Questions tagged [fluid-dynamics]
The quantitative study of how fluids (gases and liquids) move.
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Equilibrium of water level in punctured bucket?
Would a bucket with a hole in the bottom being filled at different rates with water come to different equilibrium levels with in the bucket? Or would at any fill rate above initial flow rate of the ...
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Aerodynamic Problem in regards to a ping pong ball and an open hole tube
I have a ping pong levitation system with a ping pong ball in a tube being pushed by a DC motor fan (shown below) and I'd like to define a relation of the ball's height with the air velocity or ...
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2-D water jet on oblique plane
We have a 2-D water jet on oblique plane. We are ignoring gravity and want to calculate the force on the plane. The explanation I have been given goes as follows. We assume inviscid flow. Image is ...
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Stokes stream function derivation
I want to know a concrete derivation of 3D Stokes stream function.
The statement is, for example in 3D spherical coordinates (with symmetry in rotation about the $z$-axis), if
$$\nabla \cdot u=0\tag{...
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The material time derivative of Jacobian of the deformation gradient
The key step in the derivation of Reynolds transport theorem is time derivative of $J$, the determinant of deformation gradient $F$. Its result says
$$\dot{J}=\frac{\partial J(\xi,t)}{\partial t}=\...
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Discrepancy in Flow Velocity between Y and T Junctions in PVC Pipe System
I am currently working on a project involving a PVC pipe system for drainage, where I use a 3" main pipe with 25 secondary 1" drain pipes feeding into it. In my simulation, I have considered ...
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Stress Tensor Sign Convention
I'm hoping someone can clear up this confusion I have with the stress tensor. So here is what a stress tensor looks like as described by many authors:
I understand that the shear stresses acting on ...
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Suction and discharge heights
The following is a diagram from my Fluid Mechanics module's lecture slides:
The topic is Fluid Machinery where the focus is on studying pumps. My question is on the suction and discharge heights ...
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How did the author get these three expressions?
I am reading Nonplanar Relativistic Flow by Peter G. Eltgroth, Phys. Fluids 15, 2140–2144 (1972) doi.
I do not understand how the author arrives at expressions (12), (13) and (14) at page 2. Equation (...
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Why can't Rayleigh Flow admit total temperature ratios higher than 1?
In a constant area duct inviscid flow where heat is added, there are some well established results in the literature known as Rayleigh flow (https://en.wikipedia.org/wiki/Rayleigh_flow). In this ...
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Kolmogorov/Energy spectrum for turbulent boundary layer
Previously, I have calculated energy spectrum for 3D isotropic turbulent flow data which is equally spaced in all three directions and then to compute the energy spectrum, one performs Fourier ...
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How to calculate the maximum pressure that can be applied on a rubber wall sheet?
I am planning on building a water barrier made out of rubber sheet for a school project, however, I was wondering how can I calculate the maximum pressure that the rubber wall sheet can handle. Is ...
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Question on fluid jet profile in the limit of zero surface tension
While reading on the Plateau Rayleigh instability of fluid jets, the following thought came to my mind: suppose we have a fluid jet with zero cohesion forces (and therefore zero surface tension) ...
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Can you explain the perfume bottle with the Bernoulli effect?
Someone explained the perfume bottle with the Bernoulli effect:
squeezing the bulb over the fluid creates a low pressure area due to the higher speed of the air, which subsequently draws the fluid up. ...
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Estimating pressure and flow velocity at entry and exit points of pipe used for irrigation
I am trying to calculate exit pressure of water from a pipe where the water entry is approximately 100m below ground. I know the exit flow velocity of water (20 GPM or 1.2618 litres/second); this was ...
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What is the physical explanation as to why the kinematic boundary condition must hold at the free surface of a wave?
The kinematic boundary condition at the surface of a water wave is given as: "a particle on the free surface remains there always". This is then written as the material derivative of the free surface ...
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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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Kelvin-Helmholtz instability for a continuous fluid
I have a question about Kelvin-Helmholtz instability (KHI) for a continuous fluid.
I am new to hydrodynamics and I am currently working on a project about KHI.
For the past few days, I am looking for ...
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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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Relationship between flow and pressure gradient in a one-dimensional compressible fluid
Consider a one dimensional model (tube with diamter $D$) with a compressible viscose ($\mu$) fluid (e.g. air). further assumptions are
conduction and radiation are negligible
gravity's effect is ...
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How to compute the Reynolds number of a fluid without knowing the density?
I am running a simulation with LAMMPS involving a colloid suspended in a fluid. Simple shear is applied creating flow. My question is, how can I calculate the Reynolds number of the fluid given I don'...
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Why do water surfaces have persistent "average wavelength" patches?
Have you ever stood above a river or lake and noticed that the surface has visible "patches"? It looks like the surface has different average wavelengths in some areas, leading to the light ...
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Source for Nusselt number correlation for cooling sphere under forced convection
I've been trying to find a Nusselt number correlation for a sphere cooling in a forced gas cross flow where the sphere temperature is much higher than the free stream temperature.
I want something ...
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Physical significance of $\vec{w}$ $\times$ $($curl $\vec{v})$
I think if curl of a vector field $\vec{v}$ corresponds to an applied rotation, it's cross product with a velocity vector field $\vec{w}$ (say) should give something analogous to the resulting torque. ...
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Conservation of flow rate through pump (compressible flow)
I am confused about conservation of mass through a pump for a compressible flow.
Do we have conservation of mass flow rate between the inlet and the outlet, conservation of volumetric flow rate, or ...
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What is the meaning of screened potential? [closed]
I keep reading that it is supposed to account for the particle-medium interactions, but why do we need another potential besides the Coulomb one that includes the interaction between every particle in ...
