Questions tagged [flow]
The motion of fluids (gases, liquids and granular material).
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Effect of pipe size on water flow rate in municipal water system [closed]
i am expanding my house and the town is requiring us to increase the size of the water line from the street from 3/4 inch to 1 inch diameter.
intuitively i understand that a bigger pipe results in ...
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Why don't they use golf ball dimples on cars? [duplicate]
Just watched an episode of mythbusters where they proved that a car got better fuel economy with golf ball dimples. So why don't they use that on cars?
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Compressible fluid equation
We know the continuity equation of a continuum (in this case I want to discuss fluids, equation reference):
$$\frac{\partial \rho}{\partial t} + \nabla . (\rho u) = 0$$
where $\rho$ is the mass ...
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Will hot object near ceiling vent create more draft? [closed]
As in the picture, we have a room with vents at the bottom to let cold air in and at the top to let hot air out. Normally the air flow is limited by the temperature gradient (correct me if I'm wrong). ...
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Modeling fluid flow in extremely small pores (or channels) compared to the component
I want to model a non-wetting fluid flowing into tiny pores of a component using Navier-Stokes.
Just for you to visualize, say I have a 2D rectangular component of dimensions $L*W$, and within that ...
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Relation between Sherwood and Peclet numbers
What's the relation between Sherwood number and Peclet number for mass transfer in a rectangular channel with fully developed laminar flow?
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Meaning of Lagrangian and Eulerian descriptions of the fluid velocity field
This arose out of a homework question. I solved it and asked my professor about it, but I think that I disagree with the explanation that was provided to me.
Original Problem Statement
Consider a one-...
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Can someone explain 'virtual mass' in fluids in simple words (for a dummy/high schooler)?
so I recently came across the term 'virtual mass' and when I looked up more about it, it just gave me some stuff about fluid mechanics that I dont understand properly. My understanding of virtual mass ...
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How does placing a barrier in an open channel affect the channel depth?
Suppose you have an open channel with flowing water through it with a width $y$ and a the height of the water is $z$ at constant flowrate. If you were to place a barrier in the shape of a cuboid in ...
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Questions regarding the derivation procedure of the Karman-Howarth-Monin relation
I was reading the book "Turbulence" written by Uriel Frisch (1995) and got stuck in following the proof of the Karman-Howarth-Monin relation. Although there is already a thread about it, I ...
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Non-dimensionalisation of Navier-Stokes Equations [closed]
I am trying to numerically simulate a flow in which a fluid with kinematic viscosity $\nu=0.00001167$ m$^2$/s is injected into a cylindrical tube of diameter 0.00745m at a velocity of 45.9 m/s. Thus, ...
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How to add walls or other solid obejcts to Eulers equations? [closed]
I've recently started learning about the physics of fluids and I've found that euler's equations exist and that I can use them to compute the flow of fluids with zero viscosity. But I have a problem ...
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How can flows of gases at low Mach number have approximately constant density despite varying pressure?
The Wikipedia article on Bernoulli's Principle says:
In most flows of ... gases at low Mach number, the density
of a fluid parcel can be considered to be constant, regardless of
pressure variations ...
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Why does the water go from left to right in this question?
In this problem stated by Brilliant course in "Flow in pipes", the water flows from left to right without explaining anything:
My doubt is if I'm supposed to assume there is some greater ...
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The material time derivative of Jacobian of the deformation gradient
The key step in the derivation of Reynolds transport theorem is time derivative of $J$, the determinant of deformation gradient $F$. Its result says
$$\dot{J}=\frac{\partial J(\xi,t)}{\partial t}=\...
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Understanding definition of flux as a vector field
I'm reading about conservation laws in the book Mathematical Models in Biology by Edelstein-Keshet, and I'm a bit confused by the author's definition of flux. For context this is from section 9.3, ...
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Is there specific form of Navier-Stokes equation for which mass can cross bounding surface?
In my textbook, we learned that Navier-Stokes (NS) equations can be derived from Reynolds transport theorem where the control volume is assumed to be fixed. But when the control volume is moving, can ...
