Volume Definition and 1000 Threads

Hello everyone. I have to determine the tank volume and power requirement of a tank. The teacher has done it the following way, however, I don't understand the process.

At first, I inverted the function(##f^{-1}(x)=g(x)##) and calculated the volume through the integral: $$V=\pi\int_{0}^{4}[4-(2-g(x))^2]\ dx$$ but then I questioned myself if the same result could have been obtained without inverting the function. To find such a strategy, I proceeded as follows...

Hi, I was recently reading through Systems Kinetic Modeling notes and am struggling to understand the concepts of total volume of distribution and total body clearance. As far as I understand, the total volume of distribution ## V_c ## is the "volume of the compartment into which the...

First i calculate n: 500000 g / 32 g/mol = 15625 mol Then I calculate V1: (100000 Pa * V1)/288.15 K = 15625 mol * 8.31 J/mol.k so V1 = 374.145 m^3 I calculate V2: 100000¨ Pa * (374.145 m^3)^1.3 = 300000 Pa * (V2)^1.3 So V2 = 160.703 m^3 W = ((100000 Pa * 374.145 m^3)-(300000 Pa * 160.703...

Volume of hot air ballon V=((4/3 pi R^3)/2) + (1/3 pi h (R^2 + r^2 + Rh) = 2956.24 m3 Balloon: R=9m h=15m r=1m m = 750 kg H = 5000m T = 373 K p1 = 101300 Pa p2 = 50650 Pa M(air) = 0.029 kg/mol F = mg - 7350 N

Hey there! for this problem i try to use the combinate gas ecuation. First of all the values its necesary to have it in absolutes: 70 F = 527.67 K 90 F = 549.67 K The ecuation looks like: (200 psig) (1 ft^3)/529.67 K = (0.3 InHg) V2/549.67 K I can eliminate "K" but not psig with InHg for obtain...

First, I calculated the inverse of ##y=e^x## since we're talking about y-axis rotations, which is of course ##x=lny##. Then, helping myself out with a drawing, I concluded that the total volume of the solid must've been: $$V=\pi\int_{0}^{1}1^2 \ dy \ +(\pi\int_{1}^{e}1^2 \ dy \ - \pi...

Summary:: Control volume question that has a brine solution entering a tank and mass accumulates over time. Hello, I'm currently struggling with a control volume approach question that has a brine solution entering a tank. I get to a point where I have a first order differential equation. I...

Is this right go confused with the 37 degrees Q) pV = Constant pressure of a gas is ‘10’ (kPa) and the constant ‘37 degrees celcus’ = ‘0.6’, calculate the volume that the gas. pV = C C/p = V 0.6/10 = C V = 0.06

So I basically took the integral and ended up with W=PVf-A(Vf^3)/3-PVi+A(Vf^3)/3 so 65.7=72*5.3-A(5.3)^3/3-72(2.4)+A(2.4)^3/3 But when I solve for A I get the wrong answer of 3.179 when the answer is suppose to be 5.05. I've checked my calculation with an algebra calculator too...

Hi, I have an LG K8 Android 2018. I am having trouble with the volume in conversations. I tried changing different settings without success. Any suggestions on how to raise the volume level during conversations? Is it a physical issue of wear and tear of the microphone, an issue with settings...

The surface area of the sphere is 4πr^2. dr/dt is given as 3cm^-1. dS/dt=dS/dr*dr/dt Differentiating 4πr^2 is dS/dr= 8πr dS/dt=8πr*3 dS/dt=24πr Given that r=5 dS/dt=24π*5=120 π The volume of the sphere is 4/3πr^3, differentiating which is dV/dr=4πr^2 dV/dt=dV/dr*dr/dt dV/dt= 4πr^2*3...

Hello! I am having trouble with this problem I found online,it was listed under the "easy" category yet I am somehow not seeing the trick. First I converted the V into m^3 so that V = 0,015 m^3,than I converted the hPa into Pa so p = 101300 Pa and now I used the fact that ##p1V1 = p2V2 ## We...

(a) i sketched a quarter of a sphere centred at x=0 , y=2 , z=0 (b ) ∫ ∫ √ (4-x2 - (y-2)2) dx dy with limits 0 < x < 2 and 0 < y <4 (c ) i converted to spherical polars and took the integrand as 1/r2 . the volume element is r2sinθ drdθd∅ This leads to the triple integral of sinθ with...

Sadly, I don't even know what I don't know. Could somebody generate a ballpark figure of how many moles of hydrogen you might have in a sphere 2 meters across, 75F and roughly 16 psi? Even with all that information I'm clueless. (I'll now resume twig-fishing for termites...)

What are we missing in this experiment? Thanks

I tried integrating the 4-volume of a 4-hemisphere, that is, $$\int^{R}_{0} \frac{4}{3} \pi r^3 dw$$ (along w-axis), since ##r## is proportional to ##w##, where ##r=\frac{w}{R} R##, ##r=w##, thus the integral becomes $$\int^{R}_{0} \frac{4}{3} \pi w^3 dw = \frac{\pi}{3} R^4$$ The volume of a 4-D...

Is there a smart or systematic way to determine the volume of a polyhedra with a fair amount of symmetry?

Ca(HCO3)2 -> CaCO3 + H2O + CO2 First I evaluate the moles of calcium carbonate (don't mind the units, just to save time) ##\frac {80.0}{40,00+12.01+3*16,00}= 0,799 mol## From the equation, correct me if I am wrong , one mole of CaCO3 is proportional to one mole of CO2, so from this I can...

First of all, I don't think the question was clear enough. Therefore, I had to assume they are referring to the volume of the unit cell. V=a^3, side length a aBCC=2R√2, aFCC=4√3/3R %change=(VFCC-VBCC)/VBCC I thought this was right until I checked with others who did this: so the only...