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Scalar Flow Across a Small Area Element
I've just started reading the text "Vectors, Tensors, and the Basic Equations of Fluid Mechanics" by Rutherford Aris and I came across the following problem.
If $\rho$ is any scalar property per unit ...
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Capillary action strength questions [closed]
I've been studying capillary action, and I've drawn some conclusions about the behavior which surprised me, and I want to know if I'm understanding it correctly.
According to Jurin's law, the height ...
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How the velocity of the air is slowing down in different distances from a fan?
Is it determined completely by the air pressure and the temperature? Do I need to take into account also the geometry of the "air cone" of the fan or is it determined by the speed of the air ...
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How to calculate shear force on tubing wall?
For my application, I have water entering a small diameter (D1) tubing (a hypodermic needle tubing) with pressure (P1) and exiting into the atmosphere. The tubing is also very long with respect to it'...
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Intertial finite-size effects in fluid simulations
A gradient $\nabla \rho$ in the density field $\rho$ of fluids at thermodynamic equilibrium is suppressed at a rate given by $D \nabla^{2} \rho$, allowing to measure the diffusivity $D$ of the fluid ...
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Name of Equation $Q = \Delta P / R$
A very fundamental equation in understanding fluid flow is $Q = \Delta P / R$. When the flow is through a cylindrical pipe of constant radius, $R=8\eta L/\pi r^4$ can be substituted to give Poiseuille'...
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Why does air get trapped below water pouring into a glass?
The drinking-water-tap at my workplace has a low pressure continuous stream of water. When I pour water into a glass which has at least about (depth) 5cm of water in it, surprisingly large air bubbles ...
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External v.s. internal Reynolds number for cylindrical pipe
When calculating Reynolds number for cylindrical pipe, we were taught:
$Re=vd/\nu$, where $v$ is the fluid velocity, $d$ is diameter, and $\nu$ is kinematic velocity.
If you reorient the cylinder so ...
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Soap film retraction dynamics
Let’s say you have a planar soap film, which thickness increases linearly. If you burst it, the film will retrace and the retracing speed will decrease. How exactly does the velocity of bursting ...
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What is the physical significance of the cross product of curl of a vector field $v$ with another vector field $w$?
I think if curl of a vector field v corresponds to an applied rotation, it's cross product with a velocity vector field w (say) should give something analogous to the resulting torque. Am I close?
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Query regarding approach to solve a fluid kinematics problem [closed]
Question:
Someone is washing their car, using a nozzle similar to the one sketched in the figure. The nozzle is 9.91 cm long, with an inlet diameter of 1.07 cm and an outlet diameter of 0.460 cm. The ...
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Fluid in Containers with the same Volume but Different Dimensions
Considering two (significantly large) containers with equal volumes, one thin and tall, the other wide and short, both filled with water. If pipes with identical cross-sectional areas are used to ...
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Turbulence in Spacetime [duplicate]
Is it possible for the phenomenon of turbulence – eddys and vortices on many scales – to occur in spacetime in the context of General Relativity? For example near a Kerr black hole.
If not, what is ...
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Is the pressure in a pipe equal the pressure in the tank?
In my example, there is a tank which is holding gas under pressure. Connected to this tank is an output pipe. Assuming the pipe is the same diameter for the entirety of its length, would the pressure ...
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Capillary tube under atmospheric pressure
I found that capillary tubes in refrigeration system are tubes with very small diameter and very long length. Pressure drops down suddenly due to very small diameter of the capillary and length. The ...
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Apparent paradox: Mass flow rate decreases when I increase nozzle diameter
I do computational fluid dynamics for a living. I have recently been working on a case in which I simulate the flow (assumed 2D) of a compressible gas from a large chamber at pressure $P_1$, through a ...
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How do I interpret the energy per particle in the Smoothed Particle Hydrodynamics (SPH) formulation?
I'm working on a basic Smoothed Particle Hydrodynamics simulation. I figured I would start with an ideal gas with equation of state $p=K\rho$. However, in calculating the SPH equations of motion, we ...
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Would a candle in very high gravity blow itself out?
A candle creates an upward draft of hot air, without which the flame would be spherical. The buoyancy generated is proportional to the density difference as well as the strength of gravity.
Suppose a ...
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Adding mass to a bowl until it sinks [closed]
I've been struggling with this question.
A hemispherical bowl of inner radius $r$, density $ϕ$ and thickness $t$ is floating in a fluid of density $ρ$. The bowl is being filled with sand at a constant ...
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What does the notation $(k \cdot \nabla ) v$ mean? [duplicate]
I am reading a paper and it uses a notation I am not too familiar about. Although I saw it used elsewhere, I don't remember the meaning of it and I don't want to misinterpret it and realize after ...
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Would an object stop if the only force acting against it is air friction? [closed]
This question has bothered me for some time couple of years ago, so here is the main problem:
Suppose that an object of mass $m$, is thrown with horizontal velocity $v$ on a horizontal, frictionless, ...
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Can angular momentum be transported between scales in turbulent flows?
Consider a turbulent rotating flow. You are interested in its average features so you use the Reynolds-averaged Navier-Stokes equation. Now, conservation of angular momentum implies the viscous ...
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Why is that when drop oil in a pot of heated water, that the oil globules form near perfect circles?
I noticed this while I was cooking pasta:
The oil forms globules which viewed from top to down seem as perfect circles floating on the surface of water. How does this happen? Is there some elegant ...
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Question about fluid in free fall flow
Some time ago i saw this question
Why does water falling slowly from a tap bend inwards?
Which explains why the water flowing from a tap bend inwards while falling, using an inviscid flow model. ...