Homework Statement
Hello guys!
I have a dimensional analysis problem where water is draining from a open topped tank and in a certain amount of time,t it drops from h1 to h2. and I need to find a bunch (6) of variables which apply to this problem. I have some but I am not sure about the other...
Homework Statement
Hi Guys,
I am a bit confused concerning one part of this topic. Specifically when trying to find non dimensional groups. My problem is a small thing in the finding of the indices.
So, for example, your are trying to find a pi group when finding the drag on a car.
so you...
Homework Statement :[/B]
An atomic explosion can be approximated as the release of a large amount of energy ##E## from a point source. The explosion results in an expanding spherical fireball bounded by powerful shock wave. Let ##R## be the radius of the shock wave and assume that...
Stumbled upon this problem lately. Maybe someone could help me clarify some subtleties I do not see?
1. Consider the propagation speed ##c## of periodic surface of gravity waves with wavelength ##\lambda## and amplitude ##a## in water of depth ##H##. Let ##\rho_{a}## and ##\rho_{w}## be the...
Recently, I used the metric for the traversable wormhole (the one in this link):
http://www.spacetimetravel.org/wurmlochflug/wurmlochflug.html
ds2= -c2dt2 + dl2 + (b2 + l2)(dΘ2 + sin2(Θ)dΦ2)
I derived the metric tensor from this space-time interval and then from there, I derived the...
Homework Statement
Using dimensional analysis deduce the relationship between the pressure drop per unit length along a cylindrical pipe of radius r, and the radius of the pipe, the viscosity of the fluid in the pipe, η, and the volume flow rate, V ̇ .
Homework Equations
Δp/l = 8ηV...
Homework Statement
For the following dimensional equation, find the base dimensions of the parameter f:
M M-3 = a cos( f L ) Homework Equations
M represents mass, a represents acceleration due to gravity, in terms of mass * length over seconds squared [[M * L]/[t2]] where L represents length...
Dimensional Analysis is really simple and I have read that it is only used to verify the derived equations. But I don't understand how we work with constants in Dimensional Analysis. For example, if we are given KE depends on mass and velocity, we can easily derive KE = 1/2 mv2.
In the above...
Greetings,
I'm attending a grad school in the fall whose Ph.D. comprehensive exams place a *huge* emphasis on order of magnitude estimations and dimensional analysis problems. I'm much better at problems that involve a little more mathematical playfulness and theory; I'm a little worried...
This is actually an example from Physics for Scientists and Engineers by Serway. I am confused about the way they solved it.
Homework Statement
Suppose we are told that acceleration a of a particle moving with uniform speed v in a circle of radius r is proportional to some power of r, say...
Homework Statement
Assume that in interplanetary space within the solar system there is one hydrogen atom per cubic centimeter, and that the mass of such an atom is 1.67 x 10^-27 kg. In addition, take the radius of the solar system to be 4.0 light-hours. For the sake of this calculation, take...
Homework Statement
Two spheres are cut from a certain uniform rock. One has radius 4.30 cm. The mass of the other is six times greater. Find its radius.
Homework Equations
v = (4/3)(pi)(r)^3
m = vp
The Attempt at a Solution
6[(4/3)(pi)(r1)3] = (4/3)(pi)(r2)3
8(pi)(r1)3 =...
Homework Statement
"A particle of mass m moves in a circle of radius R. Using dimensional argument,
determine the particle angular momentum."
Homework Equations
L = mvr
The Attempt at a Solution
Because L = mvr, the dimensionality would be ML2T-1. I don't know where to go from here...
I would like non-dimensionalize the equations which describe a non-Newtonian fluid model. In the constitutive equation (power-law model) there is a non-dimensional parameter: n. According to Buckingham's Pi theory, I must take all the relevant independent parameters (variables, constants, etc.)...
Homework Statement
During a short interval of time the speed v in m/s of an automobile is given by v = at2 + bt3,where the time t is in seconds and a and b are constants. The units of a and b are respectively:
Homework Equations
I'm assuming that dimensional analysis is needed for this...