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Intravenous therapy - why does blood come out of my body once the fluid is depleted? [closed]
The other day I wasn't feeling so well so I visited a doctor. He recommended that I take a break and get intravenous therapy so I did. I laid on a bed and the nurse inserted a needle into my left arm ...
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Airflow on wing, simple force analysis
(Look at the picture)
Let's assume there is an horizontal plane impacted by diagonal airflow with components from coming downwards and ahead. If we say that the airflow is fully deviated by the ...
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Why does blowing air on wet bodies dry it? [duplicate]
Suppose I blow dry a region with some water on it. Would it dry it faster than otherwise? If yes, why?
I can give one qualitative reason against it, since the blow dryer is blowing room temperature ...
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Levi-Civita symbol in cylindrical coordinate
In a paper (LINDBORG, 2007, DOI:10.1175/JAS3864.1) it is said that the Levi-Civita symbol in cylindrical coordinate can be written as(eq.8):
$$
\epsilon_{3ik} = e_{\rho_i} e_{\phi_k} - e_{\phi_i} e_{\...
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Proof of Rayleigh's stability criterion for a rotating inviscid fluid using linear perturbation equations
This question is concerned with how to prove Rayleigh's stability criterion
for a rotating inviscid fluid. I can follow the details of the proof up to the
final line, but I cannot see immediately how ...
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Understanding Momentum Conservation of a Fluid in Control Volume [closed]
I am taking a course in Fluid Dynamics, and we discussed the conservation of momentum in class:
$$ \dot{M}_{out,x} = \rho u (dydz) u|_{x+dx} + \rho v (dxdz) u|_{x+dx} + \rho v (dxdy) u|_{x+dx} $$
I ...
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How do I define the mass flow rate and the source term of the continuity equation when mass depends on the spatial coordinate? [closed]
I am studying fluid dynamics. I have questions regarding the mass flow rate and the continuity equation.
Consider the inviscid incompressible fluid flow through a pipe in various moments as ...
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Do the Euler equations always converge to a steady solution if the boundary conditions are steady?
I'm considering the compressible euler equations without any heat addition, body forces, energy addition, etc. In other words, i'm using the following equations with the assumption of an ideal gas.
$$
...
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What path will air take to leave the space station?
Hi everyone,
lets say we have a circle shaped space station and there was an accident where we got a hole (hole A on the picture) on a station and now most of the station is vacuum except for one ...
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What is the difference between Lagrangian and Eulerian description in Plasma?
I'm going to study plasma characteristics by using Particle-In-Cell (PIC) method and I know that plasma has fluid behaviour and can also consider as particle behaviour also. To understand a basic of ...
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How is the Reynolds number derived(my derivation is wrong)?
I'm a HS student so please dumb it down.
I'm looking into the Reynolds number of a sphere sinking in a fluid, here's what I got.
Inertial drag force = 0.5 * 0.47(CoefficientOfDragSphere) * rho(...
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Bernoulli equation and wind
Bernoulli equation is often used to explain how rooftops are blown off during tornados: the usual explanation is that the high speed of the wind il related to a lower pressure outside the house, ...
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How electric flux is analog to water?
The definition of electric flux is very often understood through the analogy of water. In the water example, water flux is easy to understand. Water flux is how much water flows per second in a given ...
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How to optimize the air pressure produced by a black pipe in the sun? [closed]
So, I'm thinking of ways of overdoing the passive aeration of my compost bin. Basic setup is a (60L) bin with a pipe with holes through the middle; air is supposed to flow into the pipe and its holes ...
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Reverse blood flow in an IV
When the IV drip for a patient is completed, the patient's blood will flow back.
This is apparently due to the pressure difference.
However, IV needles are inserted into veins in the direction of ...
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Open-ended pipe under water, pressure vs. flow when pump starts up
A pipe with a pump and two open ends is placed under water. When the pump is initially turned on, will the pressure at P_out and P_in initially rise/fall, but then stabilize as a flow of water V_flux ...
