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This document discusses phase diagrams and examples of using lever rule calculations to determine phase percentages and compositions. It provides an example phase diagram of the lead-tin system and asks questions about: 1) Solubility of tin in lead and lead in tin from the diagram 2) Using the Pb-10% Sn alloy and diagram to find phase percentages that form upon cooling 3) Masses of tin and lead in each phase for a Pb-10% Sn alloy cooled to 0°C
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The document describes a phase diagram for a lead-tin alloy and provides information to answer questions about the phase diagram:
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2. For a question on a 200 g lead
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This document discusses methods for estimating capital costs for chemical plants. Quick rough estimates are needed early in the design process to evaluate alternative designs. More accurate estimates require more design detail. Capital costs include fixed costs for equipment, construction, and facilities, as well as working capital for start-up. Historical cost data can be escalated using cost indices. The factorial method estimates capital cost as factors applied to the total equipment cost. Detailed factorial estimates consider individual cost factors rather than a single overall factor.
Section 9.pptx
The document discusses optimum design parameters and provides examples of determining optimum values that minimize costs. Question 1 finds the optimum insulation thickness. Question 2 determines optimum temperature and pressure values that minimize total cost. Question 3 calculates the daily profit at the production rate giving minimum cost per unit and maximum daily profit. Question 4 involves determining the batch cycle time that gives the minimum total annual cost of producing 1 million kg of chemical product.
Section 8.pptx
The document discusses several questions related to evaluating investment options for chemical plants based on their economics.
For the first question, four heat exchanger designs to recover lost heat from waste gases are evaluated based on their initial cost, operating costs, heat savings value, and annual savings. Design 4 is determined to have the highest return on incremental investment.
The second question evaluates two investment alternatives based on their rate of return, minimum payback period, and capitalized cost to determine which meets the company's investment criteria.
The third question analyzes two reactor options based on their initial cost, maintenance costs, salvage value, service time, yield, and profit to determine which meets the ROI condition and maximum 3 year pay
Section 2.pptx
1) The document discusses rules for calculating simple interest, compound interest, effective interest rates, and continuous compounding. It provides examples of calculating total amounts, interest rates, and present worth for various scenarios involving loans, bonds, and investments with different interest rates and time periods.
2) Questions are worked through calculating total amounts, interest rates, and present worth for investments with monthly, daily, semiannual compounding and continuous compounding over periods of 2, 4, 10, and 12 years.
3) Formulas used include simple interest, compound interest, effective interest rates, continuous compounding, and present worth. Results are calculated and explained for each question.
Section 1.pptx
This document discusses the importance of economics in chemical engineering and provides examples to illustrate key concepts. It notes that economics involves dealing with scarce resources efficiently to achieve optimal results at lowest cost. A case study compares the economics of an old versus new refrigerator design over time, factoring in capital costs, operating costs, and interest earnings. The document emphasizes choosing the optimum option by evaluating how variable factors like pipe diameter and insulation thickness impact both capital and operating costs. The overall goal is selecting designs that minimize total lifetime costs.
section 6 .pptx
The document discusses break even analysis for chemical plants. It provides examples of calculating the break even point in units and sales revenue for different unit retail prices and variable costs. It also contains examples of determining profit given production levels. Questions include calculating break even points, drawing break even charts, and determining if a plant is profitable based on supply and demand curves and fixed and variable costs.
section 1.pptx
The document discusses common mechanical operations involving particulate matter including calculating the shape factor of different particle shapes, performing a sieve analysis to determine properties like specific surface area and average particle diameter, and using a correlation equation between cumulative fraction and particle size to calculate constants and the average surface volume diameter. Sieve analysis data is provided for a problem involving calculating values like specific surface area, average particle diameter, median diameter, and average surface volume particle diameter.
section 4.pptx
This document discusses belt conveyor design and calculations. It provides guidelines for belt thickness and idler spacing based on material density being conveyed. It also outlines the equations needed to calculate the mass of the belt, idlers, and material per unit length, which are required for power calculations. These include factors like the number of idlers per side, mass of individual idlers, belt thickness and density, and flow rate and velocity of the material being conveyed. An example problem is provided to demonstrate how to apply these calculations.
section 2.pptx
The document provides information on calculating mass storage in stockpiles and storage facilities using bulk density, angle of repose, and dimensional measurements. It includes examples of:
1) Calculating the mass of gravel that can be stored in a 6x6m area using the given bulk density of 1700kg/m3 and angle of repose of 45°, finding the answer is 48 tons.
