Nocti Formula

Formulas for Engineering Study Guide

Geometry Formulas

  1. Area of a Circle

    • Formula: Area=πr2\text{Area} = \pi r^2Area=πr2

    • Description: The area of a circle, where rrr is the radius.

  2. Circumference of a Circle

    • Formula: Circumference=2πr\text{Circumference} = 2 \pi rCircumference=2πr

    • Description: The perimeter of a circle, where rrr is the radius.

  3. Area of a Triangle

    • Formula: Area=12×Base×Height\text{Area} = \frac{1}{2} \times \text{Base} \times \text{Height}Area=21​×Base×Height

    • Description: The area of a triangle, where Base is the length of the base and Height is the perpendicular height.

  4. Volume of a Prism

    • Formula: Volume=Base Area×Height\text{Volume} = \text{Base Area} \times \text{Height}Volume=Base Area×Height

    • Description: The volume of a prism, where Base Area is the area of the base and Height is the distance between the two bases.

Physics & Engineering Formulas

  1. Ohm’s Law

    • Formula: V=IRV = I RV=IR

    • Description: Relates voltage (VVV), current (III), and resistance (RRR).

  2. Torque

    • Formula: τ=F×r\tau = F \times rτ=F×r

    • Description: Torque (τ\tauτ), where FFF is force and rrr is the distance from the pivot.

  3. Average Speed

    • Formula: Average Speed=2×(Speed1×Speed2)Speed1+Speed2\text{Average Speed} = \frac{2 \times (\text{Speed1} \times \text{Speed2})}{\text{Speed1} + \text{Speed2}}Average Speed=Speed1+Speed22×(Speed1×Speed2)​

    • Description: Average speed for two different speeds, such as in the case of driving to and from a location with different speeds.

Excel Formulas

  1. Sum Formula

    • Formula: =SUM(B3:B10)\text{=SUM(B3:B10)}=SUM(B3:B10)

    • Description: Adds all values in the range B3 to B10.

  2. Average Formula

    • Formula: =AVERAGE(B3:B10)\text{=AVERAGE(B3:B10)}=AVERAGE(B3:B10)

    • Description: Averages the values in the range B3 to B10.

  3. Median Formula

    • Formula: =MEDIAN(B3:B10)\text{=MEDIAN(B3:B10)}=MEDIAN(B3:B10)

    • Description: Finds the median of the values in the range B3 to B10.

  4. Min Formula

    • Formula: =MIN(B3:B10)\text{=MIN(B3:B10)}=MIN(B3:B10)

    • Description: Finds the minimum value in the range B3 to B10.

Engineering Formulas

  1. Surface Area of a Prism

    • Formula: Surface Area=2×Base Area+Perimeter of Base×Height\text{Surface Area} = 2 \times \text{Base Area} + \text{Perimeter of Base} \times \text{Height}Surface Area=2×Base Area+Perimeter of Base×Height

    • Description: Surface area of a prism, where Base Area is the area of the base, Perimeter of Base is the perimeter of the base, and Height is the distance between the two bases.

  2. Topic 1: Overview of Engineering, Social, Environmental, and Ethics

    1A. What do engineers do in different types of engineering fields?

    • Mechanical Engineer: Focus on designing, analyzing, and improving mechanical systems, including tools, engines, and machines.

    • Civil Engineer: Design, build, and maintain infrastructure like bridges, roads, and buildings.

    • Environmental Engineer: Develop solutions to environmental problems, such as pollution control and sustainable resource management.

    • Electrical Engineer: Design and develop electrical systems, including circuits, motors, and power systems.

    • Chemical Engineer: Focus on chemical processes, including creating new materials or manufacturing chemicals.

    • Manufacturing Engineer: Focus on optimizing manufacturing processes, from design to mass production.

    1B. Other Fields in Technology to Study

    • Computer Science: Programming, systems analysis, artificial intelligence, etc.

    • Information Technology (IT): Network administration, cybersecurity, and systems management.

    • Biotechnology: Use of biological processes for industrial purposes like pharmaceuticals, agriculture, and healthcare.

    • Robotics: Combining engineering with computer science to build robots and automated systems.

    1C. Social or Economic Impact of Inventions

    • Archimedes Screw: Used for lifting water for irrigation or drainage; invented by Archimedes.

    • Gutenberg Press: Invented in the 15th century, revolutionized printing and contributed to the spread of knowledge.

    • Moving Assembly Line: Invented by Henry Ford in the early 20th century, revolutionized manufacturing and made products like cars more affordable.

    1D. Match Invention to Social Impact

    • Moving Assembly Line: Second Industrial Revolution.

    • Transistor: Digital Revolution.

    • Gutenberg Press: Fueled the spread of the Renaissance.

    • Cloth Weaving Loom: First Industrial Revolution.

    • Computers: Digital Revolution.

    • Steam Engine: First Industrial Revolution.

    1E. Definition of Engineering

    • Engineering is the application of scientific and mathematical principles to solve problems, create new technologies, and improve systems and processes.

    1F. External Constraints in Engineering Design

    • Constraints: Limited resources, potential for future modifications, time, and cost.

    • Design Considerations: Impact on the environment, safety standards, and economic viability.

    1G. Impacts of Engineering Design

    • Economic Impact of Assembly Line: Increased productivity, reduced cost, and increased accessibility to goods.

    • Social Impact of Gutenberg Printing Press: Increased literacy and knowledge dissemination.