To illustrate the abstract reduction to dimensionless quantities apply it to the harmonic oscillator
V(x) = (m \omega^2 x^2) / 2
using x_0 = sqrt(h-bar/(m \omega))
and fi nd a dimensionless Schrodinger equation. Translate the known solutions to the Schrodinger
equation for the harmonic...
Homework Statement
The ceiling of a single-family dwelling in a cold climate should have an R-value of 30. To give such insulation, how thick would a layer of (a) polyurethane foam and (b) silver have to be?
per my book (W/mK)
k_p = 0.024
k_s = 428
Homework Equations
This is Thermal...
Homework Statement
The total power radiated by an oscillating electric dipole is a function of the oscillation frequency ω, the dipole moment p(=Qd, where ±Q is the charge at each end of the dipole and d is the distance between charges), the speed of light c and the permittivity of free space...
Homework Statement
The aerodynamic drag of a new sports car is to be predicted at a
speed of 100 km/hr at air temperature of 25°C. Automotive engineers
build a ¼ scale model of the car to test in a wind tunnel, where the air
temperature is 10°C. A drag balance is used to measure the drag...
We are asked to transform this equation:
h=1147(1+0.05625T)\frac{V^{0.6}}{D^{0.4}}
where the units of each variable h, T, V and D are:
h->\frac{kcal}{h·m^{2}·ºC}
T->ºC
V->\frac{m}{s}
D->cm
into another equation where the units of each variable h, T, V and D now are...
Homework Statement
A=B^3C^1/2 where A has the dimensions L/M and C has dimensions L/T. What are the dimensions of B?
Homework Equations
The Attempt at a Solution
When I worked the problem I got B=M/T but it is wrong. I'm not sure how to approach the question.
I'm having trouble understanding a step. How are the values of " i , j , and k " derived? When equating the powers what step has to be done? I have been stumped on this for a while and I think I'm just over thinking it.
https://www.dropbox.com/s/agc0ga9hsjd04jn/Sample%20Problem.png
Homework Statement
The diameter of metal wire is often referred to by its American wire-gauge number. A 16-gauge wire has a diameter of 0.05082 in.
What length of wire, in meters, is found in a 1.00-lb spool of 16-gauge copper wire? The density of copper is 8.92g/cm3.
Homework...
Homework Statement
Dimensional Analysis:
The following equation was given by a student during an examination:
(1/2)(mv2) = (1/2)(mv02) + √(mgh)
Do a dimensional analysis and explain why the equation can't be correct.
Homework Equations
m = grams
v = m/s2
The Attempt at a...
Homework Statement
An flying object of mass M experiences a lift force and a drag force dependent on the it's velocity:
F_{l} \propto Wv^{2}
F_{d} \propto Av^{2}
Where W and A are wing surface area and "cross-sectional" area.
To sustain flight the object must fly at a minimum velocity...
Homework Statement
I have a tutorial question I have been struggling with. The problem is:
The flow through a closed, circular sectioned pipe may be metered by measuring the speed of
rotation of a propeller having its axis along the pipe central line. Derive a relation between
the volume...
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...
In the textbook, usually the fermion mass renormalization is introduced as follows: the mass shift \delta m must vanish when m_0=0. The mass shift must therefore be proportional to m_0. By dimensional analysis, it can only depend logarithmically on \Lambda (the ultraviolet cutoff): \delta m \sim...
I came across this equation, said to describe the relation between the resonant frequencies of air in a spherical cavity open at the top.
D = 17.87 \sqrt[3]{\frac{d}{f^{2}}}
Where D is the sphere diameter, d is the diameter of a small circular cavity at the top of the sphere and f is the...
In http://ocw.mit.edu/courses/physics/8-01-physics-i-classical-mechanics-fall-1999/video-lectures/lecture-1/ at about 23 minutes in, he starts talking about dimensional analysis. Can someone help expand on this a bit? I don't understand the Alpha, Beta and Gamma terms he uses.
Thanks.
Hi. Consider the basic eq for a falling body with air resistance
dv/dt=g-kv/m
I don't understand air resistance as a force, since it seems irreconcilable to the force equation F=ma. How is a force a function of velocity? I am also not sure how this equation makes sense in terms of...
