Three Conduits Will Be Designed For Feed Joint C As Shown

Three Conduits Will Be Designed Both Feed Joint C As Shown In The Pi

Three conduits will be designed, both feed joint C (as shown in the picture). From containers A and B, water is led to point D. The length of the pipes and the height of each point are specified in the diagram. Point A must supply 20 liters per second, point B 10 liters per second. In point D, the piezometric head should not fall below 230 meters (20 meters above ground level). The pipe diameters to be determined are L1, L2, and L3, with four available commercial sizes: 76 mm, 102 mm, 155 mm, and 203 mm. The goal is to find the most cost-effective diameters, considering the material is cast iron, which can experience up to a 25% increase in rugosity over time.

Paper For Above instruction

Designing a water conveyance system from two sources to a common outlet involves several hydraulic considerations to ensure efficient operation, minimal cost, and compliance with head requirements. The problem detailed involves selecting pipe diameters that can deliver specified flow rates while maintaining the minimum head at point D, considering pipe roughness increase over time, and choosing the minimum-cost pipe sizes from a set of commercial options.

Introduction

Hydraulic pipeline design is a crucial aspect of civil and environmental engineering, especially in water distribution systems. It combines fluid mechanics principles with economic considerations to optimize the operation and longevity of pipelines. The problem at hand involves designing a dual-feed system with specific flow demands and head constraints, considering pipe material properties and future roughness increase. Proper design ensures that the flow meets demand without excessive head loss that could impact system performance and service quality.

Hydraulic Principles and Pipe Selection

Flow in pipelines is governed primarily by the Darcy-Weisbach equation, which relates head loss due to friction to pipe diameter, length, flow rate, and pipe roughness. The head loss (H_f) can be expressed as:

H_f = (4 f L V^2) / (2 g * D),

where f is the Darcy friction factor, L is pipe length, V is velocity, g is acceleration due to gravity, and D is pipe diameter.

Flow velocity is calculated from flow rate (Q) and pipe cross-sectional area (A): V = Q / A. Increasing pipe diameter reduces velocity and head loss, but larger diameters are more expensive; thus, selecting the smallest viable size is essential for cost efficiency.

Design Constraints and Calculations

Given the supply requirements, flow rates are Q_A = 20 lt/sec and Q_B = 10 lt/sec. The total flow from container A is 20 liters/sec, and from container B is 10 liters/sec, with pipe lengths and elevations given in the schematic. The system outlet at point D must maintain a minimum piezometric head of 230 meters.

Assuming steady, incompressible flow, the total flow rate (Q_total) at point D is 30 lt/sec. To avoid head drops below 230 m, the head loss through pipelines must be minimal or compensated by other pressure sources. The initial head at source points A and B must be above the sum of the head loss and the head required at point D.

The pipe roughness (absolute rugosity) is initially standard for cast iron but may increase by 25% over time, impacting the Darcy friction factor and subsequent head loss.

Methodology

1. Estimate the velocities for each pipe diameter to prevent excessive head loss, choosing the diameters from the commercial options provided.
2. Calculate the initial head loss for each pipe size using the Darcy-Weisbach equation, considering the initial roughness coefficient.
3. Adjust for long-term roughness increase by increasing the roughness height and recalculating the head loss to ensure head at point D remains above 230 m even after deterioration.
4. Determine the optimal diameters by balancing the cost (based on pipe size and material) and hydraulic performance, aiming for the least expensive combination satisfying all head and flow requirements.

Hydraulic Calculations and Pipe Sizing

The calculation process involves selecting pipe diameters and calculating velocities to limit head loss. For example, using the Darcy-Weisbach equation with initial roughness (e.g., ε = 0.26 mm for cast iron), the friction factor f is obtained via the Colebrook-White equation or approximate explicit formulas like Swamee-Jain.

If the flow is Q = 20 lt/sec (0.02 m³/sec), the velocity V in a pipe of diameter D (meters) is V = Q/ A = 4Q / (πD²). For instance, with D = 102 mm (0.102 m), V ≈ 0.0243 m/sec, which indicates low velocity and potential head loss.

Calculations should be repeated for each size, considering the increased roughness. For each pipeline, the head loss is computed and summed to ensure the total head remains above the threshold at point D after considering elevation differences and other losses.

Economic Considerations

The most cost-effective solution balances pipe material costs against the hydraulic performance. Larger diameters reduce head loss but are more costly upfront. The incremental increase in rugosity over time affects long-term costs, as higher roughness leads to increased maintenance and energy costs due to higher pumping requirements.

An initial economic analysis involves calculating the total cost of each pipe option over the system's lifespan, factoring in initial purchase, installation, and operational costs related to energy consumption due to head losses.

Conclusion

Designing the pipeline system requires a careful evaluation of pipe diameters, considering flow requirements, head constraints, material properties, and costs. By applying hydraulic principles, accounting for the increase in roughness over time, and optimizing for cost, an efficient and sustainable water conveyance system can be developed.

In practice, iterative calculations using hydraulic modeling tools or software would refine pipe size selections further, ensuring compliance with all specifications and achieving the lowest total cost of ownership over the system's lifespan.

References

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