Questions tagged [flow]
The motion of fluids (gases, liquids and granular material).
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Why does hot water shoot out of my reusable coffee cup when I invert it during cleaning?
In an effort to keep my reusable coffee cup clean, before washing it I rinse it out and half fill it with near-boiling hot water (from an instant hot water tap at work), and invert it aimed at the ...
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Fluid-mechanics: Scalar field associated with velocity field
I have just started studying fluid mechanics (without a proper physics education :) and came across the following equation for incompressible steady-state fluids.
$$
\nabla\cdot \mathbf{u} = 0
$$
...
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Time Derivative of Fluid Map Jacobian (Page 10 of 'A Mathematical Introduction to Fluid Mechanics' by Chorin and Marsden)
Context and Notation
I'm self-studying from the book mentioned in the post title and I'm struggling to follow a calculation performed by the authors on pages 8 and 9. Please see the pictures attached ...
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Liquid or powder that passes through an orifice at a consistent rate
This I a really odd and specific question, and I'm not sure this is even where to ask.
A few weeks ago I thought about making a clock based on water flowing from an orifice. The obvious issue is that ...
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Electricity is a wave of electron. But my question is from where the electrons come and where do they go?
We know that electricity is a wave of electrons bit from where do they come and where do they go? Does electricity have mass?
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Volume of a horisontal cylindrical kerosene tank (2 methods) [closed]
Imagine a horisontal cylindrical container with a unknown amount of kerosene.
Volume = Area × Length
The Area of a circular segment is calculated
Area of Segment = Area of Sector − Area of Triangle
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Graph of velocity versus time [duplicate]
The figure shows the dependence of blood flow rate as a function of time through the aorta during a single heartbeat. Assuming that the distance of the heart to the brain is 30 cm, approximately ...
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No slip boundary condition in Hele-Shaw Cell
A Hele-Shaw cell can be used to visualise potential flow around a cylinder. See this image from Van Dyke Album of fluid motion with the z axis of the cylinder pointing out of the page:
Potential ...
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Analytical calculation for pressure loss for an external flow across a row of cylinders
I would like to know a way to find pressure loss of air flowing across a single row of cylindrical tubes of a Heat exchanger. The heat exchanger consists of a row of cylindrical pipes with rectangular ...
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Calculating water pressure
We've built a waterwheel to use in a small stream and are trying to calculate it's efficiency. The Hydropower equation goes as: KiloWatts = P * Q / 600, P being pressure in bars and Q being flow in ...
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Mass flow rate of fluid flowing over flat plate
When fluid flows over a flat plate, it forms boundary layer. Then velocity drops inside boundary layer. But how does mass conserved in this case?
Initially total mass is having constant velocity ...
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Building up pressure in the helix coil pump
My question is about building up pressure in a coil pump. Beginning at the scoop where the water pours into the hose and looking towards the center of the mill wheel, does the coil pump need to have ...
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Pulsed Fluid jets
While feeling my shower head, switched to "pulsed jet" mode, exert a higher force on my body as compared to a regular flow jet, I have wondered why a pulsed jet is stronger than a non-pulsed ...
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Do fluids flow from high pressure areas to low pressure areas? What theory explains that?
Do fluids flow from high pressure areas to low ones? Why ?
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What is the mathematical derivation for no diffusion term in the mass continuity equation of the Navier-Stokes/Euler equations?
In this post the fact that the mass continuity equation in a mixture of gases has no diffusion term, i.e.,
$$\frac{\partial\rho}{\partial t}+\nabla\cdot(\rho\vec{v})=0$$
has been discussed. ...
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Navier-Stokes equation viscosity term
I cannot understand how the term μ$\nabla^2(\vec u)$ is derived. Can anyone help?
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How does gravity affect the formation of vortices?
Context: I understand the axis of vortices can form in any direction (like underwater used by fishes). However, in large vortices in water bodies, for example, in a closed water bottle, the centre of ...
