Volume Definition and 1000 Threads

Homework Statement: Base of solid is the region bounded by graphs ##y= \sqrt x## and ##y=x/2##. The cross sections perpendicular to the x-axis are squares whose sides run across the base of the solid. Find volume of solid. Homework Equations: - As stated above, I will want to calculate the...

Summary: I wish to understand if bubble formation in milk while being sloshed around, or the formation of separation layers will affect both the pressure and volume of the air head space above the milk Hi all : ) I have a basic physics question and sorry if its a very silly question: Let's...

I need some help defining a tally volume. I want a volume bounded by three surfaces, but when I do an initial plot the volume is in red dashed lines. I know that each cell needs to be uniquely defined, but I am not seeing how my volume is not unique. The cell in question is cell 200 in the code...

Consider a continuous charge distribution in volume ##V'##. Draw a closed surface ##S## inside the volume ##V'##. Consider the following multiple integral: ##\displaystyle A=\iiint_{V'} \left[ \iint_S \dfrac{\cos(\hat{R},\hat{n})}{R^2} dS \right] \rho'\ dV' =4 \pi\ m_s## where...

I am working Organic Rankine Cycle. I studied a number of research papers and in most of them, they have calculated outlet volume flow rate from the turbine or expander, but have not mentioned the calculations. So here are the available data; Pin = Turbine Inlet Pressure, 2.5 MPa Pout = Turbine...

Let $R$ be the region $\left\{(x, y) : 0 \leq x \leq 1, 3^x − x − 1 \leq y \leq x\right\}$. Find the volume of the solid obtained by rotating $R$ around the line $y = x$.

Since ##\vec{R}/R^3 = -\nabla(\frac{1}{R}) = \nabla^\prime(\frac{1}{R})##, the standard form of the Biot-Savart law for volume currents can be re-written as: $$\frac{\mu_0}{4\pi}\int\limits_{V^\prime}\frac{\vec{J}^\prime (\vec{r}^\prime)\times\vec{R}}{R^3}d\tau^\prime =...

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 ...

I want to know that how can z=$$ \sqrt{1-x^2}$$ ever represent a surface? It graphs a curve in the x-z plane and the triangle lies in x-y plane so how can they contain a volume, they are orthogonal to each other. I have attached awn image which is drawn GeoGebra for the function...

Given a cube ABCD.EFGH whose side length is 4 cm. If the point I, K, and J is dividing EF, FG, and BG to two equal lengths respectively, determine the volume of pyramid D.IJK! I think I can work out the pyramid's base area by deriving for the formula of equilateral triangle area. What I can't...

So the other day, I was pouring beer from a can to a mug and I obviously know the flow rate depends on the height of the beer from the bottom of the can (fluid level in the vessel), angle of tilt and I think time as well. I was wondering how to best model the PDE to describe such a phenomenon (...

Here's how I approached it. We know the total mass of the cloud, it is given. Let's call it 'M'. We can also find out the mass of a single hydrogen atom from its atomic weight. Let's call this 'm'. Then N = M / m is the total number of hydrogen atoms in the cloud. The temperature (T) is given...

I set up an experiment where I put a fixed quantity of water in a cylinder fitted with a movable piston. I slowly add heat to the system, as expected both the temperature and the volume will increase but the volume will not increase significantly (steep line), until some point where some gas...

Mass = 0.12kg Initial temp = 500°c = 773K Initial pressure = 0.8 MPa = 800,000 Pa Final volume = 90L R = 287 Jkg^-1K^-1 1) Initial Volume V=mRT/P 0.12 x 287 x 773 / 800,000 = 26,662.12m^3 2) Final Pressure P2 = P1P2^1.2/V2^1.2 800,000 x 26,662.12^1.2 / 90 = 1,816,095,330 Pa = 1,816 MPa 3)...

Dear Experts, We compute Cv for gases using the idea of equipartition principle and degrees of freedom. In case of a diatomic molecule, there are minimum 3 degrees of freedom (at very low temperatures) and maximum 6 degrees of freedom one of them being vibrational (at high temperatures. Does it...

