The force, F, of the wind blowing against a building is given by F=CD ρV^2 A / 2, where V is the

The force, F, of the wind blowing against a building is...

Key Concepts

Drag Coefficient

The drag coefficient is a specific example of a dimensionless quantity used in fluid dynamics to quantify the drag or resistance of an object moving through a fluid. It encapsulates the object's shape and flow characteristics, allowing for a standardized comparison of drag effects regardless of the system's scale or the units used.

Dimensional Analysis

Dimensional analysis is the process of checking the consistency of units in equations and deriving relationships among physical quantities by comparing their dimensions. It ensures that both sides of an equation match in terms of fundamental quantities such as mass, length, and time, which is crucial for validating physical laws and calculations.

Dimensionless Quantity

A dimensionless quantity is a number without any physical units, meaning it does not change when the scale of measurement changes. Such quantities often appear as coefficients in physical formulas, indicating a pure ratio or proportionality between different effects, which makes them universal in character.

Transcript

00:01 So in this question, we are given the force f, right? now, this force f is basically, it's of the wind that is blowing against a building, right? and the expression of this force is c sub d times row times v square times a.

00:23 And this is divided by two.

00:26 Right.

00:26 Now over here this row, right, it is the density of air, right? this a, it's the cross -sectional area of the building, right? of the building and this c sub d is the constant termed the drive the drag coefficient right and this we it's the speed of the air right and what we are here is that we are required to determine the dimensions of drag coefficient right so the solution for this question it's very easy right so let's start with a solution now you should know this thing that when we need to find out the dimension dimensions of some constant involved, right? so some constant involved with some more composite expression, right? first of all, what we should do is that we should first elaborate the dimensions corresponding to corresponding to every other term right that is present in the expression right so the first thing that we need to do whenever we are required to find the dimensions of any constant right that constant which is involved with some more composite expression so the first thing that we need to do is to elaborate the dimensions corresponding to every other term that is present in the expression right and afterwards what we need to do is that we need to perform a set of dimensional a set of dimensional algebra algebra transformations to solve for other constants dimension, right? so it basically involves two major steps, right? and by doing those steps, we can easily find out the dimensions of the constant that is required in the question, right? now, in this case, as you can see, we have the drag force, right? we have drag force and this drag force is given by this expression that is f sub d equal to 1 divided by 2 into c sub d times v square times row time a right now what we are going to do is that we are going to express the dimensions corresponding to each term so first of all we'll start with row right that is the density so row is equal to m divided by l q and then we will express the dimension corresponding to the speed of the air right so that is v and v is equal to m divided by t right then um we will discuss the dimension for the drag force so that is f sub d and it is equal to m times l divided by t square right and the last that is led for us is the area and the dimensions of area is l square now what we are going to do is that we are going to substitute um the dimensions into the dark force expression right it means that um we are going to substitute all of these dimensions over here in this expression right so let's take a look at that how it uh will look like right so we have m times l times t raised a negative 2 that is equal to c times l times 1 .2, right? and we have t raised 1 negative 1 .2.

06:11 Then we have m, right? then again, l raised 2, and then we have l raised 2 bar...

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