$$\begin{equation}
0 = ({\rho}_m + P_m)u^{m}_iu^{m}_j + \frac{4}{3}{\rho}_ru^{r}_iu^{r}_j
\end{equation}$$
where i,j = 1,2,3 and different. That is the off-diagonal elements of the tresstensor for matter fluid and radiation fluid.
The energy conditions imply that
##\rho_m + p_m > 0## and...
If a fluid is compressible, will the density be directly proportional to the pressure?
(I'm sure there's a limit where an increase in pressure stops producing a change in density, but I'm talking about for more "normal" (smaller) amounts of pressure.)
Homework Statement
A solid sphere of aluminum (density 2.7 g/cm^3) is gently dropped into a deep ocean. (The density of ocean water is approximately 1.03 g/cm^3.) Calculate the sphere's acceleration at the point where it is completely submerged into the ocean. As the sphere drops deeper...
Homework Statement
Small part of fluid which in the moment ##t=0## was at the point ##(X_1,X_2,X_3)## in some other moment is in the point ##(x_1,x_2,x_3)##. Where
x_1(t)=X_1
x_2(t)=X_2+\sin \pi t\sin \pi X_1
x_3(t)=X_3
We know that the piece of the fluid is in the t=0 in line which connects...
Homework Statement
Which of the following phases is capable of permanently withstanding a force perpendicular to its surface?
A. Gas
B. Liquid
C. Solid
D. All of the above
Homework Equations
The Attempt at a Solution
I understand that the answer is D.
However, what does...
Hi, I get two contradicting sections of the book "Concepts in Thermal Physics":
Earlier in the section they used the grand partition function to derive the mean occupation number ##<n_i> = -\frac{1}{\beta}\frac{\partial ln Z}{\partial E_i}##
Later in the section, they said ##<n_k> =...
Homework Statement The Euler equations for ideal compressible flow are given by
\partial_t v + (v\cdot \nabla)v = g-\frac{1}{\rho}\nabla p \\
\partial_t \rho + \nabla \cdot(\rho v) = 0
In my book these are written in terms of the small-value expansions \rho = \rho_0 + \delta \rho, p = p_0 +...
I am working on this project for Diff eq's and I seem to be stuck. i think I am messing something up but I need a fresh pair of eyes to show me where it is.
imgur: the simple image sharer
imgur: the simple image sharer (this is the same page as ^ just scrolled down)
imgur: the simple image...
I was reading an example problem in my fluid mechanics textbook that talks about the difference between liquids and gases. I am not sure why this is the case, if someone can explain that'd be great.
So the problem is about two coaxial cylinders that rotate. There is a fluid in the gap between...
High school student here trying to learn fluids. This is not a homework question, just a concept that I am trying to grasp but can't. The picture below is in my book:
The book tells me that the acceleration of the fluid after experiencing the decrease in cross sectional area is due to a...
I'm trying to understand some fluids concepts that don't seem to be covered in very much detail in introductory fluid mechanics textbook. Specifically, these topics include pumps (gear pumps mainly) and shear-thickening fluid behavior in pipe flows and in said pumps. Any ideas on good...
I do not understand why B is not true. There is much greater fluid molecules above point A, and given P = density x g x depth, pressure should be greater at point A...making B true. But then again if u use poiseuilles' law for nonideal fluids you see that in order to keep flow rate Q constant...
Hello all,
I'm choosing my classes for spring semester and am unsure about which of these two classes I should pick (topic title). My major is electrical engineering and I want to hopefully go to graduate school at my current school for their micro-systems nano-systems program listed here (...
Let's say you have a stream of water leaking out of an elevated barrel, and we ignore the effects of air resistance and assume water is incompressible.
So, the lower (and faster) the waterstream falls, the more it will contract. Sure, you say, that's because of the chemical forces between the...
If I were to rotate a basin of fluid at a given angular speed, I would have two acceleration components.. one gravity and one centrifugal. What would happen if I added gravity to both components of acceleration (from tilting the basin). The fluid should move to one side correct? But, what if...