I have a compressed pure gas at a specific temperature and volume. (T1, V1) It suddenly (adiabatically) expands until it's at ambient pressure and a specific temperature. (P2, T2). Given: T1, V1, T2, and P2, I want to find P1 and V2. There's a great example in wikipedia which is almost...

i'am trying to find the ratio between the volume of the nucleus for the hydrogen atom to its electron , but when i try to use the previous equations it seems wrong as i'am getting a low number like if the electron is bigger . i used the the classical electron radius as it was the only thing that...

Hi, Can anyone guide me with an approach to find the liquid volume of CO2 when a gas of 4.14x10-6 m3 at -20°C and 1 bar is compressed to liquid at 25bar, without change in temperature?

I've set up a simple experiment to look at the ideal gas laws. My experiment is relatively simple in that I have a metal tube which is capped on one side. I am then pressurising the tube with air to 100 psi and locking it off. My thought is that as the pressure increased, with volume held...

Problem Statement Assumptions: a. The universe is finite. That is, it is (approximately) a 3D boundary of a 4D hyper-sphere of radius r. b. [The following is based on https://arxiv.org/pdf/1502.01589.pdf as discussed in the thread...

I am reading D. J. H. Garling's book: "A Course in Mathematical Analysis: Volume I: Foundations and Elementary Real Analysis ... ... I am focused on Chapter 1: The Axioms of Set Theory ... ... I need some help to clarify an aspect of Garling's definition of a partial order...

The expected shape of the deflected roof will look like a pyramid with a water height of 'h'. I am having a hard time to find the a formula for the new shape. Can some one provide me some guidance please, will I have to use calculus to find the volume for this particular shape?

My volume integral is... $$\pi\int y^2 dx$$ My surface area integral is... $$2\pi\int y \sqrt {1+x'^2} dy$$I'm fairly sure the variable of integration on my volume and surface area integrals has to be the same, is that right? But when I change the variable in the surface area integral to...

So, I was thinking that the total volume of the cube divided by the number of atoms (or rubber balls) should intuitively give the average distance between each ball. What I did was: N = number of balls D = avg distance between balls (2.5)^3 / N = D (2.5)^3 / D = N D = 2.8 - 2 * radius (I'm...

I would like to ask a question on whether there is a proportionality between volume of a balloon, and the time it takes to deflate. I have conducted several balloon hovercraft experiments. I need to find the relationship between the amount of air pumped into the balloon and how long the...

Wet basis 0.75mol C4H10 Requires 4.875 mols O2 Produces 3 mols of CO2 and 3.75 mols of H2O 0.1mol C3H8 Requires 0.5 mols O2 Produces 0.3 mols of CO2 and 0.4 mols of H2O 0.15mol C4H8 Requires 0.9 mols O2 Produces 0.6 mols of CO2 and 0.6 mols of H2O Theoretical oxygen= 6.3mol +10% excess...

In a human body we have two relatively similar structures -pulmonary...

By Volume: Butane 0.75x6.5= 4.875 moles of O2 Propane 0.1x5= 0.5 moles of O2 Butene 0.15x6= 0.9 moles of O2 Total O2 4.875+0.5+9= 6.275 moles Air required 6.275/0.21=29.88 moles/m^3 With 10% excess air 29.88x1.1= 32.868moles 1 mole fuel:32.87 moles of air By Mass: CO2 Moles...

Hello, I'm trying to calculate what is the effective volume of a molecule of N2 in the most precise way possible (I'm a high school student so "in the most precise way possible" is probably not that precise considering my lack of advanced mathematical knowledge). What I want to know is, if I had...

The final result must be V=2π2α3 Hint says we must use the dV in the spherical system (dV=r2sin2θdrdθdφ) as well as the equation of the three-dimensional metric ds2= c2dt2 - a2[ dr2/(1-kr2) +r2(dθ2 +sin2θ dφ2) ] For a closed universe we know k=+1 and with dt=0 My problem is, I don't understand...

Hello everybody, I am currently working on an experiment investigating the formation of planets. I have a vacuum chamber in which dust particles form bigger agglomerates through accretion (sticking together). From the imagery I can see those agglomerates which are build up by smaller...

So, I am casually sifting through a chapter in a thermodynamics textbook talking about the multiphase process that pure substances go through. I understand how the P-v and T-v diagram works and that out of the three properties (specific volume, temperature and pressure), two of them are...