2) Finding the minimum dimension H of 8.5m for a storage compartment with a 5x5m base to store 360 tons of bauxite ore over 3 days at a furnace rate of 5 tons/hr, using the given bulk density of 2000kg/m3 and angle of repose of
section 5.pptx
This document provides rules and examples for calculating mechanical operations related to bulk solids storage and transport. It includes formulas for calculating volume and mass flow rate of cones, as well as vertical and lateral pressures at the bottom of a bin. An example calculates these pressures for a given bin geometry. It also discusses belt conveyor design, including belt and idler specifications and formulas for power calculations. The final example uses these formulas to calculate the motor power and storage bin dimensions needed for a given solid transportation rate and production period.
section7.pptx
1. The document discusses various rules and equations related to mechanical operations like crushing, grinding and milling including Rittinger's law, Kick's law, and equations for calculating ball mill dimensions, rotation speeds, and charge volumes.
2. It provides an example calculation for estimating the theoretical power required to grind a one ton batch in a roller mill over 30 minutes given the feed and product screen analyses.
3. Questions and examples are given for calculating reasonable ball mill speeds, ball charges, and rock feed charges given mill dimensions and properties of the balls and feed material.
section 9.pptx
This document discusses three questions related to mechanical operations and flow through porous media:
1. It calculates the pressure drop across a catalyst bed packed with cylindrical pellets for an air stream, and how this would change with larger pellet size.
2. It estimates the inlet pressure of a catalyst tower given the outlet pressure, dimensions, flow properties, and contact time.
3. It calculates the porosity of a bed packed with Raschig rings given the pressure drop and flow properties of an air stream.
section 8.pptx
This document provides information on mechanical operations like crushing and grinding. It includes:
- Rules for operations like Rittinger's law, Kick's law, and Bond work index.
- Parameters for equipment like ball mill rotation speed, ball size, and charge mass.
- Worked examples calculating time required to achieve a specific surface increase in crushing and grinding, based on parameters like feed size, product size, power, and work index.
- An example calculating the time required to grind one ton of material in a batch rod mill, given the motor power, grinding efficiency, feed and product sizes, and work index.
section 6.pptx
This document discusses common mechanical operations used to transport materials, including bucket elevators, screw conveyors, and pneumatic transportation. It provides examples of how to calculate the power required for a bucket elevator to lift crushed alumina, the design of a screw conveyor to transport fly ash horizontally, and the conveying capacity of a pneumatic transportation system moving ground rock vertically and horizontally through pipes and elbows. Key parameters discussed include bulk density, spacing, pitch, filling ratio, pressure change, flow rate, and power.
material science 1 .pptx
This document provides notes on material science concepts. It discusses key points about assignments, quizzes, reports and presentations. It also covers classifications of materials, basic concepts like deformation, stress, strain and mechanical properties including elasticity, ductility, brittleness, hardness and toughness. Graphs of stress-strain curves are presented and terms like elastic limit, yield point and ultimate tensile strength are defined. Students are instructed to submit assignments on time and follow the instructor's directions.
material science 2 .pptx
This document discusses material science concepts including stress, strain, Young's modulus, shear modulus, and bulk modulus. It provides definitions and formulas for these terms and includes examples of calculating stress, strain, elongation, shear stress, and changes in volume using given material properties and applied forces. Several practice problems are worked through applying these concepts to situations like stretching a cylinder, cutting a sheet, and determining changes to a bowling ball underwater.
Material 5.pptx
This document discusses phase diagrams for binary systems with different types of solubility between liquid and solid phases. It provides examples of phase diagrams for systems with: (1) complete liquid and solid solubility, (2) complete liquid but zero solid solubility, and (3) complete liquid and limited solid solubility. It also works through examples of determining phase compositions and amounts for steel alloys based on their placement on an iron-carbon phase diagram.
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material 4.pptx
- 1. MATERIAL SCIENCE-4 PHASE DIAGRAMS (1) ENG. KAREEM. H. MOKHTAR
- 2. AMOUNT OF EACH PHASE
- 3. LEVER ARM RULE • The lever rule in general can be written as • Phase percent = 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑎𝑟𝑚 𝑜𝑓𝑙𝑒𝑣𝑒𝑟 total length of tie line x 100
- 4. PHASE PERCENT AT 1250 (OC) • Phase percent = 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑎𝑟𝑚 𝑜𝑓𝑙𝑒𝑣𝑒𝑟 total length of tie line x 100 • Ni in alpha= 45% • Ni in Liquid= 32% • Ni in alloy= 40% • Alpha phase percent= 40−32 45 − 32 x 100 = 62%
- 5. EXAMPLE 3 • Regarding the cupper nickel phase diagram • Find the following for 60%Cu-Ni alloy at 1250 a) while freezing, The first temperature at which the first solid particle form? b) while freezing, The first temperature at which the alloy become totally solid?
