/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 63 Arsenic contamination of aquifer... [FREE SOLUTION] | 91影视

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Chapter 7: Problem 63

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?

Short Answer

Expert verified
Pump horsepower is dependent on fluid flow rate, height difference, and pump efficiency. We have found that even though the iron oxide binds 100% of the arsenic, other factors such as power supply, maintenance of the iron oxide, disposal of arsenic-laden iron oxide, potential recontamination during water return, and the scale of operation limit the effectiveness of arsenic removal operation.

Step by step solution

01

Calculation of the required pump energy

Let鈥檚 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/ft鲁 and the gravity \(g\) is approximately 32.2 ft/s虏, 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/ft鲁.
  • \(g\) is the gravitational acceleration, approximately 32.2 ft/s虏.
  • \(F_{frictionloss}\) 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.

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Most popular questions from this chapter

A piston-fitted cylinder with a 6 -cm inner diameter contains \(1.40 \mathrm{g}\) of nitrogen. The mass of the piston is 4.50 kg, and a 25.00-kg weight rests on the piston. The gas temperature is 30^ C, and the pressure outside the cylinder is 2.50 atm. (a) Prove that the absolute pressure of the gas in the cylinder is \(3.55 \times 10^{5} \mathrm{Pa}\). Then calculate the volume occupied by the gas, assuming ideal- gas behavior. (b) Suppose the weight is abruptly lifted and the piston rises to a new equilibrium position. Further suppose that the process takes place in two steps: a rapid step in which a negligible amount of heat is exchanged with the surroundings, followed by a slow step in which the gas returns to \(30^{\circ} \mathrm{C}\). Considering the gas as the system, write the energy balances for step \(1,\) step \(2,\) and the overall process. In all cases, neglect \(\Delta E_{\mathrm{k}}\) and \(\Delta E_{\mathrm{p}} .\) If \(\tilde{U}\) varies proportionally with \(T\), does the gas temperature increase or decrease in step 1? Briefly explain your answer. (c) The work done by the gas equals the restraining force (the weight of the piston plus the force due to atmospheric pressure) times the distance traveled by the piston. Calculate this quantity and use it to determine the heat transferred to or from (state which) the surroundings during the process.

The specific enthalpy of liquid \(n\) -hexane at 1 atm varies linearly with temperature and equals \(25.8 \mathrm{kJ} / \mathrm{kg}\) at \(30^{\circ} \mathrm{C}\) and \(129.8 \mathrm{kJ} / \mathrm{kg}\) at \(50^{\circ} \mathrm{C}\) (a) Determine the equation that relates \(\hat{H}(\mathrm{kJ} / \mathrm{kg})\) to \(T\left(^{\circ} \mathrm{C}\right)\) and calculate the reference temperature on which the given enthalpies are based. Then derive an equation for \(\hat{U}(T)(\mathrm{kJ} / \mathrm{kg})\) at 1 atm. (b) Calculate the heat transfer rate required to cool liquid \(n\) -hexane flowing at a rate of \(20 \mathrm{kg} / \mathrm{min}\) from \(60^{\circ} \mathrm{C}\) to \(25^{\circ} \mathrm{C}\) at a constant pressure of 1 atm. Estimate the change in specific internal energy \((\mathrm{kJ} / \mathrm{kg})\) as the n-hexane is cooled at the given conditions.

A rigid 6.00-liter vessel contains 4.00 L of liquid water in equilibrium with 2.00 L of water vapor at \(25^{\circ} \mathrm{C} .\) Heat is transferred to the water by means of an immersed electrical coil. The volume of the coil is negligible. Use the steam tables to calculate the final temperature and pressure (bar) of the system and the mass of water vaporized (g) if 3915 kJ is added to the water and no heat is transferred from the water to its surroundings. (Note: A trial-and-error calculation is required.)

Horatio Meshuggeneh has his own ideas of how to do things. For instance, when given the task of determining an oven temperature, most people would use a thermometer. Being allergic to doing anything most people would do, however, Meshuggeneh instead performs the following experiment. He puts acopper bar with a mass of 5.0 kg in the oven and puts an identical bar in a well- insulated 20.0-liter vessel containing 5.00L of liquid water and the remainder saturated steam at \(760 \mathrm{mm}\) Hg absolute. He waits long enough for both bars to reachthermal equilibrium with their surroundings, then quickly takes the first bar out of the oven, removes the second bar from the vessel, drops the first bar in its place, covers the vessel tightly, waits for the contents to come to equilibrium, and notes the reading on a pressure gauge built into the vessel. The value he reads is 50.1 mm Hg. He then uses the facts that copper has a specific gravity of 8.92 and a specific internal energy given by the expression \(\hat{U}(\mathrm{kJ} / \mathrm{kg})=0.36 T\left(^{\circ} \mathrm{C}\right)\) to calculate the oven temperature. (a) The Meshuggeneh assumption is that the bar can be transferred from the oven to the vessel without any heat being lost. If he makes this assumption, what oven temperature does Meshuggeneh calculate? How many grams of water evaporate in the process? (Neglect the heat transferred to the vessel wall- -i.e., assume that the heat lost by the bar is transferred entirely to the water in the vessel. Also, remember that you are dealing with a closed system once the hot bar goes into the vessel.) (b) In fact, the bar lost 8.3 kJ of heat between the oven and the vessel. What is the true oven temperature? (c) The experiment just described was actually Meshuggeneh's second attempt. The first time he tried it, the final gauge pressure in the vessel was negative. What had he forgotten to do?

