Dimensional analysis Definition and 254 Threads

Our professor introduced us to dimensional analysis and told us that we can use it to predict how some variables are proportional to others, for example: I have a ball at a certain height and i want to know the time it requires to touch the grond, i can make a guess that it will depend on the...

This is the problem I'm currently working on: The pi groups I identified were h1, h2, d, D, g, t, and velocity, but when I looked at the solution, it selected Δh, D, t, ρ, d, ϒ, h1, with no explanation why those variables are needed. If I was solving with the Bernoulli equation, I wouldn't...

I am stuck on the questions, 5.3.10 and 5.3.11 which are part of a chapter on dimensional analysis in fluid mechanics by Streeter. Question 5.3.10 (see also the attachment): It asks me for the given fluid dynamic problems, where is the inertial force not important. It lists several fluid...

This is more of a concept question; if I choose different repeating parameters to someone else, say my lecturer, and got different pi groups to him/her, however my groups are still dimensionless (i.e. the units for each pi group cancel to 1), is my answer still correct?

Homework Statement There is a paper in 1973: T. Kushida, "Energy Transfer and Cooperative Optical Transitions in Rare-Earth Doped Inorganic Materials I. Transition Probability Calculation", J. Phys. Soc. Jpn. 1973, 34, 1318-1326. DOI: http://dx.doi.org/10.1143/JPSJ.34.1318 that explains the...

Homework Statement I am tasked with solving and creating a dimensionless equation from a differential equation given. Homework Equations This is the given equation: The Attempt at a Solution When doing the dimensional analysis I see that we are left with units of [m-3][kg1][s-2]. These...

Hi, this problem is bugging me for several days now. In ”200 Puzzling Physics Problems”, Gnadik, Honyek, Riley there is this Problem 59: The solution to this is an ingenious resort to dimensional analysis, as follows: Now, I don't have a problem with this. I wonder however, what if we...

Homework Statement The American Petroleum Institute has published a correlation for determining the hydrocarbon emissions from fixed-roof storage tanks Ly = (24/1000) * (p/(14.7-p))^0.68 * D^1.73 * H^0.51 * T^0.5 * Fp * C where: Ly is breathing emissions, bbl/yr; p is the true vapor pressure...

Suppose I am given some charge density profile ρ(x). Poisson's equation in 1D reads d2φ/dx2 = ρ(x)/ε Is there a simple way to see what the order of magnitude of the electrostatic potential should be from a dimensional analysis?

From the equation of motion of inflation, $$\frac{d^2\phi}{dt^2} + 3H\frac{d\phi}{dt} + \frac{dV}{d\phi} = 0$$ Example: ##V= \frac{1}{2}m^2\phi^2## $$\frac{d^2\phi}{dt^2} + 3H\frac{d\phi}{dt} + m^2\phi = 0$$ If I want to make the DE dimensionless then I let ##~t = \frac{1}{H_o} \tilde t~## and...

I've been making my way through Matthew Schwartz's QFT book "Quantum Field Theory and the Standard Model". In chapter 6 he derives the differential cross-section for a ##2\rightarrow n## interaction. As part of the derivation, he introduces the Lorentz invariant phase space measure (LIPS), and...

Pretend that we do not know gravitational law at all, and want to investigate the gravitational law by dimensional analysis: Let's suppose the gravitational force are proportional to both masses, distance, hence: F \propto m_1^am_2^br_{12}^c But obviously, there is no way to equal the...

lets say for example, the air drag (ϑ) that wind exerts on a tile is a function of the tile's width (w), height (h), viscosity of air (μ), density of air (ρ) and velocity of the air (V) then ϑ = f(w,h, μ, ρ, V) ϑ : MLT-2 w: L h: L μ : ML-1T-1 ρ: ML-3 V: LT-1 I understand there are 3 basic...

How can you use dimensional analysis to estimate the force between two plates, as a function of the area of the plates and their separation?

Hello, I have been doing high school physics for about 3 years now and I am perfectly fine with it. However, Something tricked me off few days ago. It is how we treat units. I was kind of hesitant to post this thread because I have seen multiple threads about it before and some member really...

Homework Statement ii)Rayleigh method gives me inverse of expected result.Would really appreciate your help. Homework Equations show that ##f(gamma)##=##(\frac {ro*R^5} {E*t^2})## where ro=density R=radius E=energy The Attempt at a Solution We will do dimensional analysis on the elements...