Homework Statement
(1.1.10) The diagram below shows a U-shaped tube. The fluids in the tube are glycerine (blue
shading) and mercury (gray shading). The height of the glycerine column on the left side of the
tube is h1 = 5.00 cm. The density of the mercury is 13.53 g/cm3
.
(a) What is h2...
I did BA Maths at Cambridge with a First Class back in 2009-12, worked in i-banking for one year (partially because I need to fund my graduate study) and will continue with a Master in Maths at Cam this coming autumn. My courses had been (and will continue to be) concentrated in Fluid Dynamics...
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
Theres a atmospheric tank with a goose neck vent on the top and also an inlet pipe [a diameter 2 inch schedule 40] on the top. There is a compressed air line [from a 50 psi compressor] going into the inlet. The pressure inside the tank should not be above 2 psi. Size the...
Homework Statement
The fluid in a manometer tube is 40% water and 60% alcohol (specific gravity = 0.8). What is the manometer fluid height difference if a 50kPa pressure difference is applied across the two ends of manometer?
Homework Equations
P1-P2=50 kPa
P3-P2=(ρgh)alc
P3-P1=(ρgh)h2o...
Homework Statement
In a plane onset flow of 4 m/s, a source of strength 13 m2/s per metre is located at the origin (x=0, y=0) and another source of strength 18 m2/s per metre is located at (x=3m, y=0). Calculate the gauge pressure at the point (0, 2m), Take ρ =1.2kg/m3
Homework...
Hi all!
I was wondering what will happen if you have two aqueous solutions with the same refractive index and you mix them? Would you end up with the same refractive index as the both solutions or will the refractive index change?
In my case I'm using a aqueous 40% wt. potassium...
FLUIDS: Potential Flow Question -- URGENT HELP NEEDED
I need to submit this soon and I am way behind in this topic. I would appreciate it a lot if you can help me out figure the answer.
Homework Statement
In a uniform onset flow of 7 m/s parallel with the x axis, a source of strength 19...
When using bernoullis and momentum, gauge pressure is only used in calculations, any atmospheric pressure is generally omitted, i could understand if, for example, using bernoullis, pressure 1 and pressure 2 were both atmospheric, therefore they would cancel out, but when one pressure is...
I recently learned about the pressure of the atmosphere against the human body. It just so happens that this force is in equilibrium with the human body, so we do not feel any pressure. Although if we fly an airplane, we do.
This got me to thinking, what of the blood in our veins? Does...
I was thinking about the rotational kinetic energy of fluids the other day and I realized that I have a huge gap in my knowledge of physics. Why doesn't rigid body rotational kinetic energy (KE = 1/2*I*ω^2) not apply to fluids or deformable bodies (it should at least be proportional to that...
Homework Statement
"Suppose that a liquid has an appreciable compressibility. Its density therefore varies with depth and pressure. The density at the surface is ρ0
(a) Show that the density varies with pressure according to ρ=ρ0ekp where P is gauge pressure at any depth and k is the...
A cube of osmium with a volume of 166 cm³ is placed in fresh water. The cube's apparent weight is 35.0 N. What is the density of osmium?This is what I did:
I converted force to mass by : 35 N / 9.8 = 3.57 kg
then changed the 166 cm³ to m³ which is : .000166 m³
After that i divided the mass...
Homework Statement
"Texbooks that describe perfect fluids are often a little unclear about what is being assumed. It may not be immediately obvious why can't the pressures be different in different directions? Let's examine this. Suppose Tαβ = diag(ρ,(1+ε)P,P,P) . Show that if one performs a...
1.A tube of radius 5 cm is connected to tube of radius 1 cm. Water is forced through the tube at a rate of 10 liters/min. The pressure in the 5 cm tube is 1×10^5 Pa. The density of water is 1000 kg/m3. Assume that the water is nonviscous and uncompressible.
What is the velocity of the water in...
I have a lot of confusion and I hope someone can help me in clearing my doubts.
considering a right cylindrical container with a liquid filled in ,if we take two points, y1 and y2(near the bottom)
1) first of all I thought that pressure inside a fluid arose because of the weight of the fluid...
1. Homework Statement :
The expressions you obtained for acceleration and drainage time (equations 3 and 4 in the manual) both contain the following factor or something equivalent: (D/d)^4-1
In the lab, we will be dealing with a bottle with a diameter around 9 cm. A typical diameter of the...