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Inaccurate flow rate measurements of an engine diesel fuel due to change of its viscosity
I am measuring the volumetric flow rate of a diesel fuel using "Turbines" flow meter, both in the supply and return fuel lines of an industrial diesel engine (Caterpillar 3512B – coupled ...
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Why does air not flow backwards in Jet Engines in the combustion chamber? [duplicate]
In jet engines air is taken in, compressed and then fuel is injected and then ignited forcing the turbine to spin powering the compressor. What I am curious about is why the combusted air isn't forced ...
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Potential flow involving a sphere
I am currently working on a problem involving a sphere being dragged through a fluid at constant velocity.
Working in the rest frame of the sphere I'm told the potential is of the form:
$$\frac{k\cos(\...
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Continuity and Bernoulli's Equation in a vertical pipe with different cross sections [closed]
Consider the following situation where the amount of water that goes through a cross section $A_1$ per second is the same as it goes through $A_0$ (just continuity) and is always constant:
I setup ...
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Is incompressible fluid flow isentropic?
I was asked to verify the relation $\partial_t(\nabla \times v)=\nabla \times (v \times (\nabla \times v))$ of an incompressible fluid flow, where $v$ is the flow velocity. I was looking at Landau and ...
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Molten metal flow due to high currents
It is mentioned in the book "Ampere-Neumann Electrodynamics of Metals", Peter Graneau, that Carl Hering in 1923 operated furnaces by passing high currents through the molten metal pool. He ...
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Meaning of potentials in Helmholtz decomposition
I am trying to understand the meaning of the potentials $U$ and $A$ arising in the Helmholtz decomposition of a vector field $\vec{V}$:
$\vec{V} = \nabla U + \nabla \times A$
Let's focus on the curl-...
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Calculating hole size on the side of a pipe
I have a fluid channel through which a fluid with known properties (viscosity, density etc.) flows at a known velocity with a known pressure and temperature and mass flow rate. The external pressure (...
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Can we use Darcys flow equation through porous media for pipe flow?
I am looking at flow in a pipe with no solid matrix. Therefore, the porosity is always equal to one. For such a set-up, I can use the Direct Numerical Simulations (DNS) on a 2D framework.
However, a ...
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Water flows from a hose with or without nozzle with different speeds
My question is about the speed of a water jet from a garden hose without and with nozzle. I know the answer as experimental findings and ask for the physical reason.
I calculate with Bernoulli along a ...
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Adjusting the airflow through plane using Venturi effect etc
Lets pretend we got an infinite plane in an air filled space. We want to move air or some other gas from one side of the plane to the other.
In this plane, there is one hole, and you got some kind of ...
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Calculation of velocity of water flowing along inclined plane by applying Navier-Stokes theorem
Assume that water flows along a inlined plane through a circular irrigation waterway.
The inclined plane has its bottom length $B=50 m$, and has height $H=10 m$. So the
angle of inclination $\theta$ ...
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Questions about Hagen-Poiseuille Equation: Non-constant Pressure Drop?
The Hagen–Poiseuille equation states that the fluid flow rate in a tube is proportional to the pressure gradient across that tube. Mathematically, it's stated here:
$$\Delta p=\frac{8\mu LQ}{\pi R^{4}}...
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When the mass flux is constant, why does $ v d\rho = - \rho dv$?
I'm reading about mass fluxes and I came across when the mass flux is constant $$ j = \rho v$$ then the following equation is true $$ v d\rho = - \rho dv$$ What does that last equation even represent? ...
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How do the macroscopic observables $T$, $ρ$, and $P$ change in an ideal gas after flowing through a turbine?
I’m trying to better understand how turbines effect the flow of gas and gain or expend energy in the process. It’s easy to understand with incompressible fluids as all you need to know is the pressure ...
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Depressurization formula for multiple holes with varying outside pressures
I'm working on a simulation that should with relative accuracy simulate the flow of air/pressure in a system of rooms (on a space ship).
I found http://www.spaceacademy.net.au/flight/emg/spcdp.htm ...