A liquid mixture of benzene and toluene is to be separated in a continuous single-stage equilibrium flash tank. The pressure in the unit may be adjusted to any desired value, and the heat input may similarly be adjusted to vary the temperature at which the separation is conducted. The vapor and liquid product streams both emerge at the temperature \(T\left(^{\circ} \mathrm{C}\right)\) and pressure \(P(\mathrm{mm} \mathrm{Hg})\) maintained in the vessel. Assume that the vapor pressures of benzene and toluene are given by the Antoine equation, Table B.4 or APEx; that Raoult's law- -Equation 6.4-1 - applies; and that the enthalpies of benzene and toluene liquid and vapor are linear functions of temperature. Specific enthalpies at two temperagiven here for each substance in each phase. \(\mathrm{C}_{6} \mathrm{H}_{6}(\mathrm{l}) \quad\left(T=0^{\circ} \mathrm{C}, \quad \hat{H}=0 \mathrm{kJ} / \mathrm{mol}\right) \quad\left(T=80^{\circ} \mathrm{C}, \quad \hat{H}=10.85 \mathrm{kJ} / \mathrm{mol}\right)\) \(\mathrm{C}_{6} \mathrm{H}_{6}(\mathrm{v}) \quad\left(T=80^{\circ} \mathrm{C}, \hat{H}=41.61 \mathrm{kJ} / \mathrm{mol}\right) \quad\left(T=120^{\circ} \mathrm{C}, \hat{H}=45.79 \mathrm{kJ} / \mathrm{mol}\right)\) \(\mathrm{C}_{7} \mathrm{H}_{8}(\mathrm{l}) \quad\left(T=0^{\circ} \mathrm{C}, \quad \hat{H}=0 \mathrm{kJ} / \mathrm{mol}\right) \quad\left(T=111^{\circ} \mathrm{C}, \hat{H}=18.58 \mathrm{kJ} / \mathrm{mol}\right)\) \(\mathrm{C}_{7} \mathrm{H}_{8}(\mathrm{v}) \quad\left(T=89^{\circ} \mathrm{C}, \hat{H}=49.18 \mathrm{kJ} / \mathrm{mol}\right) \quad\left(T=111^{\circ} \mathrm{C}, \hat{H}=52.05 \mathrm{kJ} / \mathrm{mol}\right)\) (a) Suppose the feed is equimolar in benzene and toluene \(\left(z_{\mathrm{B}}=0.500\right) .\) Take a basis of 1 mol of feed and do the degree-of-freedom analysis on the unit to show that if \(T\) and \(P\) are specified, you can calculate the molar compositions of each phase \(\left(x_{\mathrm{B}} \text { and } y_{\mathrm{B}}\right),\) the moles of the liquid and vapor products \(\left(n_{\mathrm{L}} \text { and } n_{\mathrm{V}}\right),\) and the required heat input \((Q) .\) Don't do any numerical calculations in this part. (b) Do the calculations of Part (a) for \(T=90^{\circ} \mathrm{C}\) and \(P=652 \mathrm{mm} \mathrm{Hg}\). (c) For \(z_{B}=0.5\) and \(T=90^{\circ} \mathrm{C},\) there is a range of feasible operating pressures for the evaporator, \(P_{\min }P_{\max } ?[\) Hint: Look at your solution to Part (b) and think about how it would change if you lowered \(P .]\) (d) Set up a spreadsheet to perform the calculation of Part (b) and then use it to determine \(P_{\max }\) and \(P_{\text {min. }}\) The spreadsheet should appear as follows (some solutions are shown): Additional columns may be used to store other calculated variables (e.g., specific enthalpies). Briefly explain why \(Q\) is positive when \(P=652 \mathrm{mm}\) Hg and negative when \(P=714 \mathrm{mm} \mathrm{Hg}\). (e) In successive rows, repeat the calculation for the same \(z_{\mathrm{B}}\) and \(T\) at several pressures between \(P_{\min }\) and \(P_{\text {max. Generate a plot }}\) (using the spreadsheet program itself, if possible) of \(n_{\mathrm{V}}\) versus \(P . \mathrm{At}\) approximately what pressure is half of the feed stream vaporized?

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