Hi The relation between torque, moment of inertia and angular acceleration is: T=Ia Have a look to it's units: (N.m)=(kg.m^2).(Rad/s^2) >>>> N=kg.m.Rad/s^2 Please explain the equation Dimensionally. How (kg.m.Rad/s^2) is equal to N? Thanks.

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Homework Statement The period of a simple pendulum, defined as the time necessary for one complete oscillation, is measured in time units and is given by T = 2π ℓ/g where ℓ is the length of the pendulum and g is the acceleration due to gravity, in units of length divided by time squared. Show...

Homework Statement Equation 1: Find the dimensions of a,b F = at + bt2 F - force a - Some unkown value b - Some unkown value t - time In this equation we must find the dimensions of a and b which i did but, in the next similar equation Equation 2: Find the dimensions of a,b,c F = at + bt2...

this question is about dimensional analysis involving a number with units and a number with no units, if the question is already answered in another post please redirect me if not here is a simple example, for example, : say i have 2[in]-1. the 1 is dimensionless and the 2 has units of [in]...

Homework Statement It is found the terminal velocity ut of a spherical particle in a fluid depends upon the diameter d of particle, the dynamic viscosity μ of fluid and the buoyancy weight W of the particle [given by the difference in density between the particle and the fluid (∆ρ) ×...

In my lectures and notes my professor keeps writing out density as lbs/ft3 and unit weight as lbs/ft3. For a material such as concrete it could have a density of 167 lbs/ft3 but a unit weight of 103 lbs/ft3. I am confused as to how these two values are different even though they have the exact...

Homework Statement The speed v of sound in a gas depends on the density p and pressure P of the gass. If this dependence is in the form of a power law that is, v = kpaPb where k, a and b are constants (k a dimensionless one). a. Determine by dimensional analysis the values of a and b. b...

Homework Statement Hello, I am new to physics and i was wondering what i should do for the following equation to simplify it. Homework Equations [T]-2/[T] The Attempt at a Solution I tried 1/[T]3 Which I'm not sure is possible when dimensional analyzing. EDIT: Is it [T]-3

Homework Statement Check if the equation is dimensionally correct The frequency f of vibration of a pendulum of length L is given by the equation: f = L/2π √(g/L) I'm assuming 'g' is the gravitation field strength (?), which is [L]1[T]-2 The Attempt at a Solution [/B] I did not know what...

Hi All, My question is twofold and follows: 1) Why the dimension of torque is not Joule, as it is Newton times meter? 2) Why the derivative of the velocity with respect to the distance cannot be measured in Hertz? Thank you all, Best Regards, DaTario

As far as I understand, a natural system of units is one in which the numerical values of ##c## and ##\hbar## are unity. However, they still have dimensions, indeed ##[c]=LT^{-1}## and ##[\hbar]=ML^{2}T^{-1}##. How is it the case then, that certain quantities, such as the action ##S##, can be...

1. I ´m trying to do the dimensional analysis of the Delta Dirac in 3 Dimensions. [PLAIN]http://[url=http://postimg.org/image/oif09fcd5/] 3. This is my atempt [PLAIN]http://[url=http://postimg.org/image/4qavbtv4p/]

Homework Statement In a desperate attempt to come up with an equation to use during an examination, a student tries the following equations. Use dimensional analysis to determine which of these equations could be correct. Here x, v, and a, are the position, velocity and acceleration. v2=ax...

Homework Statement A capillary filled with water is placed in a container filled with a chemical of concentration C_{0} , measured in number of molecules per unit volume. The chemical diffuses into the capillary of water according to the following relation (where x is distance along...

This question arose as I was studying mathematical modeling in fluid mechanics. It was posted to math.stackexchange, but there a was a lack of response, probably due to the applied nature of the problem. One form of the Buckingham Pi Theorem says that for nn variables with kk dimensions, the...

Hello world! I'm busy working through Halliday/Resnick Fundamentals of Physics chapter 1 and I'm having some difficulty with this particular question. I'll do my best to explain my reasoning and attempt at the problem 1. Homework Statement The problem: Three different clocks A, B and C run at...

I was trying to convert a quantity in BTU/(ft*hr*F) to W/(m*C) and I can do it just fine by using a conversion factor from a table online, but what I want to know is how to come up with that conversion factor. The conversion factor I looked up and have been using is 1 BTU/(ft*hr*F) = 1.73...

