Fluid Definition and 1000 Threads

in class we derived the following relationship: $$\frac{1}{V}\frac{dV}{dt}= \nabla \cdot \vec{v}$$ This was derived though the analysis of linear deformation for a fluid-volume, where: $$dV = dV_x +dV_y + dV_z$$ I understood the derived relation as: 1/V * (derivative wrt time) = div (velocity)...

I am a First Year Undergraduate Physics student. Which will be the best textbook for me to study properties of matter (Elasticity) and fluid mechanics? I prefer a better theoretical understanding.

Can someone please tell me a basic and easy-to-understand example of Residual in CFD? Thank you

Let's consider the Taylor power series of a function on real numbers. Some of them represent elementary functions, and some of them represent special functions. The special functions cannot be expressed via finite combination of elementary functions on real or complex numbers. Now, take some...

My attempt to try and convert book equation to FE manual equation in 3rd pic Fx = QpV1 + P1A1 - QpV2Cosa - P2A2Cosa Fx = P1A1 - P2A2Cosa+ Qp(V2Cosa +V1) P1A1 - P2A2Cos(a) - Fx = -Qp(V2Cosa +V1)

Hi, In a text describing solution to linearized shallow water equations, I am not able to move forward. It's a 1 dimensional shallow water setup. There is a steady state (velocity) and (height of free surface). On top of this steady state there are u' and h' as disturbances. The goal is to...

I have to estimate the Reynolds number of the fluid flowing around a blade but I only have one detail: the length of the blade is 0.66m. I have no idea how to do it and I got to submit the assignment in a week, I am desperate for help here.

Stress tensor for the fluid is ##T_{ab} = \rho u_a u_b + P(\eta_{ab} + u_a u_b)##, whilst the equation of motion (assuming the system is isolated) is given by ##\partial^a T_{ab} = 0##. So I tried$$\begin{align*} \partial^a T_{ab} &= \partial^a \rho u_a u_b + \partial^a P(\eta_{ab} + u_a u_b)...

why is ro = 0.2255? Thank you

Hi, Can anyone let me know if I had done this Q correctly? Thanks for any help!

(this problem is slightly modified from the original problem.) There is a contact force(friction and normal force) between the wedge and the walls of the container and there is a fluid thrust acting on the side of the wedge in contact with the fluid( this force is normal to the slanted surface...

This is actually right at the start of another derivation, but I can't understand how the author gets the formula for ##q##. So the discharge per unit thickness is the circumference of the circle, multiplied by the velocity at that point (at ##r##)? I thought the formula for flow rate was...

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Hey everyone! Here is the problem I have been tackling but did not end up with the correct answer The extra red arrows I have labelled in myself and called these distances h1,h2 and h3. I assumed the pressure to be the same at levels A & B, hence i have established expressions for both of...

According to one explanation, the left hand acceleration terms of Navier Stokes equations are the called the inertial terms. If you were to balance forces on the fluid particle, they would have to be equal and opposite to the forces on the right hand side (pressure gradient, viscous, and body)...

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...

Consider a cylindrical container filled with an ideal fluid. Let it rotate at a constant angular speed (about the symmetry axis which is oriented vertically) and let the fluid be in the steady state. Lets just talk about a horizontal slice so that the gravitational potential is constant. The...

That's a good question, i am not sure how the water in liquid state will influence in the motion, but i imagine that can not exert any torque, i would say in the first case: Hollow sphere inertia moment: 2mr²/3 + ml² (2mr²/3 + ml²)θ'' = -mglθ (1) In the second case, otherwise, we will have...

I have few conceptual doubts in fluid mechanics. Here is the one I will ask first. I want to understand the force direction acting on the solid liq interface during fluid flow, Let's say a fluid is flowing in a pipe. Now the fluid applies a shear stress at the walls of pipe in the direction of...

For the wing of a plane, as an example, I think that the circulation around the wing due to faster flow on the top is balanced by the circulation of a vortex which is formed off of the tail. Since the greater speed on the top is necessary for the lift, would that also mean the turbulent flow...

Pressure gradient normal to the local flow direction balance the centrifugal force associated with the curvature of flow.. Which centrifugal force inertial or "reactive" centrifugal force?

What forces act at air particle at curved streamline, looking from inertial and non-inertial frame of reference? (show free body diagram)

Here i added a page from my fluid dynamics book where it shows particle model for deriving the equation. My question is why pressure is more at stream side aka 'positive "s" direction'.I would expected more pressure on the other side because for example when you trying to push a rigid object or...

Hello everyone, in one of my projects I am dealing with the following problem: We have a tank filled of water. If we assumed that a focused ultrasond beam hit the water perpendicularly to the surface. How can I calculate the displacement of the water surface? In particular, I am interested in...

Hello all I am trying to understand the forces that are acting on a pipe bend when a fluid is passing through it. I have been given the following diagram:- The bit i cannot get my head around is why does P2A2 point the way it does i.e. down towards the left shouldn't is point the opposite...