    • Environmental Impact of Steam Engine: Contributed to pollution and environmental degradation due to reliance on coal.

    Topic 2: Design Process/Problem Solving

    2A. Fundamental Principles of Design

    • Principles: Functionality, efficiency, aesthetics, sustainability, safety, and cost-effectiveness.

    2B. Decision Matrix in Engineering Design

    • Decision Matrix: Tool used to compare and evaluate multiple design options based on different criteria such as cost, performance, and feasibility.

    2C. Roles of Problem Identification, Search, Criteria, and Communication

    • Problem Identification: Defining the problem that needs a solution.

    • Search: Researching potential solutions and technologies.

    • Criteria: Setting benchmarks for the solution to meet.

    • Communication: Ensuring that ideas and solutions are shared effectively with the team.

    2D. Constraints Relevant to Design

    • Realistic Constraints: Physical limitations, regulatory standards, material availability, and cost.

    2E. Universal Systems Model

    • System Model:

      • Open Loop: Example: A fan running without feedback.

      • Closed Loop: Example: A thermostat-controlled heating system.

    2F. Role of Resources in Universal Systems Model

    • Time, People, Tools, Materials, Information: These are essential resources in any system, affecting production flow and efficiency.

    2G. Optimizing Design

    • Optimization: Adjusting design parameters to meet the desired criteria while minimizing costs and maximizing efficiency.

    2H. Predictive Analysis in Design

    • Predictive Analysis: The use of models and simulations to predict how a system will perform under different conditions.

    2I. Engineering Modeling Techniques

    • Modeling Techniques: Use of prototypes, simulations, and calculations to visualize and test design solutions.

    2J. Core Concepts of Technology

    • Core Concepts: The fundamental principles that govern the development and use of technology, such as systems thinking, process control, and human impact.

    Topic 3: Tools, Measures, and Materials

    3A. Saw Types and Tasks

    • Table Saw: Ideal for making straight cuts on large pieces of wood.

    • Mitre Saw: Ideal for cutting precise angles.

    • Scroll Saw: Ideal for intricate curved cuts.

    • Band Saw: Ideal for making continuous cuts through thick material.

    • Radial Arm Saw: Similar to a table saw but allows for more flexibility in cutting angles and depth.

    3B. Drills and Tasks

    • Drill Press: Ideal for drilling precise, vertical holes.

    • Impact Driver: Ideal for driving screws and bolts with high torque.

    • Hand Drill: Versatile tool for drilling small to medium holes.

    • Milling Machine: Ideal for shaping materials and drilling precise holes in a variety of materials.

    3C. Material Properties

    • Ductility: The ability of a material to deform under stress.

    • Corrosion Resistance: The ability of a material to resist rust and deterioration.

    • Conductivity: The ability of a material to conduct electricity.

    • Malleability: The ability to be shaped or bent.

    • Elasticity/Stiffness: The ability of a material to return to its original shape after deformation.

    • Fracture Toughness: The ability of a material to resist crack propagation.

    • Hardness: The ability to resist surface indentation.

    • Plasticity: The ability of a material to undergo permanent deformation without breaking.

    • Strength: The ability to withstand applied forces without failure.

    3D. Casting and Molding

    • Casting: The process of pouring molten material into a mold to create a desired shape.

    • Molding: Similar to casting but typically involves the use of a flexible mold to create detailed parts.

    3E. Lathe Use

    • Lathe: A machine used for shaping materials by rotating them against a cutting tool.

    3F. Concrete Types

    • Concrete: A mixture of cement, water, and aggregates.

    • Reinforced Concrete: Concrete that includes steel reinforcement to increase its tensile strength.

    • Prestressed Concrete: Concrete that is pre-tensioned or post-tensioned to improve its strength and durability.

    3G. Cold vs. Hot Rolled Steel

    • Cold Rolled Steel: Steel that is rolled at room temperature, resulting in a smoother finish and better dimensional accuracy.

    • Hot Rolled Steel: Steel that is rolled at high temperatures, making it easier to shape but with less precision.

    Topic 4: Engineering Graphics

    4A. Symbols in Engineering Drawings

    • Center Symbol: Indicates the center of a circle or arc.

    • Parallel Lines: Indicates that lines are parallel.

    • Concentric Circles: Circles that share the same center point.

    4B. Types of Views in Technical Drawings

    • Orthographic View: A 2D representation of an object showing different perspectives (top, front, side).

    • Isometric View: A 3D view showing all three dimensions at once.

    • Cavalier Oblique: A 3D view where depth is represented at full scale.

    • Cabinet Oblique: Similar to cavalier but with depth scaled to half.

    • One Point Perspective: A drawing method where lines converge to a single point on the horizon.

    • Two Point Perspective: A drawing with two vanishing points.

    • Three Point Perspective: A drawing with three vanishing points.

    • Multi-View Projection: A system of representing 3D objects in multiple 2D views.

    4C. Tolerances in Technical Drawings

    • Tolerances: The allowable variation in dimensions and geometry in technical drawings.

    Topic 5: Safety

    5A. Table Saw Safety

    • PPE Required: Safety glasses, hearing protection, dust mask, and proper clothing.

    • Safety Tips: Always use a fence, avoid standing directly behind the blade, and keep hands away from the cutting area.

    5B. Lathe Safety

    • PPE Required: Safety glasses, hearing protection, and protective gloves.

    • Safety Tips: Ensure all tools are securely mounted, and use the proper feed speeds.