Dimensional analysis Definition and 262 Threads

One would assume that: $$t \propto h^\alpha m^\beta g^\gamma$$ Where t = time taken for object to fall, h = height dropped from, m = mass, g = acceleration due to gravity. By doing some dimensional analysis one can find that: $$t \propto h^\frac{1}{2} g^\frac{-1}{2}$$ and that t is...

Homework Statement In some cases waves on deep water are driven by surface tension effects and not by gravity. The surface tension is the energy per unit area of the water surface. The area of the water surface increases by a factor proportional to (Ak)^2 in the presence of a wave amplitude...

The velocity of waves in a liquid depends on the wavelength λ, surface tension γ, and density ρ, of the liquid, Derive an equation to relate v, with wavelength, surface tension and density, (note: surface tension, has a formula of force per unlit length and SI unit of Nm^-1)

Homework Statement Homework Equations n/aThe Attempt at a Solution Conversions from EE units to CGS units: psi -> g/cm*s^2 = 68948 lb/gal -> g/cm*s^3 = 0.1198 in -> cm = 2.54 ft/sec -> cm/s = 30.48 ft -> cm...

Speed of sound The speed of sound c in a gas depends on among other things on the pressure on the gas, the density and probably, possibly on their viscosity. Determine c- My Variable list: Pressure p ML^-1T^-2 Density ρ ML^-3 Speed v LT^-1 My matrix: | | M | L | T | | p | 1 |...

The period T of a pendulum of length L, mass m in a gravitational field g ms-2 is suspected to be a function of L, m and g. If it is postulated that T=KLxmygz where K is a dimensionless constant, use dimensional analysis to obtain the constants x, y and z. There's only one pi group I came up...

Throwing height: A rock is thrown straight up with initial speed v. Determine a expression for the maximum height h the rock reach.The air resistance is neglected and the throwing height are dependent on the gravity. Variable list: Speed: V, LT^-1 Height h, L gravity g, LT^-2...

we can use the dimensional analysis to check the homogeneity of a physical quantity. based on the question : ''can the equation V=ut + at be correct? '', we know that the LHS isn't the same as the RHS.. since the equation is not dimensionally homogenous,so it can never be correct..(the answer...

This question is on the radius of a shell, which is: R[shell] = ((Luminosity*time^3)/(density))^1/5 I have been asked to prove this using dimensional analysis, and have broken the quantities down into their basic units, but seem to be getting really funny answers (with most of the powers...

Homework Statement Pressure(water)~density(water)xg(grav. accel.)xz(depth) Homework Equations The Attempt at a Solution basically I'm doing a fermi problem regarding the pressure of water on Jupiter's moon Europa. Now i tried coming up with the equation for pressure my self by...

Homework Statement I have an equation for motion: x(t) = x(0) + x(0) * k * t^{1.5} x is in meters and t is in seconds. I have to determine the unit of k. Homework Equations The Attempt at a Solution x(t) = x(0) + x(0) * k * t^{1.5} [x(t)] = meters Therefore, [x(0)] = meters...

Homework Statement A birchwood table company has an individual who does all its finishing work and it wishes to use him in this capacity at least 36 hours each week. By union contract, the assembly area can be used at most 48 hours each week. The company has three models of birch tables, T1...

؟؟؟simple dimensional analysis question? what combination of force and one other physical quantity has the dimensions of power??

I'm teaching myself physics by reading notes online posted as an OpenCourseWare physics course at MIT: http://ocw.mit.edu/courses/physics/8-01sc-physics-i-classical-mechanics-fall-2010/ I'm already frustrated in the first module. One major lesson involves guessing a formula based on...

Determine which of the following equations are dimensionally homogeneous. Show your work ΔP/Q = 17L(μ)/(w^4) where ΔP is the pressure drop in a channel of triangular cross-section, Q is the volumetric flowrate, L is the channel length, μ is the fluid viscosity, and 2w is the length of one...

2 questions,actually: 1-Why in Dymensional Analysis is eletric charge a basic physical dimension instead of eletric current(as Ampere is a SI base unit and Coulomb isn't)? 2-I've read CIPM(or International Committee for Weights and Measures in English) is proposing new definitions for some of...

