A cylinder (from Greek κύλινδρος – kulindros, "roller", "tumbler") has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes. It is the idealized version of a solid physical tin can having lids on top and bottom.
This traditional view is still used in elementary treatments of geometry, but the advanced mathematical viewpoint has shifted to the infinite curvilinear surface and this is how a cylinder is now defined in various modern branches of geometry and topology.
The shift in the basic meaning (solid versus surface) has created some ambiguity with terminology. It is generally hoped that context makes the meaning clear. Both points of view are typically presented and distinguished by referring to solid cylinders and cylindrical surfaces, but in the literature the unadorned term cylinder could refer to either of these or to an even more specialized object, the right circular cylinder.
I want to work out how to calculate the pressure change in a gas cylinder if it is used to fill another cylinder to a lower pressure.
For example, if a 50 litre gas cylinder initially at 200 bara is used to fill a 600 litre cylinder from atmospheric pressure to 1.5 Bara. What would the change...
For this problem,
The solution is,
However, I thought the answer would be (b) and (e). I choose (b) because from the formula ##P = \frac{F}{A}## then since the vessel A has more water, then the water will have a larger weight ##W_A > W_C > W_B##, therefore from##P = \frac{mg}{A}## we conclude...
Consider an LC circuit consisting of a parallel plate capacitor and a solenoid inductor in series. The formula for the resonant frequency of this circuit is 1/√(LC) where “L” is the inductance of the solenoid and “C” is the capacitance of the capacitor.
Now consider a high-frequency cavity...
Because my little work project involves fluids I thought this the best topic to post under.
I took the route of biological sciences and computer science. This area is out of my league at the moment I'm not sure the amount of time that would be required to get the material applicable to this...
Greetings
i´m trying to find the Force applied by the upper roller to calculate the contact surface.
Here is indeed my solution
2*FR1* cos31,38=F=1500N
FR1=878,57N (which is wrong the correct solution says 818,1N)
FR1 is the force normal to the surface of contact.
any help would highly...
I've been able to prove the following inequality $$\frac{2\pi\epsilon_0}{\log\left(\frac{b_1b_2}{a_1^2}\right)}\leq C \leq \frac{2\pi\epsilon_0}{\log\left(\frac{a_1a_2}{b_1^2}\right)}$$ but have no clue how to obtain exact value. Can someone check whether this inequality is correct and show how...
There are n vertical identical parallel identical cilinders rotating around their length axes with the same angular velocity. The are somehow fixed wrt to Earth and brought together (on a rail?). After the contact there is no slipping and the cilinders are coupled to their neighbor cilinders. It...
The task is to find the magnetic field between the 2 long cylinders, which extend to infinity. Integration is involved to find the total current passing through the Amperian Loop shown below. What I do not understand is why only sides 1 and 3 contribute to that B ds part of Ampere's Law. Isn't...
I used a couple ways to do this question, but I got neither correct. Can someone help, please? Thank you.
1. E= V/r = 700 / (60*10^-3) = 11667 (very far from the given answer)
2. E = (-kQ/r)⋅ dr
= kQ/r^2
= kQ/ [( 1/20/ 10^-3)^2 - (1/80/10^-3)^2]
(For this method, I stuck...
A solution I found online claims that the effective capacitance between the middle and inner shell can be seen as:
C (effective) = C1 + C2,
where C1 is the capacitance between the inner and outermost shell, and C2 is the capacitance between the middle and outermost shell. Apparently C1 and C2...
Just some idle Sunday musings. I have a steel pipe that is 2" ID, 2.5" OD, 10' long. I want to place a coil inside the pipe midpoint along the pipe and detect it's presence with a transmitter / receiver array. The array can consist of two coils wrapped around the outside of the pipe and can be...
If I understand correctly, Gauss’ Law is (roughly) derived as follows:
Part A
Electric Flux = EA
E = q / (∈4πr^2)
A of the surface of a sphere is 4πr^2
They cancel out and therefore EA =q/∈
Line 4 seems to only apply to a sphere, as it is based on line 3.
Now, Gauss’ Law is applied to...
At first, I started with the result from an earlier problem regarding the capacitance of a cylindrical capacitor:
$$C=\frac{Q}{V}=\frac{2\pi \varepsilon _0\varepsilon _rl}{ln(R_1/R_2)}$$
$$\Rightarrow V=\frac{Qln(R_2/R_1)}{2\pi \varepsilon _0\varepsilon _rl }$$
Then I used the equation...
