Volume Definition and 1000 Threads

Hi, I am working on a leak testing project in which i have a leaking valve and I am trying to determine the volume of nitrogen leaking through the valve. Side A (upstream of valve) starts at 4000psi with an unknown volume. Side B (downstream of valve) starts at 0psi with a pressure contained...

Homework Statement A fluid flows through a pipe. The flow varies with time. We want to estimate the volume of fluid (##V##, in ##L##) that passes through the pipe between time ##t = 10 s## and ##t = 14 s## (i.e. we want to integrate the flow between these times). The available instrumentation...

I'm trying to practice for my final. The sample problem is: "Find the volume of the solid generated when the region bounded by y = x4and y = x1/3, 0<=x<=1, is revolved about the x-axis." To start, I set the two y equations equal to each to find the points of intersection. x4 = x1/3, : raise...

Homework Statement The problem and its solution are attached as TheProblemAndSolution.jpg. Homework Equations V(D) = ∫∫∫_D ρ^2 sinθ dρ dϕ dθ The Attempt at a Solution How exactly does the solution get cos α = 1/√(3)? Also, when the solution goes from the step with two integrals to the step...

I had an exam question where I had to find the volume taken up by a gas consisting of 32 grams of oxygen and 4 grams of helium at STP conditions. I ended up getting a supposedly incorrect answer of about 44.8 liters by finding the volume of both gases and adding them together. However, my...

Hey guys, can some of ou help me with this question: I need to calculate the volumic flow rate for air by using the ideal gas law. Things i know from the assignment: molarmass = 28,96 kg/kmol Pressure = 1 bar mass flow = 2 kg/s t in = 20 degrees celcius t out = 50 degrees celcius (sorry for bad...

difference between pitch and volume?if a sound is high pitched ,doesn't it mean that sound is loud?I don't think so because loudness is related with amplitude and pitch has to do with frequency,right?BUT please someone explain how can we say whether a sound is high pitched or loud just by...

Help with the following problem will be much appreciated: Find the volume of the solid obtained by rotating the region bounded by y=x^7, y=1, and the y-axis about the line y=−4

Hi everyone, I'm doing a simulation and need some help. A capillary which is closed on both ends with the length l (x=0 to x=l), with a radius R and the volume pi*R^2*l is dropped on a parachut at the time t=0 from a hight h above ground. At t=0 the pressure inside the capillary is p_i0 (this...

Hello everyone, I have a small question regarding mass and volume flow rates. It is shown in my book that there is a difference between path functions and point functions. I can understand why work or heat for example are path functions. However, I don't understand why mass transfer is also...

Homework Statement find the volume of teh solid based on the interior of the circle, r=cos(theta), and capped by the plane z=x. Homework EquationsThe Attempt at a Solution i have drawn out the circle of equation r=cos(theta). I think that since z=x and is above the region, we have to use the...

Hi, I've had an idea for a school physics project but I'm not sure if it will work. I want to measure the volume of water in a fixed shape container by passing an electrical current though it and monitoring how the resistance changes (with a potential divider circuit). My idea is that if I...

Hi, In chapter 12 of GSW volume 2, the authors remark, "spinors form a representation of SO(n) that does not arise from a representation of GL(2,R)." What do they mean by this? More generally, since SO(n) is a subgroup of GL(2,R) won't every representation of GL(2,R) be a representation of...

Homework Statement http://postimg.org/image/4a8sv6umh/ Why do the pressure forces due to p1 and p2 act in the same direction? Homework EquationsThe Attempt at a Solution I thought that, given the direction of the flow, the pressure force on the bottom and top would act in opposite directions

Homework Statement http://postimg.org/image/i4p19540z/ Homework Equations Resultant force on the control volume = Mass flow rate (Velocity outlets -Velocity inlets) The Attempt at a Solution I am just wondering if the 4cm is called depth, then what is the term for the "into the paper"...

Homework Statement Sand falls from a conveyor belt at the rate of 10m^3/min onto the top of a conical pile. The height of the pile is always 3/8ths of the base diameter. How fast is the radius changing when the pile is 4 m high? 3. The Attempt at a Solution V = pir^2 (4/3) -- volume of a...

Hi, I was just wondering, is there any way to estimate the vollume of a MOT (formed by 3 incoming and 3 counterpropating beams at a point where the magnetic field B=0) just by seeing its 2D projection (maybe through a camera) ? I could only measure its 2 dimensions in the picture: h=0.9 mm...