- 6. EXAMPLE 2 • Regarding the cupper nickel phase diagram • Find the following for Cu-50% Ni alloy at 1280oC a) The phases present b) The composition of each phase c) the amount of each phase.
- 7. EXAMPLE 2 • A) Solid and liquid • B) Liquid 40% Ni and 60% Cu Solid 55% Ni and 45% Cu • C) Liquid phase = (55-50)/(55-40)= 33.33% and the rest is solid
- 8. • If we have Cu-20% Ni, and Ni and we want to produce 100Kg of alloy that has 40% Cu, find the amounts needed. • Solution • Total amount of Ni = amount of Ni in (Cu-20%Ni) + amount of Ni • 60 = 0.2 x + (100-x) • X = 50KG • So we need 50Kg of alloy Cu-20% Ni and 50 kg of pure Ni
- 10. FROM 0 % TO 2% SN
- 11. AT 15% SN
- 12. THREE PHASE REACTIONS IN BINARY PHASE DIAGRAM
- 13. QUESTION 1 • Using the following diagram determine • (a) the solubility of tin in solid lead at 100°C • (b) the maximum solubility of lead in solid tin • (c) the amount of B that forms if a Pb-10% Sn alloy is cooled to 0°C • (d) the masses of tin contained in the ⍺ and B phases • (e) the mass of lead contained in the and phases. Assume that the total mass of the Pb-10% Sn alloy is 100 grams.
- 14. A) THE SOLUBILITY OF TIN IN SOLID LEAD AT 100°C Answer 6%
- 15. B) THE MAXIMUM SOLUBILITY OF LEAD IN SOLID TIN • Answer 97.5% Sn or 2.5% Pb
- 16. C) THE AMOUNT OF B THAT FORMS IF A PB-10% SN ALLOY IS COOLED TO 0°C • B = 10−2 100−2 = 8.2 %
- 17. D) THE MASSES OF TIN CONTAINED IN THE ⍺ AND B PHASES AT 0°C(ALLOY MASS=100GRAMS) Mass of tin in ⍺ phase = percent of Sn x mass (⍺) Mass of tin in B phase = percent of Sn x mass (B) Percent of Sn at ⍺ = 2% Percent of Sn at B = 100% From (C) we found that B= 8.2% and ⍺ = 91.8% As the total alloy mass is 100g B= 8.2 g and ⍺ = 91.8 g Mass of tin in ⍺ = 1.836 g Mass of tin in B = 8.2 g
- 18. E) THE MASS OF LEAD CONTAINED IN THE ⍺ AND B PHASES. ASSUME THAT THE TOTAL MASS OF THE PB-10% SN ALLOY IS 100 GRAMS. • Mass of Pb in ⍺ phase = percent of Pb x mass (⍺) • = 0.98 x 91.8= 89.964 g • Mass of Pb in B phase = • Total mass of pb – mass of Pb in ⍺ phase • 90 - 89.964 = 0.036 g
- 19. QUESTION 2 • Determine the amount and composition of each phase in 200 g of a lead-tin alloy of eutectic composition immediately after the eutectic reaction has been completed. (b) Calculate the mass of phases present. (c) Calculate the masses of lead and tin in each phase.
- 20. DETERMINE THE AMOUNT AND COMPOSITION OF EACH PHASE • Composition • ⍺ = 19% Sn • B = 97% Sn • Amount • ⍺ = 97−62 97−19 = 45 % • B = 62−19 97−19 = 55%
- 21. B) CALCULATE THE MASS OF PHASES PRESENT • Mass of ⍺ = total mass x percent of ⍺ =200 x 0.45= 90 g • Mass of B = total mass x percent of B =200 x 0.55= 110 g
- 22. CALCULATE THE MASSES OF LEAD AND TIN IN EACH PHASE. • Mass of Sn in ⍺ = 0.19 x 90 = 17.1 g • Mass of Sn in B = 0.97 x 110 = 106.7 g • Mass of Pb in ⍺ = 90 - 17.1 = 72.9 g • Mass of Pb in B = 110 – 106.7 =3.3 g What we have calculated in (a) Composition ⍺ = 19% Sn B = 97% Sn Amount ⍺ = 97−62 97−19 = 45 % B = 62−19 97−19 = 55% What we have calculated in (B) Mass of ⍺ = total mass x percent of ⍺ =200 x 0.45= 90 g Mass of B = total mass x percent of B =200 x 0.55= 110
Editor's Notes
- A)1350 B)1300