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Why is the unsteady Bernoulli equation inconsistent when applying at different points? I've probably misconceptualised the theory
Unsteady Bernoulli equation:
$$\frac{P_1}{\rho}+\frac{{v_1}^2}{2}+gz_1 = \frac{P_2}{\rho}+\frac{{v_2}^2}{2}+gz_2 + \frac{f_hg}{\rho} +\int_{1}^{2}{{\frac{dv}{dt}}ds}$$
I've attempted to apply the ...
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Taylor Couette flow of a charged fluid in a magnetic field
Suppose we have a fluid comprised of charged particles. This fluid, is kept in the annular region between two concentric cylinders, and the inner cylinder is made to rotate with some angular velocity $...
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Why do we feel cool after switching fan? [duplicate]
Please see that my actual question is not similar to this: Why do we feel cool when we turn our fans on?
Suppose I switched my fan on. The air particles start moving. Since, their kinetic energy ...
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How to calculate the flow rate of a convection current?
If a convection current is streamlined (no turbulent flow) and you know the heat energy input, how would you calculate the flow rate? If it's not possible to calculate with just the heat energy input, ...
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How much heat energy would translate into the kinetic energy of a convection current in water if the flow is streamlined?
Assuming that we have a mechanism by which a convection current can be perfectly streamlined, how much of the heat energy absorbed by the water would translate into the kinetic energy of the ...
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Why does the shape of water flowing down from a squared orifice looks like a chain?
Hello I'm a high school student in Taiwan. My classmate and I are doing a project about the shape of water flowing down from a squared orifice, something like this video.
We wanna know is there a ...
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How to calculate the required pipe diameter to achieve a certain mass flow rate at a certain pressure? [duplicate]
Assume incompressible fluid with known density. Any gravity effect can be ignored.
I need to have a certain mass flow rate through a pipe. The pressure of the fluid arriving at the pipe is known (...
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Deducing the velocity field of wind from the motion of plants
I am developing a project for the subject of fluid mechanics and I had a question. The project we want to develop involves using wind and a small hill as a giant wind tunnel. The hill is filled with ...
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Why do we use cubic fluid elements when deriving fluid equations?
Recently I've been delving into fluid dynamics but is frequently troubled by a conceptual issue that I could never get my head around with.
To derive fluid equations, we have to separate fluid into ...
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Fan in a sealed box
Let's say that there is a helium balloon attached to a large, sealed box. The box is off the ground and there is neutral buoyancy. The box + balloon are simply floating in air, not moving.
Inside the ...
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Warm air syphon to cool down greenhouse
I'm thinking about a very energy efficient way of controlling temperature inside a greenhouse when it's too hot.
The goal is to use the syphon effect in order to draw hot air from the top of the ...
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Velocity gradient in a liquid
When we consider the motion of fluid in terms of many thin layers sliding over each other , we say that layer at a top of a layer forces it to move forward while layer below a layer forces it to move ...
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Fluid Momentum Equation
I have a equation regarding the fluid equation of momentum. What exactly is being accelerated/acted on?
My understanding is this:
The momentum is equation (at least in my textbook) is derived by ...
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Analytical equation for time to empty a pressurized water tank [closed]
I need help determining an equation for time to empty a pressurized tank. I have a sealed water tank pressurized with nitrogen, where the cross-sectional area of the water inside the tank is and the ...
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Physics behind the falling of water in the bucket which is intially being rotated at some angular velocity
A horizontal wheel with light buckets fixed on its circumference revolves about a frictionless and vertical axis. Water falling from a fixed tap with a uniform rate of mass $m$ per unit of time is ...
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"Contradiction" Between 2D Steady-State Continuity and Navier-Stokes Equations
I am looking for some clarification on the incompressible, 2D, steady-state, cartesian Navier-Stokes equations for flow through a straight cylinder (flow aligned with the $x$-axis, so $u_y =0$), with ...
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The local and average Nusselt number in a square cavity
I am in the process of programming the local & average Nusselt number in a left vertical wall but my Matlab script gives me inappropriate values and it doesn't change with changing of Rayleigh ...
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