Homework Statement a Basin contains water , a beaker is put upside down to a depth of 3m inside it , if the volume of the beaker is 250 cm^3 . and its C.S area = 200 cm2 calculate the length of the water column which rises inside the baker , supposed that their is no air leakage from the...

Homework Statement The charge of uniform density 50 nC/m3 is distributed throughout the inside of a long nonconducting cylindrical rod (radius = 5.0 cm). Determine the magnitude of the potential difference of point A (2.0 cm from the axis of the rod) and point B (4.0 cm from the axis). a . 2.7...

how much rotation needs to start volume flow for a adjustable variable pump?.I get it 5pi from the book. Is there any rule that it needs such rotation to start volume flow. From where I get it?I think that pump designer does not give the information on the manual.

Find the region bounded above by the line y = 4, below by the curve y = 4 - x², and on the right by the line x = 2, about the line y = 4. The Correct answer was: 32pi/5 I integrated from 0 to 2 of pi [(4)² - (4 - x²)²] and got the answer of 224pi/15. I tried every other possible ways and...

Homework Statement 1) Calculate the density of states for a free particle in a three dimensional box of linear size L. 2) Show that ##\int f \nabla g \, d^3 x=-\int g \nabla f \, d^3 x## provided that ##lim_{r \rightarrow \inf} [f(x)g(x)]=0## 3) Calculate the integral ##\int...

I have a calculus 2 midterm coming up and given the exam review questions, this seems like this question can potentially be on it. I've tried to look it up, but I always find the famous painters example, which I don't find satisfying.

I'm trying to figure out this volume integral, a triple integral, of a 9-variable function. 3 Cartesian-dimension variables, and 6 primed and un-primed co-ordinates. After the volume integration, the un-primed co-ordinates will have been gotten rid of, leaving a field function in terms of...

Homework Statement A volume of highly purified water is added to dried primer to create 100uM stock solution. How many ul of water needs to be added to 26.6nMoles of dried primer in order to create uM stock solution? Hint: You may need to convert primer value from nMoles to uMoles. Homework...

Trying to figure out how much air can (or would) flow through an air intake on a vehicle. I have a rectangular intake opening that is 13.52 square inches, the vehicle is traveling at 60 MPH for 1 hour. Obviously more air is being forced into the intake due to the speed but I can't sort out...

Homework Statement Find the volume between the planes ##y=0## and ##y=x## and inside the ellipsoid ##\frac{x^2}{a^2} + \frac{y^2}{b^2} + \frac{z^2}{c^2} = 1##The Attempt at a Solution I understand we can approach this problem under the change of variables: $$x=au; y= bv; z=cw$$ Thus we get...

I’m trying to derive the infinitesimal volume element in spherical coordinates. Obviously there are several ways to do this. The way I was attempting it was to start with the cartesian volume element, dxdydz, and transform it using $$dxdydz = \left (\frac{\partial x}{\partial r}dr +...

I am trying to calculate pressure losses. I've attached an image to show what I mean. Starting out tank 1 is 92.8 litres at 155 psi and when the shutoff valve is open the volume goes from 92.8 to 192.8 and so I thought the pressure would drop by the same factor that the volume increased by so...

I was assigned an example problem today and i can do the math, look at my tables and get the right answer no problem. What i want to understand, is why when specific volume increases for r134a, that it means its supper heated? My given value for sv was .1384m3/kg which is above the .09 in the...

Homework Statement A typical human cell is approximately 10 μm in diameter and enclosed by a membrane that is 4.2 nm thick. To simplify the calculations, model the cell as a sphere. 1) What is the volume of cell? (in μm^3) 2) What is the volume of cell membrane? (in μm^3) 3) Percent cell volume...

Homework Statement For the reaction below, the constant pressure heat of reaction is qp = −3256 kJ mol−1 at 25 °C. What is the constant volume heat of reaction, qV , at 25 °C? 16 CO(g) + 33 H2(g) ⟶ C16H34(l) + 16 H2O(l) Enter your answer in kJ mol−1, rounded to the nearest kilojoule...

Homework Statement [/B] Find the equation of state of a solid that has an isobaric expansion coefficient dV/dT = 2cT - bp and an isothermal pressure-volume coefficient dV/dp = -bT (Assume the solid has a volume Vo at zero temperature and pressure. Enter a mathematical equation. Use any variable...

Can an expanding balloon be considered a control volume?