Dimensional Analysis in Architecture EPS

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Questions and Answers

Match the following physical quantities with their corresponding dimensions:

Linear density (λ) = ML−1 Area density (σ) = ML−2 Volumetric density (ρ) = ML−3 Specific weight (γ) = ML−2 T−2

Match the following physical quantities with their corresponding SI Units:

Linear density (λ) = kg/m Area density (σ) = kg/m2 Volumetric density (ρ) = kg/m3 Specific weight (γ) = N/m3

Match the following terms from Buckingham's Pi Theorem with their corresponding descriptions based on the provided text:

n = The total number of variables in the problem k = The number of fundamental physical dimensions involved p = The number of dimensionless groups derived using Buckingham's Pi Theorem π groups = Dimensionless combinations of the original variables

Match the following physical quantities with their corresponding descriptions:

Latent heat (λ) = The amount of heat required to change the phase of a substance Thermal gradient (dT/dr) = The rate of change of temperature with respect to distance Hydraulic head (h) = The total energy head of a fluid at a given point Film coefficient (h) = A measure of the heat transfer rate per unit area per unit temperature difference Signup and view all the answers

Match the following physical quantities with their corresponding symbols:

Volumetric flow rate = Q Thermal resistance = R Heat flux = q/A Emissivity = ϵ Signup and view all the answers

Match the following physical quantities with their corresponding applications:

Specific heat (Cp) = Calculating the amount of heat required to raise the temperature of a substance Thermal conductivity (k) = Determining the rate of heat transfer through a material Volumetric flow rate (Q) = Measuring the rate of fluid flow through a pipe Thermal resistance (R) = Analyzing the heat transfer through a composite wall Signup and view all the answers

Match the following derived physical quantities with their corresponding dimensions, based on the provided information about the physical fundamentals in building systems.

Area (A) = L² Volume (V) = L³ Force (F) = MLT⁻² Weight (W) = MLT⁻² Energy (E) = ML²T⁻² Work (w) = ML²T⁻² Heat (Q) = ML²T⁻² Power (P) = ML²T⁻³ Efficiency (η) = 1 Signup and view all the answers

Match the following derived physical quantities with their corresponding SI Units, based on the provided information about the physical fundamentals in building systems.

Area (A) = m² Volume (V) = m³ Force (F) = N Weight (W) = N Energy (E) = J Work (w) = J Heat (Q) = J Power (P) = W Efficiency (η) = 1 Signup and view all the answers

Match the following derived physical quantities with their corresponding descriptions, based on the provided information about the physical fundamentals in building systems.

Area (A) = The amount of two-dimensional space enclosed by a closed boundary. Volume (V) = The amount of three-dimensional space enclosed by a closed surface. Force (F) = A push or pull that can cause a change in motion. Weight (W) = The force exerted on an object by gravity. Energy (E) = The capacity to do work. Work (w) = The energy transferred to an object by a force when it moves through a distance. Heat (Q) = The transfer of thermal energy between objects at different temperatures. Power (P) = The rate at which work is done or energy is transferred. Efficiency (η) = The ratio of useful output energy to total input energy. Signup and view all the answers

Match the following derived physical quantities with their corresponding mathematical relationships, based on the provided information about the physical fundamentals in building systems.

Area (A) = A = l × w Volume (V) = V = l × w × h Force (F) = F = m × a Weight (W) = W = m × g Energy (E) = E = 1/2 × m × v² Work (w) = w = F × d Heat (Q) = Q = m × c × ΔT Power (P) = P = w/t Efficiency (η) = η = (useful output energy) / (total input energy) Signup and view all the answers

Match the following derived physical quantities with their corresponding application examples in building systems, based on the provided information about the physical fundamentals in building systems.

Area (A) = Calculating the floor area of a building Volume (V) = Determining the cubic volume of a room Force (F) = Analyzing the forces acting on a structural beam Weight (W) = Evaluating the load capacity of a foundation Energy (E) = Analyzing the energy efficiency of a building Work (w) = Estimating the energy required to lift a load Heat (Q) = Designing a heating and ventilation system Power (P) = Assessing the power consumption of a building Efficiency (η) = Evaluating the performance of a solar panel system Signup and view all the answers

Match the following derived physical quantities with their corresponding units of measurement, based on the provided information about the physical fundamentals in building systems.