I have an exercise at the moment where I am supposed to put the Schrödingerin dimensionless form (the exact exercise is attached). I must admit that this idea of dimensional analysis is quite new to me. I don't understand how you can write the SED in the dimensionless form described. Therefore I...
I am actually going to post the problem that sparked the question I am about to ask, but I don't need help with the answer and that's why I didn't start this thread in the homework and coursework section. Actually, I just realized I read the problem statement in the wrong way, which makes my...
Homework Statement
Use dimensional analysis to determine the dependence of the period T of
a simple pendulum on its mass m , weight w , length l and arc-length of
swing s.
Homework Equations
g= [L/T2]
The Attempt at a Solution
T =cst * malbgcsd
[T]=malbgcsd
=[M]a[L]b[g]c[L]d
okay I am...
Homework Statement
One formula for measuring the speed of sound in air is:
v=\sqrt\frac{kTg}{m}
v=velocity
T=temperature
g=dimensionless constant
m=average mass of an air molecule
If all units are SI, what are the units of k?
The Attempt at a Solution
I've done a lot of...
Homework Statement
How do I convert kg/m3 to g/cm3?.
3200kg/m^3 ---> 3.2g/cm^3
Homework Equations
The question was 3200kg/m3 = 3.2g/cm3. I don't understand the steps involved?
The Attempt at a Solution
I know how to do dimensional analysis, but I just don't really...
Homework Statement
The drag force F on a car depends upon its speed V, length L, the density ρ of the air
and the dynamic viscosity of the air µ . Show that this statement regarding five
physical quantities can be re-written in terms of two independent non-dimensional
groups...
This is something I've been wondering for a while, but I thought that the inputs for things like ln(x), e(x), sin(x), etc. had to be unitless. Then how come concentration, which has units of moles per volume (or I guess just per volume, since moles are just a number? I've never been sure about...
Homework Statement
I'm trying to work out if the following is dimensionally correct. I think I'm getting stuck at the (x - x0)
Homework Equations
In this case v is velocity (L/T), a is acceleration (L/T²), and x represents displacement, which is a length (L)
The Attempt at a...
Homework Statement
angular frequency omega, speed of light and gravitational constant
Homework Equations
Just the expression,
\frac{2 \omega c}{\sqrt{G}}
The Attempt at a Solution
Still learning dimensional analysis. So I am simply wanting to know if I have done this right...
This may sound like a homework-type, but it isn't from any piece of homework, I just want to know how to do dimensional analysis by giving an example.
Let's have this simple equation:
k = a^{b}
Where k is a certain property of an object, a is the mass of the object, b is the length of...
I started taking MIT's online physics course a couple of days ago, and since I have no physics background at all, I'm getting a bit confused with dimensional analysis.
I'm trying to find a formula for the terminal velocity of a rocket, using air density ρ, gravity g, area of rocket affected by...
In some work I have been following, I keep seeing notation like:
for energy ... ML^2 T^{-2}
How is this supposed to be read? I understand this is using mass, length and time, but what is it saying? Would I be right in thinking it says
''mass times length squared divided by time...
Homework Statement
i have attached a copy of the full question and my answer to part a (i'm stuck on part b which i have written below. The diagram is a bit too complicated to describe in words)
In an examination of this problem Edge (1968) assumed one-dimensional inviscid, incompressible...
1. Homework Statement
how do i deduce the dimension of the following using dimensional analysis
Power enthropy, surface charge density, inductance, permitivity, radius of gyration
tried deducing the dimension of power like this:
p=work done/time
work done w= force x distance...
Homework Statement
how do i deduce the dimension of the following using dimensional analysis
enthropy, surface charge density, inductance, permitivity, radius of gyration
Homework Equations
The Attempt at a Solution
tried deducing the dimension of power like this:
p=work...
Homework Statement
I was supposed to use dimensional analysis to approximate the length scale (in classical and quantum mechanics). The results I got(same as those in the answer sheet): classicalyl_c≈\frac{e^2}{4πm_ec^2ε_0}≈2.8*10^-15m In quantum mechanicsl_q≈\frac{h}{m_ec}≈2.4*10^-12m...