Firstly the normal reaction force of the bottom cylinder is ##R## and because all three cylinders are identical ##2R=3mg##, and so the frictional force is going to be ##F_r={(3mg)/(2}{\mu})##. I don't use this, though.
If the normal reaction force between the top cylinder and one of the bottoms...
I am not sure about my free body diagram. I assume the cylinder rolls without slipping so the forces acting on the cylinder are:
Weight directed vertically downwards
Normal force directed perpendicular to the plane
friction directed upwards, parallel to the plane
Am I correct till this point...
Some time ago there was a problem with the following picture somewhere out here. I think this problem was underestimated a little bit.
Let us reformulate the problem. Assume that each cylinder, if it was not influenced by the other one, could rotate freely about its fixed axis. But the...
A single pair of points will be in contact between P and Q. The frictional force will try to make the velocity of these points equal.
Say the final angular velocity of Q is ωq.
The velocity of points in contact can never be equal because of difference in directions of ωq and ωp. If I break...
I have put a picture of the problem above. The picture below shows my free body diagram. Fg is the component of the gravitational force in the direction fo the tangent at the point of contact and Ff is the frictional force between the plank and cylinder. I put Ff in the opposite direction as Fg...
Here is the picture on the system.
I have to find the period (T). The masses, R and dX is given. The systam at first is at rest, then at t = 0 we pull the plank to dX distance from its originial position.
In the thread...
Hi! I need help with this problem. m1-2-3-4 and R are given. There is no slip in the system. I have to give F1-2-3-4 in respect of the masses and R.
Here is what I managed to
m1 is easy: m1*a = m1*g - T(tension of the rope)
m2: m2*a = T - (?) <-- I have a problem with this. F1 and F3 is the...
My initial attempt: Total Centripetal force on the cylinder would be given by $$\textbf{F}_{net} = mR\omega^2 \textbf{e}_1+mr_{cm}\omega^2 \textbf{e}_2$$ where the vectors e_1 and e_2 have magnitude 1 and point radially outwards (and continuously changing as the cylinder rolls down) as marked in...
Please excuse my ignorance. I work for a Natural gas company and have an issue that needs addressed. When gas comes out of the ground it goes into a piece of equipment that separates the water from the gas. The gas goes into a pipeline and the water is dumped into a tank. We are currently trying...
The first part of the problem I just used Stevin's law:
$$p_{atm}=P+ρg(h_1-h_2)=> h_2=(P-p_{atm}+ρgh_1)/(ρg) =>h_2=0.94m$$
Is this right? I considered ##ρ=10^3 {kg/m^3}##
About the second part... how can I be sure that ##h_1## remains unchanged? If it is unchanged, then can I use Bernoulli's...
I know that to find the volume under a surface and above a boundary we have to integrate twice. I can explain myself with an example :-
Lets' consider that we need to find the volume under the surface z = \sqrt{1-x^2} and above the region bounded by y^2 = x and positive x-axis and x=5 ...
Homework Statement
A thin plank of mass M is placed centrally across two solid cylindrical rollers each
of mass m, and the system is allowed to move freely from rest without slip down a
slope of angle θ as shown in the figure below.
(a) Derive expressions for the initial accelerations of the...
Dear colleagues of Physics Forum:
I am trying to estimate the inclination (angle) at which the figure presented with the enclosed photo, composed by two cylinders of different densities (ρ1=2650 kg/m3 and ρ2=7000 kg/m3), will topple, when progressively inclined from a horizontal position. Let's...
Homework Statement
.A cylinder P of radius rP is being rotated at a constant angular velocity ωP along positive y-axis with the help of a motor about its axis that is fixed. Another cylinder Q of radius rQ free to rotate about its axis that is also fixed is touched with and pressed on P making...
Homework Statement
A cylinder is well-insulated at the base and sides (radially). No heat sources and assume steady state. All other BCs are free (I'm aware the problem is underconstrained). Then we have
$$\nabla^2 f = 0\\
\partial_rf(r=R_0) = \partial_rf(r=R_1) = 0\\
\partial_z f(z=0) = 0\\...
Homework Statement
Consider an infinitely long cylindrical rod with radius a carrying a uniform charge density ##\rho##. The rod is surrounded by a co-axial cylindrical metal-sheet with radius b that is connected to ground. The volume between the sheet and the rod is filled with a dielectric...
I have an outer cylinder and an inner cylinder given. They are hollow(like if you were to take a sheet of paper and tape one edge to the other), grounded, and the inner cylinder is inside the outer cylinder. Between these cylinders is an ungrounded cylinder. I am now asked to calculate the...