Homework Statement
Oil and water are put in a cylindrical container. They can rotate at various frequency around the rotational symmetry axis.
Consider gravitational and radial forces to find the form of the surface between the fluids.
no friction, no mixing
the surface has the form of a...
Homework Statement
In a cylindrical container (with radius R) there are 2 fluids (separated like water and oil, fluid 1 lies under fluid 2) with given volumes V_i, given densities ρ_i.
You let them rotate with respective angular frequencies ω_i.
There is no friction.
Find the functions of...
I want to test several different fluids on an inclined planes and figure out which one is the most slippery. What would be the most scientifically sound way to measure this?
If i have a syringe used to pump blood through a set of tubing that becomes smaller and smaller, the pressure will obviously increase until it gets to the smallest diameter of the tubing. However, if I create a piece that expands when the blood flows through it, will this decrease the pressure...
Homework Statement
Water is flowing from a container through a 50mm diameter hole at 36 liters a minute. Calculate the flow rate in L/s and the flow velocity through the hole.
Homework Equations
The Attempt at a Solution
flow rate all i did was 36L/60s to get 0.6 L/s
flow...
1/2/3. Homework Statement and equations
Hi everyone,
So, I have a fluids problem to do and I think there may be a slight typo or maybe I am missing something. The image of the problem is attached.
So, the only problem I have is how L is defined. Since L is defined from below the zero...
Hey, so my situation is a positive displacement pump churning out 30gpm. Theres a bunch of pipe losses that I can deal with, and then a long 1.5" pipe with 8 possible outlets (you can screw on a hose). When one hose is attached the pressure is a we will say P1 (read from a gauge on the 1.5"...
I've known this fact for a long time and have thought about an explanation for it for just as long. I've observed its effects such as in the shower: as the water flows down it moves the air with it causing the curtain to move inward into the shower. It just seems that with a moving fluid that...
Hey all, I apologize if this question has a really obvious, basic answer, but I've done a lot of searching and haven't come across anything that explains it satisfactorily for me.
So, I know that Pascal's principle underlies the workings of the hydraulic lift, and I know that while force is...
Using the metric $$ds^2=-V^2 dt^2 +g_{ab} dx^a dx^b$$, where $$g_{ij}$$ is the Riemannian metric of the constant t-surfaces, and V is the gravitational potential, show that Einstein's equation $$G_{ij}=8\pi T_{ij}$$ for perfect fluids reduces to the system
$$D^a D_a V= 4 \pi V( \rho +3p)\\...
Homework Statement
Two cylindrical pipes both carry an ideal fluid (zero viscosity) in laminar flow. Pipe A has radius Ra = 2 and flow velocity Va = 8cm/s. Pipe B has radius Rb = 4cm and flow velocity Vb = 4cm/s.
A) Calculate the cross section of pipe A and pipe B.
B) Calculate the rate of...
Homework Statement
You are designing an underwater maintences schedule for an offsore oil rig. The Divers work at a depth of 15m and the seawater Denisty is 1027Kgm^-3. They Are know to Consume 130L of air at the ambient temperature of 10C over the time to do the job. Atmospheric pressure is...
Problem Statement:
Blood is a pseudoplastic fluid that has a variable viscosity at 37 °C that depends on the percent composition of hematocrit and plasma. It will usually range between 3 x 10^-3 to 4 x 10^-3 Pa s. A small sample of blood is tested in a viscometer and the following results are...
Hi.
I am working on visualization of flow with thermal infrared camera. As it is known, water is not transparent for IR spectrum of light, so you can`t watch phenomena that are occurring "inside". You can only see things that are occurring on the interface of water and wall.
I have been...
Given two objects of identical density and weight, one is floating on water and the other is floating on saltwater. Is the magnitude of buoyant force acting on the object the same in the two situations? From my thinking, it seems that the weight of the object in the the two situations should not...
Hello, I'm new to PF and looking for some guidance!
I'm currently investigating a simple experiment involving two different capacity syringes filled with water and then applying a constant force to see their maximum verticle squirting height; My basic apparatus is basically this;
We have a...