Hi, sorry for asking this but my brain still seems to be on lockdown from the summer. I have a pretty good idea of how dimensional analysis works and only seem to be having issues on one type of problem currently. something like: t=(Cm^x)(k^y) where: t-oscillations of mass m-mass spring...

1. Convert 1.2 in^2 to cm^2 2. 1 CM = 10^-2 and 1 inch = 2.54 centimeteres The Attempt at a Solution Can't we just do 1.2*2.54=3.048 and write that as our answer?

hello, in the Wikipedia page for http://en.wikipedia.org/wiki/Dimensional_analysis#Proof_of_the_Pythagorean_theorem" how do we know that area = "largest edge2 • f (angle1, angle2)"? Isn't it just as reasonable to say something like area= (largest edge/40000)2 • f (angle1, angle2) ?

I wasn't sure whether to put this here or in the Chemistry forum, so if it's in the wrong place I'd prefer it be moved rather than deleted. ;) Anyway. I'm struggling a bit with Dimensional Analysis, particularly of volumes/density and recognizing conversion factors when I see them. As more...

I decided to take physics this year, my senior year in high school, and my teacher has decided he isn't going to explain things before he assigns us homework. Any and all help is appreciated. 1. The period T of a simple pendulum is the amount of time required for it to undergo one complete...

Can you work units cubed the same way you can work units that aren't cubed in dimensional analysis? Like...does 1m3 equal 250cm3 like it would if they weren't cubed?

Homework Statement 1) A string is stretched between two walls. When its plucked, a transverse wave travels from one end to the other. The length of the string is l, the mass of the string is m. There is a tensional force of F Newtons present in the string. The velocity of the resultant wave...

Homework Statement "Power is the rate at which work is performed. Power is signified by W for watts. Power is also the amount of energy transmitted in a unit of time (s). Energy is measured in joules. Joules have the units of Newton∙meters. A Newton is a unit of force. It...

1. The problem statement Use dimensional analysis to find \int\sqrt{\ a\ - \ b\ x^2\ }\ dx . A useful result is \int\sqrt{\ 1\ - \ x^2\ }\ dx\ = \frac{arcsin{x}}{2}\ + \frac{x\sqrt{\ 1\ - \ x^2\ }}{2}\ + \ C . 2. The attempt at a solution If I let [b] = L^2 and [x] = M , then...

1. The problem statement Use dimensional analysis to find \int\frac{ dx }{ x^2 + a^2} . A useful result is \int\frac{ dx} {x^2 + 1}\, \ = \, \ arctan{x} + C . p.11, prob.1.11 http://mitpress.mit.edu/books/full_pdfs/Street-Fighting_Mathematics.pdf 2. The attempt at a solution 2.1. If I let...

Homework Statement How many centimeters are there in 3.25 miles? Homework Equations So basically, convert 3.25 mi to cm. The Attempt at a Solution http://img688.imageshack.us/img688/4916/problemwc.jpg Uploaded with ImageShack.us The teacher put the answer for this problem as...

Homework Statement You are performing experiments on a pump and you are interested in investigating how the working pressure (L1P) and power (P) of the pump vary with respect to different design conditions. Knowing that in the lab you can manipulate the volumetric flow (Q), angular...

I've been trying to come up with a function to express velocity in terms of length, mass, pressure, area, and density but I've been having some trouble. If anyone can help it would be greatly appreciated. Thanks.

Homework Statement If you could hypothetically experience 1 femtosecond (1E-15 s) the same way you do normally for 1 second, how long would it seem to experience 7.078E-4 seconds? Homework Equations note: 1 femtosecond is to 1 second, what 1 second is to 31.7 million years. The...

Homework Statement Does anyone know where can i find (book?) the dimensional analysis of emissivity? Homework Equations The Attempt at a Solution

Homework Statement The terminal velocity of a mass m, moving at 'high speeds' through a fluid of density ρ(kg m^-3), is given by v = sqrt(2mg/DρA) where A is the cross sectional area of the object (m^2) and D a dimensionless "drag coefficient". i) Show that equation is dimensionally...

