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Arsenic contamination of aquifers is a major health problem in much of the world and is particularly severe in Bangladesh. One method of removing the arsenic is to pump water from an aquifer to the surface and through a bed packed with granular material containing iron oxide, which binds the arsenic. The purified water is then either used or allowed to seep back through the ground into the aquifer. In an installation of the type just described, a pump draws 69.1 gallons per minute of contaminated water from an aquifer through a 3 -inch ID pipe and then discharges the water through a 2-inch ID pipe to an open overhead tank filled with granular material. The water leaves the end of the discharge line 80 feet above the water in the aquifer. The friction losses in the piping system are \(10 \mathrm{ft} \cdot \mathrm{lb}_{\mathrm{f}} / \mathrm{lb}_{\mathrm{m}}\) (a) If the pump is \(70 \%\) efficient (i.e., \(30 \%\) of the electrical energy delivered to the pump is not used in pumping the water), what is the required pump horsepower? (b) Even if we assume that the iron oxide binds \(100 \%\) of the arsenic, what other factors limit the effectiveness of this operation?

Step by step solution

01

Calculation of the required pump energy

Let’s first focus on the energy calculation for the pump, based on the information given in the exercise. The total energy \(E_{total}\) required for the pump can be calculated as follows:\(E_{total} = \Delta P Q + \Delta h Q \rho g + F_{frictionloss} \)Here, - \(\Delta P\) is the difference in pressure between the aquifer and the open overhead tank, - \(Q\) is the volumetric flow rate of the water, - \(\Delta h\) is the height difference between the water in the aquifer and the end of the discharge line (80 feet),- \(\rho\) is the density of water, and - \(g\) is the gravitational acceleration. Since the overhead tank is open, the pressure difference \(\Delta P\) is zero. Given that the density \(\rho\) of water is approximately 62.4 lb/ft³ and the gravity \(g\) is approximately 32.2 ft/s², We can then calculate the pump power given the pump efficiency and the total energy required:Power = total energy / pump efficiency. Because the efficiency is given as 70%, we will divide the total energy calculated by 0.7 to get the power in ft.lb_f/s or horsepower, noting that 1 horsepower = 550 ft.lb_f/s

02

Identifying other factors affecting the operation's effectiveness

Given that the iron oxide is 100% effective in binding the arsenic, several factors can still limit the operation's effectiveness: 1. The continuous power supply required to pump the water to the surface;2. The maintenance of the granulated iron-oxide bed, which may need replacement or replenishment;3. The disposal of arsenic-laden iron oxide;4. The return of purified water to the aquifer, which could be affected by contaminants in the ground.5. The scale of the operation, i.e., it might not be feasible to clean an entire aquifer using this method if the contamination is widespread.

03

Summary

Given the pump's efficiency, water contamination rate, and the system's physical parameters, we've calculated the pump's required energy and identified other factors that impact arsenic removal effectiveness. A thorough understanding of fluid mechanics and system efficiency is critical to find practical solutions to environmental problems.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Pump Efficiency

Pump efficiency is a measure of how well a pump converts energy into useful power for moving fluids, like contaminated water in an aquifer remediation setup. When we consider pump efficiency, we essentially want to know how much of the electrical energy provided actually goes into pumping water, versus how much is lost to other factors such as friction and heat. In the provided exercise, the pump's efficiency is 70%. This means 30% of the input energy is lost and only 70% is used for actual water movement.
To find out the required pump power, we must calculate the total energy needed using the formula: \(E_{total} = \Delta P Q + \Delta h Q \rho g + F_{frictionloss}\). Here,

• \(\Delta P\) is the pressure difference.
• \(Q\) is the flow rate of 69.1 gallons per minute.
• \(\Delta h\) is 80 feet, corresponding to the height the water is lifted.
• \(\rho\) is the density of water, around 62.4 lb/ft³.
• \(g\) is the gravitational acceleration, approximately 32.2 ft/s².
• \(F_{frictionloss}\) accounts for the energy lost due to friction in the system.

With these values, once the total energy is calculated, converting it to horsepower involves adjusting for the pump's efficiency. A 70% efficient pump means you need to divide the required energy by 0.7 to find the necessary power input in horsepower.

Fluid Mechanics

Fluid mechanics is the field of science that studies the behavior of fluids (liquids and gases) and how they interact with forces. In the context of the exercise, fluid mechanics principles are applied to calculate how water flows through the pipes and the energy required to lift the water from the aquifer to an elevated tank.
This involves understanding concepts such as pressure, flow rate, and friction loss. For instance, the flow rate \(Q\) is essential to figuring out how much water can be moved through the system over a given time. Here, it is crucial to calculate energy losses due to friction as water moves through pipes. Friction causes energy loss, proportional to the distance and the complexity of the pipe work design, affecting the pump's total power requirement.
These fluid mechanics principles help engineers optimize environmental systems like arsenic removal plants, ensuring they operate efficiently and effectively.

Environmental Engineering

Environmental engineering is a discipline that applies scientific principles to improve the natural environment and solve environmental problems such as pollution. In the case of arsenic contamination in water, environmental engineers design and implement systems to remove arsenic safely and sustainably.
One critical challenge is generating energy-efficient solutions. This requires understanding both the technical aspects of design (like pump efficiency and system layout) and the bigger picture, including sustainability, long-term environmental impact, and public health. Engineers must also consider socio-economic factors like cost and community acceptance to ensure implemented measures are both effective and practical.
Effective environmental engineering helps balance today's needs by providing clean water without depleting natural resources for future generations.

Aquifer Remediation

Aquifer remediation is the process of cleaning contaminated groundwater sources to restore them to safe and usable conditions. The exercise provided discusses using a pump system that removes arsenic-laden water from an aquifer, treats it, and then returns it either to an aquifer or for usage.
This remediation method, using iron oxide beds, is efficient in arsenic binding but poses challenges such as the need for continuous power supply, maintenance of the treatment system, and handling of waste byproducts like arsenic-laden iron oxide. Another factor is ensuring the aquifer does not get re-contaminated during water reinfiltration.
Aquifer remediation is vital in areas like Bangladesh, where arsenic contamination is severe. It requires multi-disciplinary cooperation and innovation to develop sustainable techniques that ensure community health and access to clean water.