Area (A) = Square meters (m²) Volume (V) = Cubic meters (m³) Force (F) = Newtons (N) Weight (W) = Newtons (N) Energy (E) = Joules (J) Work (w) = Joules (J) Heat (Q) = Joules (J) Power (P) = Watts (W) Efficiency (η) = 1 (dimensionless) Signup and view all the answers

Match the following derived physical quantities with their corresponding definitions, based on the provided information about the physical fundamentals in building systems. Be careful in choosing the most accurate definition.

Area (A) = The measure of the extent of a two-dimensional surface. Volume (V) = The measure of the amount of space occupied by a three-dimensional object. Force (F) = An interaction that can cause a change in motion of an object. Weight (W) = The force exerted on an object due to gravity. Energy (E) = The ability to do work or produce heat. Work (w) = The amount of energy transferred when a force moves an object over a distance. Heat (Q) = The transfer of thermal energy between objects at different temperatures. Power (P) = The rate at which energy is transferred or work is done. Efficiency (η) = The ratio of the useful energy output to the total energy input of a system. Signup and view all the answers

Match the following terms related to Rayleigh's method with their corresponding explanations:

Rayleigh’s method = A method for determining the number of dimensionless groups in a physical problem Exponents = Powers to which variables are raised in a dimensional analysis equation Equations = Mathematical statements that express relationships between variables Unknowns = Variables whose values are not yet determined Signup and view all the answers

Match the following conditions with their implications in Rayleigh’s method:

Number of equations equals the number of unknowns = The problem can be solved directly Fewer equations than unknowns = Some exponents must be expressed as functions of others More equations than unknowns = The system of equations is overdetermined and may have no solution Signup and view all the answers

Match the following steps in Rayleigh's method with their respective descriptions:

Gather all variables involved = Identify all quantities that influence the phenomenon under study Relate the dependent variable to others = Express the dependent variable as a function of the remaining variables Write the function in a specific form = Represent the relationship using a product of variables raised to exponents Express dimensions in terms of base quantities = Represent the dimensions of each variable using fundamental units Substitute dimensions into the equation = Replace the variables with their corresponding dimensions in the function Obtain equations relating exponents = Generate equations by equating the exponents of each base quantity on both sides of the equation Substitute exponent values and group variables = Replace the determined exponents into the main equation and group terms with the same exponent Signup and view all the answers

Match the following terms related to Buckingham's π theorem with their corresponding explanations:

Dimensionless groups = Combinations of variables that have no units Base quantities = Fundamental units like length, mass, and time Dependent variable = The quantity that is being studied π1, π2, π3… = Labels used to denote the different dimensionless groups Signup and view all the answers

Match the following statements with their implications for applying Buckingham's π theorem:

Number of dimensionless groups equals the number of variables minus the base quantities = The result determines the number of independent dimensionless groups needed to express the relationship Dimensionless groups can be called π1, π2, π3… = These labels are used for convenience and organization The dependent variable can be expressed as a function of dimensionless groups = This expression represents the relationship between the variables in a dimensionless form Signup and view all the answers

Based on the content provided, match the following features of the text with their corresponding values:

Total number of pages mentioned = Number of times the phrase "dimensional analysis" is used in the text = Number of variables involved in the example of centripetal force = Signup and view all the answers

Match the following concepts with their applications in the text:

Rayleigh's method = Deriving a relationship between variables by balancing dimensions Buckingham's π theorem = Determining the number of dimensionless groups for a given problem Centripetal force = An example of a physical phenomenon that can be analyzed dimensionally Signup and view all the answers

Match the following tools with their corresponding functionalities:

Rayleigh's method = Deriving dimensionless groups from a given set of variables Buckingham's π theorem = Determining the necessary number of independent dimensionless groups for a given problem Dimensional analysis = A general technique for analyzing the relationship between physical quantities Signup and view all the answers

Match the following terms with their definitions within the context of dimensional analysis:

Variable = A quantity that can change or take on different values Dimension = The fundamental property associated with a physical quantity Exponent = The power to which a variable is raised Equation = A mathematical statement expressing a relationship between variables Signup and view all the answers

Match the following scenarios with the appropriate application of dimensional analysis:

Designing a bridge = Determining the relationship between load, span, and material properties Calculating the speed of a falling object = Identifying the variables influencing the speed and their impact on the result Predicting the flow rate of a fluid through a pipe = Analyzing the relationship between pressure, viscosity, and pipe diameter Signup and view all the answers

Flashcards

Plane angle (θ)

A measure of rotation in a plane, measured in radians.

Solid angle (Ω)

A measure of three-dimensional angular extent, measured in steradians.