Homework Statement:: Oil Lamp ( Paraffin help ) Relevant Equations:: Not sure what to write here HI folks, I'm trying to make an oil lamp from an old Vodka bottle. The bottle is the usual 750ml and is in a skull shape bottle. ( maybe you know it ) Anyhow I have all the materials and almost...

If the question was asking for (dry) volume, how would you do that?

What are the number of significant figures of 225.0? I think it is 4, but the solution says it's 3. Also, is the significant figures of molar volume at STP (22.7 L/mol) considered? Thanks.

How much does a typical solid shrink when cooled from room temperature to absolute zero. I can't solve this myself because the coefficient of linear thermal expansion varies with temperature

Some notation: - the difference between the heights of mercury, which is effectively the height of the mercury in the open end of the tube is ##h_{diff}## - the volume of gas inside the sealed off end is ##V_{inside}## - the volume of gas when let outside, "normal volume", is ##V_{outside}## -...

Summary:: Can anyone help me with this 3d Volumetric Strain and Volume Change. The is question is attached as a document below with the question and my attempt at the answer All questions and attempted answers are in the attached file below

Spatial slices of the Robertson-Walker metrics are maximally symmetric so they must have a constant curvature. Is it true that in three Riemannian dimensions that a constant curvature scalar determines whether the volume is finite or infinite? Carroll seems to have given a counter-example for...

Hi, If I had a volume of Brown's gas at 20°C / 1atm, what would the expected volume [of the resultant steam] be immediately after it was ignited? Thanks! Bob

Homework Statement:: How to control volume by hovering and scrolling anywhere in Mac Menu Bar Relevant Equations:: none Hi, 
 I use both Mac's and pc's. Mac's are great but here's one thing I can do in my pc's that I have not been able to find how to do in my Mac. 
 In my pc's (Win7, Win10)...

In this explanation we need to involve the Dirac delta functions(maybe) but I clearly have a difficulty in understanding it can some one explain me the whole concept of constant or non constant volume charge density.

We know that we humans have roughly 5 liters of blood circulating in our body. The volume also may be varying. We also know that its volume is tightly regulated and multiple organs are involved in it. My question is, how we calculated that we have 5 liters of blood? Is it an approximation or...

Hello folks, a recent theoretical discussion with a materials engineer has left my head spinning, this sort of thing is beyond me but I am curious if any of the clever folks on here could solve my problem. I want to find the Force and Energy applied by my Indenter within the following...

Can you check it for me please that I have done it right or not ? Thank you in advance.

The question is: how do I know the increase in the minor and greater radius, given just the ratio of the heights?

Can you check it for me that I done it right or not ? Thank you in advance.

I'm assuming the way to go about it is to integrate in spherical coordinates, but I have no idea what the bounds would be since the bottom edges of the square pyramid are some function of r, theta, and phi.

Can you please help me ? I have tried to do it but I end up getting the wrong answer.

the equation of a parabola that is obtained by taking a cross-section passing through the center of the paraboloid is ##y = ax^2## breaking the paraboloid into cylinders of height ##(dy)## the volume of each tiny cylinder is given by ##\pi x^2 dy## since ##y = ax^2## we have ##\pi (y/a) dy##...

The question is: If the compression ratio of car engines is increased by 10% (from 10 to 11), estimate the volume reduction in annual CO2 emission. Assume there are 30 million cars each consuming one cubic meter of fuel annually. The question is looking for a rough estimate for an answer. I...

Hi, I tried to do this question in two different approaches one of them was using the equation PV=mRT where I got the right answer which is 4.305 m**2. However, I tried using this Density = Mass/Volume, where I substituted Denisity= 1.225 and Mass equals 5kg to get the volume as 4.08. Can...

Made an attempt at this Q but I'm unsure on how to do part c) or if I had even done part a) and b) right What difference does it make to the volume flow rate equation when the valve goes from open to closed? Any help would be appreciated! Thanks

As summarized.

The answer to the primary question in the summary is the first step in seeking an answer to a more complicated question I plan to post in a separate thread later. This more complicated question is a consequence of the thread...

Am I right to assume that the equivalents for phenyl magnesium bromide would be 3 (magnesium, bromobenzene and ether (?)) And the number for 2-phenyl-propanal 1 as it says "...was added to 2-phenylpropionaldehyde" which is the same thing as 2-phenylpropanal? I don't know if I understood this...

Robert Boyle's law states that at constant temperature, the pressure of fixed amount ( i-e number of moles n) of gas varies inversely with its volume. Mathematically, it can be written as $p ∝ \frac1V $(at constant T and n) $\Rightarrow p = k_1 \times \frac1V $ where $k_1$is a proportionality...

Hello. How does a bullet propell inside a bore? What determine its velocity? I read that a bullet in cal .44 propelled by black powder from a 3” barrel is as powerful as a .25 ACP, however with a longer barrel, the velocity increase significant. With a 8” barrel a .44 black powder bullet is as...

A recipient (cube) of 1m³ is filled of small spheres, there are for example 1000³ spheres inside the recipient. There are also 1000³ elastics that attract the spheres to the bottom. The elastic are always vertical. One elastic for each sphere. One end of the elastic is fixed on a sphere and the...

Hi, just wondering how I would calculate the volume of this wedge? see photo attached

This is a long post with limited amount of physics in it (but it is a physics question, so hopefully it is allowed). I am a scientist but trained as an ecologist (PhD) and despite my long interest in physics, my knowledge of it remains rather rudimentary. Apologies for that, in advance. I am...

1#Find the area of the region, enclosed by: 2#Find the area of the region bounded by: 3#in the region limited by: find the solid volume of revolution that is generated by rotating that region about the x axis