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Why is it called Heat Flow, if its units are not consistent with the definition of flux
Im studing Heat Transfer and I see how they refer to the heat flux as:
$\dot{q} = \frac{\dot{Q}}{A}$
And I've seen a flux is the quantity of something transpassing an area throught its normal ...
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Spatial coordinates in Eulerian specification of velocity field
The Wikipedia page summarized the relationship between Eulerian and Lagrangian specification as follows:
$$\mathbf{u}\left(\mathbf{X}(\mathbf{x}_0,t), t \right) = \frac{\partial \mathbf{X}}{\partial t}...
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Understanding notation for differential mass flow rate of a control volume
Was reviewing some notes on fluid dynamics, and the notes go as follows (conservation of mass for a qubic CV),
$$\frac{dm_{out}}{dt} = \rho u (dydz)_{x+dx} + \rho v (dxdz)_{y+dy} + (similarly,forZ) = \...
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Derivation of the exit velocity of water through a hole by force analysis at hole [closed]
As it is the setup with Torricelli's law, consider a hole (of negligible height difference) of area A at a height of h from the top of a cylinder filled with a non-viscous liquid of density $\rho$.
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Why are these balloons attracted when there is air blowing between them?
There are two party air balloons pending by their own weight through strings. When we blow strongly in the pipe, they move to approximate from each other as shown in the picture.
It seems that the ...
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Interchange of Lagrangian/material derivative and volume integral
In hydrodynamics there are two basic approaches. The first is the Eulerian specification where the coordinate system is fixed. In that case, the partial time derivative and volume integral operators ...
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Calculating the Lyapunov exponents spectrum from particle trajectories
I am simulating a forced, compressible 2D flow, that is turbulent and statistically steady, but not stationary.
I want to calculate the Lyapunov exponents spectrum from the trajectories of Lagrangian ...
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Airflow between two rooms (one hot, one cold) [closed]
Scenario —
It is night time and somewhat cold outside.
Room 1 (Bedroom): The window is slightly creaked open. I have a space heater going on continually heating room 1. One door is closed to the ...
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Time dependence in Eulerian description of fluid flow
In the Eulerian description of velocity field, suppose $x,y,z$ are fixed coordinates, the velocity at that point at time $t$ is $\mathbf{u}(x,y,z,t)$.
I am confused whether $x,y,z$ depend on time or ...
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Fluid compression against wall
A compressible fluid within a fixed cubic container is compressed at time $t=0$ by a spatially homogeneous force against one face of the cube. After a long time the mass distribution of the fluid ...
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Flow down an incline - Understanding boundary conditions
After working with some problems regarding flow, I came up to a similiar problem as the one presented here:
In solving the problem, we assume a laminar flow in steady state.
When using Navier-Stokes ...
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Is There a Field for the Overlap of Geometry and Physics? [closed]
What I mean is how the shape of an object affects it's physical properties.
I've been studying Marine Biology and there's constant talk of how a fish's shape determines how well it can swim but no ...
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How does air resist a piston?
The pipe is long, so the moving air never gets to circulate with the outside air. The piston starts off in the middle of the pipe, so it's pushing the air in front of it and pulling the air behind it. ...
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Can someone explain the creeping flow approximation?
Hello I’m a HS student so I apologize if my knowledge isn’t adequate enough, or if you have to dumb down concepts for me.
I’m writing an IB extended essay, and right now I’m trying to understand ...
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Why does Bernoulli's principle say higher water velocity is at a lower pressure? [duplicate]
I'm reading Khan Academy which says in this picture:
That P1 > P2 since P1's positive work is greater than ...
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In the derivation for Poiseuille’s formula for laminar flow through a cylindrical tube the speed parallel to the central axis increases. Why?
To start off with, I'm a first year undergrad and do not have much knowledge at all about fluids, and am simply working with context that has been provided to me from a lab script (of a lab I did not ...
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Cross sectional area of impinging streams (2 dimensional)
I am trying to calculate the cross sectional area of the impingement zone created by two equal, two-dimensional streams impinging upon one another. The attached diagram shows Stream 1 impinging with ...
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