Homework Statement Is the following equation dimensionally correct? Homework Equations E = (1/2) mv where: E = energy m = mass v = speed The Attempt at a Solution 1. I understand that the 1/2 is irrelevant. 2. I broke everything down into length, time, and mass. 3. I got ML^2/T^2 = ML/T 4. My...

Hello! So in looking at black hole thermodynamics, I came across the equation ## l_p = \sqrt{G\hbar} ## But in doing a dimensional analysis of ## \sqrt{G\hbar} ## I get ## [\sqrt{G \hbar}] = \sqrt{ \frac{Nm^2}{kg^2} \frac{m^3}{kgs} } ## This obviously doesn't amount to a length. What...

Hi all, I post a question about the dimension of wave function in position space before and people help me to identify that the unit of wave function should be in the unit of ##\text{m}^{-1/2}##. I am verifying that by doing the dimension analysis on Schrodinger equation...

Homework Statement Consider the Euclidean classical action ##S_{cl}[\phi] = \int d^{4}x (\frac{1}{2}(\partial_{\mu} \phi)^{2} + U(\phi))##, with ##U(\phi) = \frac{\lambda}{8}(\phi^{2}-a^{2})^{2}-\frac{\epsilon}{2a}(\phi - a)##. (a) Show that, in four-dimensional space-time, the mass...

Hello! May I first please direct your attention to Walter Lewin's first Classical Mechanics lecture on Units, Dimensions and Scaling Arguments? He first carried out a dimensional analysis to determine the relation between the time taken for a ball to fall from a particular height to the height...

Homework Statement The following equation is presented in my textbook, with very little context and J is simply described as the "trans-membrane fluid flux, which can be modeled by using Darcy’s law." Typically in this bioseparations class, when we discuss permeate flux, it is a unit volume...

I would like to use the Buckingham-Pi theorem in order to "algorithmify" non-dimensionalization of existing equations. I can get things to work for very simple problems, but am running into issues with a harder example. I posted my question on physics.stackexchange.com the day before yesterday...

i know it sounds like a very stupid question, stated that it's very much given that the further away the observer is from the source of light, the smaller they seem... BUT WHY? i just can't wrap my head around the fact... can someone explain to me, why it seems like that, and do you think this...

I'm learning QFT from Srednicki's book. He introduces dimensional analysis in section 12. Coupling constant needs to be dimensionless in order to avoid a number of problems. So phi-cubed theory needs 6 space time dimensions to make sense, but isn't phi-4th-powered theory just right for our 4...

Homework Statement a) A orifice, diameter d (m), in the walls of a tank discharges water under a head, h (m), subjected to gravitational acceleration, g (m/s2). If the fluid has density, ρ (kg/m3)and viscosity, μ (Ns/m2), show that the quantity of fluid Q (m3/s) flowing out of the tank may...

Hi, this is my first post, so sorry if this is posted on wrong section etc. Do not worry about the initial part of dimensional analysis, that was fine - use Buckingham pi therem, but here's the prob... Below is the question, I am stuck on being part C, however to show you guys what needs to be...

Homework Statement How do I set up a matrix to find the combination of ( M(L^2)/T ) and I ( L^4) that results in units of M/ ( L^2 T^2 ) ? Homework EquationsThe Attempt at a Solution I think it looks something like [ 1 0 2 4 -2 0 ] * [ a1, a2, a3] = [1 -2 -2] but the dimensions of those...

Under the standard form of dimensional analysis, I know that we relate a dependent variable to a function of the independent variable(s). However, what if there is some additive variable needed in the equation? How does this method, which expresses all of the independent variables as a product...

Once an equation is well put and there is dimensional homogeneity like: ##mx''+\beta x' + kx=f(x)## ; ##Lq''+Rq'+q/c=E(t)## (mass-spring; Kirchoff's diff eq.) One proceeds with the math as if there were no actual units involved and just solved a problem dealing with only numbers. Is there...

Hi! Sorry if this is the wrong section to post this: I am doing a laboration on physical pendulums and I have a bit of trouble making sense of it all and I am in need of some guidance. When I do the analysis I get the standard mathematical pendulum. [T]=[m]^a*[l]^b*[g]^c, where a = 0, b = -c...

Homework Statement Hi Guys, I have this question: b. A model scaled to one-third the size of the prototype has the following characteristics: Omegam = 900 rpm Dm = 5 in deltaHm = 10 ft Qm = 3 ft^3/s Pm = 2 hp If the full-size pump is to run at 300 rpm, what is the power required for this pump...