Dimensional Analysis in Architecture EPS

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

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

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

<p>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</p> Signup and view all the answers

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

<p>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</p> Signup and view all the answers

<p>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</p> Signup and view all the answers

<p>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</p> Signup and view all the answers

<p>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.</p> Signup and view all the answers

<p>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)</p> Signup and view all the answers

<p>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</p> Signup and view all the answers

<p>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)</p> Signup and view all the answers

<p>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.</p> Signup and view all the answers

<p>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</p> Signup and view all the answers

<p>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</p> Signup and view all the answers

<p>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</p> Signup and view all the answers

<p>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</p> Signup and view all the answers

<p>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</p> Signup and view all the answers

<p>Total number of pages mentioned = Number of times the phrase &quot;dimensional analysis&quot; is used in the text = Number of variables involved in the example of centripetal force =</p> Signup and view all the answers

<p>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</p> Signup and view all the answers

<p>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</p> Signup and view all the answers

<p>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</p> Signup and view all the answers

<p>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</p> Signup and view all the answers