Hello.Can you please help me find an expression for the volume of the left body which is actually 4 cylinders with diameter = D placed on the vertices of the cube with side length L (the cylinders are being "cut" by the corners of the cube). Thank you!
Homework Statement
Problem 1.24 (this is unimportant; it's just a different way of calculating the potential energy of a solid cylinder) gives one way of calculating the energy per unit length stored in a solid cylinder with radius a and uniform volume charge density ##\rho##. Calculate the...
Homework Statement
Hello everyone,
I am writing here regarding a doubt I have about electric fields. Our set up consists on two rod shape electrodes in a cylindrical glass vessel separated by 6 mm from each other, with one of the electrodes grounded (electrodes dimensions: 0.5 mm diameter and...
Homework Statement
I am looking for the line of intersection of two cylinders (x^2+y^=1 and x^2+z^2=1) to find the curve for a line integral. However, I am getting z=y, which is a patently false answer. Mathematically, it seems to work out though.
Homework Equations
x^2+y^=1
x^2+z^2=1
The...
Hi.
All technical implementations of the Magnus effect I can find on Google (such as ships) seem to use fairly smooth cylinders. Why? Shouldn't the efficiency increase with increasing friction between cylinder and fluid, for example with a rough surface or even attaching blades?
a)Design and draw a circuit using the cascade system to operate 2 cylinders (A&B) which, on the operation of the start valve produces the sequence A- B+ B- A+. The cylinders should park in the positions B- A+ when the start switch is in the off position
b)Modify the circuit designed for part...
Homework Statement
two cylinders of radii r1, and r2
having moments of inertia I1, and I2, about their
respective axes. Initially, the cylinders rotate about their
axes with angular speeds w1, and w 2 as shown in the
figure. The cylinders are moved closer to touch each other
keeping the axes...
Homework Statement
A point mass m is fixed inside a hollow cylinder of radius R, mass M and moment of inertia I = MR^2. The cylinder rolls without slipping
i) express the position (x2, y2) of the point mass in terms of the cylinders centre x. Choose x = 0 to be when the point mass is at the...
Homework Statement
A cylinder is placed on bars.The separation of each bar is l.The cylinder is then pulled with a force F through its center.Find the terminal velocity of the object.Assume l<<R and the ball rolls without slipping.
Homework Equations
1/2 mv^2 +1/2 Iω^2 = kinetic energy
Work is...
Say we have 2 cylinders with the same volume capacities, but different radii, and a plunger to 'squeeze' the contents. We apply the same force to each plunger. Will the cylinder with the larger radii lose volume faster? Or will they be equal?
As part of an ongoing project I have been working on, I have been reading through J.J. Thomson's Cathode Ray Experiment. As part of his setup Thomson writes, "The arrangement used was as follows: — Two coaxial cylinders (fig. 1) with slits in them are placed in a bulb connected with the...
Hi everyone: I need the brain of an engineer if anyone out there cares to help. I have a masters in Math from UofT but could use some knowledge from the smartest people- Engineers, I am now an experienced builder and yes everyone, we need smart people doing construction too- my math degree has...
Hi PF!
If we have two concentric cylinders with Newtonian fluid between them, and the small cylinder is at rest and the larger cylinder with radius ##R## rotates at some angular velocity ##\Omega##, how would you calculate torque ##\vec{T}## on the outer edge?
My thoughts: ##\vec{T} =...
if i have two cylinders with same mass and radius placed over each other vertically and there is a motor inside the top cylinder welded in the cylinder itself, and connected to the bottom cylinder to rotate the bottom cylinder. assume it's the whole thing is resting on the ground and neglect...
Homework Statement
A thin hollow cylinder of radius a is surrounded co-axially by another hollow cylinder of radius b, where b>a. An electric current I flows through them (I is into the plane of paper (x) in outer cylinder and coming out of plane of paper (.) in inner cylinder). Find the:
a)...
I have been wondering about how Propane is stored in a liquid state at 12 bar in cylinders. If a cylinder of propane was connected to a cylinder of the same size that was not pressurised would the pressure then across the two cylinders be reduced to 6 bar and the propane possibly expand? If this...
Homework Statement
a cylinder sits inside of another fixed cylinder without friction and an internal force acts on the cylinder as shown in the diagram. Draw the normal force vector and write down the force and moment equations.
I drew in my normal vector to counteract the A force vector and...
I have a pipe holding liquid at 80°C. The outside atmosphere is -2°C.
The pipe gets a temperature gradient over the wall thickness. The outside fibers will thus restrain the inner fibers from expanding. I would like to know the increase in the inner dia of the pipe.
I have found temperature...