This is not a homework problem this is just a problem I was thinking about whether or not it would be possible to solve without cylinderical shells The region bounded by y=1/(x^2) x=e x=e^3 and the x-axis Rotated around y axis.. I did cylindrical shells and got 4pi and then wondered if I...

Homework Statement find the volume of the solid below the plane z = 4x and above the circle x^2 + y^2 = 16 in the xy plane Homework EquationsThe Attempt at a Solution This totally confused me. I didn't think the plane z = 4x sat above the xy plane. If that is true then there would be no solid...

Homework Statement This is part of the online tutorial I'm reading: http://farside.ph.utexas.edu/teaching/em/lectures/node49.html I'm so confused about the notation of Dirac Delta. It's said that 3-dimensional delta function is denoted as \delta^3(x, y, z)=\delta(x)\delta(y)\delta(z) in...

Homework Statement find the volume using spherical coordinates of the region bounded above by z=9 and below by z=sqrt(x^2+y^2) in the first octant. Homework EquationsThe Attempt at a Solution I found this volume using cartesian and cylindrical coordinates, so I know the answer I am looking...

Homework Statement I have a problem: So one tank is pressurised and then a pipe connecting this tank to a smaller one is opened so air can flow into the smaller tank. You then wait for the pressure to settle and read some pressure for each cylinder values. I need to find two ways to measure...

Homework Statement A rock is suspended by a light string. When the rock is in air, the tension in the string is 35.7N . When the rock is totally immersed in water, the tension is 25.9N . When the rock is totally immersed in an unknown liquid, the tension is 19.6N . Homework Equations Density =...

Homework Statement Steam is raised as saturated steam at 6 bar (g) and supplied to the first ( high pressure ) piston. The steam then exhausts from piston 1 at 3 bar (g). The steam is thought to expand adiabatically in accordance with PV^( 135 .1)= Constant Given the initial volume is...

Hi, I am wondering if anyone can help me out with this, I'm looking to create 9 ± 1 bar (131 ± 15 psi) of Entry Water pressure for 15-25 seconds to create a 25 ± 2.5 mL of volume as it pass through 7 ± 0.5 g (0.25 ± 0.02 oz) of finelyy ground material. If I were to pressurize an air chamber...

Homework Statement I need to find the volume of an egg with a shape described by: z = 1/2(x2 + y2) and z = 6 - x2 - y2 I am also given that the egg is 6cm in length.Homework Equations I roughly graphed the two surfaces. The first being paraboloid that opens up from the origin, and the second...

So in a cnc machine, the screw that drives the x,y,z axiis are called "lead screws". I am constructing a machine that displences fluid at percise volumes. It will be essencially a seringe with one way valves coming in and going out. To open the "check valve" it requires at least 1.5 psi. If I am...

Homework Statement Given T=572 ºF, pressure= 145 psi (g) using the steam tables and ideal gas law Molar Mass= 18 g/mol for water Find: Is the water vapour acting ideally? Homework Equations Ideal Gas Law: PV=nRT P is the pressure =145 psi (g) V is the molar volume n= mol R= Ideal gas constant...

Water density at 0 C is 990 kg/m3. Water density at 100 C is 1030 kg/m3 - 1 m3 of water "loses" about 4 % of its mass. Water expansion rate is 1.0002 for each 1 C increase in temperature - 2 % for the above rise from 0 C to 100 C.. How comes that water density decreases 4 % but its volume...

Homework Statement Deep sea fish experience a tremendous amount of atmospheric pressure. When you are at a depth of 2000 m in the sea, the pressure that you will experience is about 200 times atmospheric pressure (1atm=1.0×105N/m2)which you will experience on land. If you are lowering a...

Homework Statement An ideal monoatomic gas undergoes the following cycle: from 1.) V1 = 1m3, p1=2.5kPa, T1=200k to 2) V2=1m3, p2=7.5kPa then to 3)V3=3m3, p3=2.5kPA, and 4) back to 1). a. Sketch b. How many mole of gas are in the process? c. Give the missing temperatures at positions 2. and 3...

if a swimming pool has a volume of y^3-y and a height of y-1 then what is the length and width?

Homework Statement Hello everyone! I recently did an experiment, one of the parts was rapidly releasing some gas from a large vessel. We had previously increased the pressure, let it settle and then opened a value to let some out. I am wondering which thermodynamic process this approximates...

