³

2009.28 × 5,048.33 ≈ 10,155,795.9 lb·ft²/sec

10,155,795.9 × 2040 ft ≈ 20,740,058,036 lb·ft³/sec

Now, dividing by 550 ft·lb/sec to convert to horsepower:

P_hydraulic

= 20,740,058,036 / 550 ≈ 37,800,104.607 hp

Since power is typically expressed in kilowatts, convert horsepower to kilowatts:

Power (kW) = horsepower × 0.746

Power (kW) = 37,800,104.607 × 0.746 ≈ 28,232,493.32 kW

Step 5: Adjust for pump/motor efficiency

The total efficiency of the system (pump and motor combined) is 65%, or 0.65.

Therefore, the electrical power demand (P_electric) is:

P_electric

= P_hydraulic

/ 0.65 ≈ 28,232,493.32 / 0.65 ≈ 43,419,224.3 kW

Considering all pumps operate simultaneously, the maximum power demand for the entire plant is approximately 43,419,224 kW, or about 43.42 GW. This significant power requirement underscores the importance of efficient energy management and the reliance on substantial electrical infrastructure for such large-scale water lifting operations.

Conclusion

In conclusion, the maximum power demand of the Edmonston Pumping Plant, operating at full capacity with the given parameters, is approximately 43.42 gigawatts. This comprehensive calculation accounts for elevation lift, frictional energy losses, system efficiencies, and conversions necessary to quantify the electrical energy required for continuous operation. Such analyses are vital for infrastructure planning, energy resource allocation, and ensuring sustainable water supply systems in large-scale applications.

References

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