Hi! I want to use Euler's equations to model a 2 dimensional, incompressible, non-viscous fluid under steady flow (essentially the simplest case I can think of). I'm trying to use the finite difference method and convert the differential equations into matrices to be solved using MATLAB. I set...

Let’s say we have a unit volume of some fluid in a column on the Earth surface. Let ##\mathbf F## be the gravitational force that acts on the unit volume of the fluid. Consider a small volume element ##\Delta \tau## in the fluid and let’s assume it to be a cuboid with dimensions ##\Delta x##...

I am learning about hypersonic flow now and there seems to be a lot of discussion about the effects on oblique shock as the Mach tends to be very large. I was wondering what happens to the normal shock as the Mach number tends to be high and I can't seem to find anything about it. Is it because...

In Landau-Lifshitz Volume 6 Fluid-Mechanics the following problem is given Where the equation of continuity is given earlier:As is Euler's equation:And the equation of continuity for entropy:I don't understand how this conclusion was reached. I can understand the derivation for the equation of...

I figured out stokes law equation but I am unable to proceed further

My first post here! I have calculated everything i need, except the thickness of the second layer dZ*, therefore i can't solve V3/V2=(R2ˇ2)/(R3ˇ2) Trying for days now, i would appreciate any help.

A reservoir supply tunnel transfers water from a high level storage reservoir via a 200mm diameter pipe to a lower intermediate reservoir. The total height difference between the free surfaces of each reservoir is 76 m. The pipe is 700 m long and the coefficient of friction, Cf is 0.009. The...

Hi PF! I'm running a two-phase simulation, which takes a long time to run. The simulation is simply a partially filled tank being drained in zero gravity, and the tank is a little smaller than a mailbox (~ 160 X 40 X 40 mm). Before running the simulation I would like to know if my mesh is...

The question :- My attempt :- The confusion that I am having is that to get the required form of the equation of motion, I had to approximate ##\theta## to be small to get ##x=l\theta## so that I could get the acceleration and the velocity. But, I had to leave the ##sin(\theta)## in the...

So, I was studying about general properties of matter and topics like surface tension. I came across the phenomenon of water rising along a glass plate like in the picture. I looked for some mathematical interpretation of this on the internet and in some books. [![enter image description...

Hi sorry about the way I've posted I'm new to this site. Anyway basically I've been set this question which should be attached to this post, I have attempted to do this question but I'm having trouble in forming an equation in the first place. I'm unsure where to start, I understand I need to...

Let me preface this by saying I have no background in physics or any of the above other than hours and hours of reading. Could someone explain why (if a method was developed) we couldn't use EFA as a thrust system for a rocket? My reasoning is instead of using fuel to fight gravity and push...

By Fluid Mechanics I mean the mechanics of fluids, both at rest and in motion. I'm unable to find introductory books on Fluid Mechanics which contains everything in itself, for example I downloaded Fundamentals of Fluid Mechanics by Munson, Young, Okiishi, Huebsch and I don't know why but I...

This is my first thread here, so let me know if I didn't adhere to a format i was to follow. I'm in the middle of a project depicting the change that an oscillation of fluid inside a drinking straw faces depending on the viscosity of the liquid. For reference, this is exactly the same example...

Summary:: In need of help determining the exhaust velocity of a rocket nozzle given temperature and propellant molar mass Greetings and salutations! My name is Robert DeVries, world builder extraordinaire. I have come with questions in search of answers. So for the last few days I've been...

Hi, I am trying to find out Force on a rigid body when it is completely inside a fluid with density p, i.e. the body is completely drowned in the liquid and then another liquid is pushed into the container with different density 'r' (such than r > p). Thanks.

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The current of fluid is the vector J^{\nu}. In free-falling laboratory due to Equivalence principle holds the know Continuity Equation J^{\nu}_{, \nu}=0, where the ordinary 4-divergence is used. Latter equation was derived in Minkowski spacetime, thus the Christoffel Symbols are all zero for...

Hello everyone, I want to ask something. Can we design a tube that can completely resist the flow of a fluid? Maybe using either viscosity or surface tension approach? Thanks

Can anyone suggest me a Fluid Mechanics textbook? I am currently in High School in my Junior Year. I am looking for a entry-level textbook so I will be able to solve I.E. Irodov's Hydrodynamics section. (My Mathematics is quite strong)

According to this definition I am unable to understand why does surface tension acts tangentially to surface of contact of liquid and capillary tube. And is the force of surface tension balancing the adhesive forces which lead to capillary rise OR it is the reason behind the capillary rise?

Hi, I am a high school student doing a project on fluid dynamics and need to understand the relevant maths so that I can understand how to apply the mathematics of fluid flow (particularly air flow around a cylinder). I have a basic calculus understanding and need to understand the navier...