Homework Statement The equation P+av2=b is dimensionally correct. P and v represent pressure and velocity respectively. The unit of ''a'' is similar to...? The answer provided is density... Homework Equations The Attempt at a Solution In the question... it doesn't state that...

The men's world record for the shot put, 23.12m, was set by Randy Barnes of the United States on May 20, 1999. If the shot was launched from 6 ft above the ground at an initial angle of 42 degrees, what was its initial speed? Known Data Is Height, angle of where it was shot, and how far it...

I'm having trouble understanding what exactly a dimensionally correct equation is..here's my problem- In the following expressions: V-volume A-area P-pressure p(lowercase)-density t-time m-mass v-velocity g-acceleration due to gravity I'm supposed to state whether the following...

Homework Statement Nutrition experts recommend that you drink at least 8 cups of water daily. If your local water supply contains 1.00 part fluoride (by mass) per million parts water, how many milligrams of fluoride would you consume daily in your 8 cups of water? (use 1.00 g cm^-3 as the...

Homework Statement The volume of an object is given as a function of time by V= A + B/t + Ct^4 Find the dimension of the constant C. Homework Equations N/A The Attempt at a Solution I don't understand dimensional analysis completely .. I understand it on simpler terms, but in...

Homework Statement Porous rock through which groundwater can move is called an aquifer. The volume V of water that, in time t, moves through a cross section of area A of the aquifer is given by: V/t=KA(H/L) where H is the vertical drop of the aquifer over the horizontal distance L. The...

Is there good list of common units (good as in including the unit, symbol, and quantity it measures) anywhere out there? I did some searching and came up with this, but I'm unsure how good it is as a source. http://www.alcyone.com/max/reference/physics/units.html Any supplementary list or...

I’m currently investigation the fluid motion (diffusion) of gas's so see how well they can ventilate in an enclosure. I would like to simulate this using a (1/10) scale model. The enclosure has already been built, and smoke pellets are going to be placed inside to help visualize fluid...

In Dimensional analysis if L=Lenght why is L/L=1 (a dimensionless number), and not just nothing more than L/L ? It started with that I was thinking of why degrees do not have any dimension, and then I thought of the definition of radians: q = "angle" s = "a length on the circles...

Hi, So according to the Thomas-Fermi theory, the formula for atomic radius is R=Z^(-1/3)*(hbar ^2)/m*e^2. (in other words Z^(-1/3) times the Bohr radius) While the total energy has a Z^(7/3) dependence. I need to get this from dimensional analysis. I can get the dependence on h, m, and...

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Homework Statement I am going crazy! The problem tells me to use the ideal gas equation to solve for the specific volume. They give the pressure, 15 MPa, and the temperature, 623 K. However, solving it is not the problem. The problem is that I keep on getting the answer off by a factor of...

Homework Statement The speed v of sound waves in air depends on the atmospheric presure P and density. By using the method of dimensional analysis, find an expression for v in terms of P and density. Homework Equations What I have so far; V= density x P I found a textbook...

Homework Statement stars form by gravitational collapse of interstellar gas clouds. use dimensional analysis to estimate how long it takes for a cloud with a density p=Mo pc^-3 to collapse Mo= 1.9898e33 g Homework Equations The Attempt at a Solution I just have no idea how to use...

Homework Statement In the equation below, x and x0 are distances in meters, t is the time in seconds, and v0 is a speed in meters per second. Find the units of a. x-x0 = v0(t) + (1/2)a(t^2) Find the dimensions (or units) of v0 that will make this equation dimensionally correct. The...

Homework Statement The velocity of a traverse wave traveling along a string depends on the tension of the string, F, which has units of force, and its mass per length unit u. Assume v = F^x * u^y. The values may be found using dimensional analysis. Homework Equations I am pretty sure I...

Homework Statement I am looking for a proof of Buckingham PI theorem in dimensional analysis, but can't really find one anywhere. I saw a proof involving posing the problem as a question in linear algebra, but it was quite unclear.