In my textbook, it says that pV=C (Boyle's Law), V/T=C (Charle's Law) and that P/T=C (pressure Law). The problem is that I cannot see how the first two equations combine to give the last one. If I divide the first equation by the second, I get that pT=C, which certainly is not the same as the...

Homework Statement There is a vessel with 10 Liters of Liquid Nitrogen. The normal pressure is 100 Psi. After a couple hours the pressure is dropped to 47 Psi because of leak in the vessel. How much of the Liquid Nitrogen did we lose/is left in the vessel? Homework Equations I'm really not...

Homework Statement Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. y=http://msr02.math.mcgill.ca/webwork2_files/jsMath/fonts/cmsy10/alpha/144/char70.png...

Okay, so this is quite hard to explain in words so I will use pictures. Suppose you have a Square with the length of W You also know the distance from the pink surface to the center of the square is X. The rotation of the square is theta. As shown in the picture above... So the problem is: Is...

Hey everyone, I was recently reading a paper on surface enhanced Raman scattering, and it mentioned that plasmons (and for that matter surface plasmon polaritons-where my interest lies) are sensitive to the surface to volume ratio of the structure. I can begin to understand intuitively with...

hi guys, this is the first time i post a thread. I have an issue on proving the scalar products for arbitrary momenta. Can anyone help me ? I always end up with N(p)N*(p')(D(L^-1(p)L(p'))_rowrow'detla I have been spending hours on proving this..still i can't prove it...

Homework Statement Evaluate: \int_{0}^{a} \int_{0}^{b} e^{max(b^{2}x^{2}, a^{2}y^{2})} dy \hspace{1 mm} dx Where a and b are positive. Homework EquationsThe Attempt at a Solution I'm having some trouble getting started with this problem, mostly because I am not very familiar with the...

I'm still confused on some of these volume problems, so please bear with me :) Homework Statement Find the volume of a reentry spacecraft nose cone that has a cross-section radius of (1/4)x2 taken x feet from the nose and perpendicular to the axis of sym. We are given that the length of...

I have a problem for a written assignment in my calc 2 class involving the volume of a cylindrical glass. A cylindrical drinking glass 10 in tall and 4 in in diameter is filled with water, and then tilted so that the water pours out until half the base is exposed. Write an integral to find the...

I have say a 250cm3 liquid with a solid dissolved inside filled in a container. If I pour 50cm^3 of that liquid in another container, would the number of moles of the solid inside the 50cm^3 container be different to the number of moles in the original 250cm^3 container? I've been told the...

Homework Statement Integrate $$\int_V \delta^3(\vec r)~ d\tau$$ over all of space by using V as a sphere of radius r centered at the origin, by having r go to infinity. Homework EquationsThe Attempt at a Solution This integral actually came up in a homework problem for my E&M class and I'm...

Homework Statement Hello, I am to find the volume of the solid given by x2 + (y-1)2=1 rotated about the y-axis. I may use either shells or cylindrical method. I attempted shell method, but am just learning this, still foggy and this is the one question that isn't coming out right. Homework...

I started reading Schwinger's first volume of the monograph: "particles, sources and fields" And I must say it's hard book to read, has anyone read it or wish to correspond here or on PMs about any thing that is being deduced in the book/s? Or am I the only bloke who read this book, besides...

Hello, I am looking at reactions that change volume during the reaction, for example ammonia synthesis N_{2} + 3H_{2} \rightleftharpoons 2NH_{3} where it is clear that the products are less moles than the reactants. However, I am thinking of a scenario in a plug flow reactor where this is...

Homework Statement Suppose that the volume transport associated with the wind-driven circulation's western boundary current (such as the Gulf Stream) is 50 x 10^6 m^3/second. Assume that this volume transport is carried in a current of uniform speed which is 50 km wide and 1 km thick...

Suppose that volume transport of an ocean current is 50 x 10^6 m^3/s. Assume that this volume transport is carried in a current of uniform speed which is 50 km wide and 1 km thick. What is the average velocity of the current? Suppose that the velocity of a current is 0.2 m/s. Assume that...

Homework Statement So we know Enthalpy under constant Pressure and Internal Energy under Constant Volume. By H = U + dPdV U= I + W W= -PdV under Isobaric conditions H = I -PdV + dPdV = U Enthalpy = Internal Energy _________________________________________ Under Isochoric Conditions W= O...