Questions tagged [fluid-dynamics]

The quantitative study of how fluids (gases and liquids) move.

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2 answers
3k views

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 ...
2 votes
0 answers
105 views

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 ...
1 vote
1 answer
195 views

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 ...
2 votes
1 answer
55 views

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{...
1 vote
1 answer
492 views

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}=\...
2 votes
0 answers
37 views

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 ...
4 votes
1 answer
2k views

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 ...
0 votes
1 answer
20 views

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 ...
1 vote
0 answers
89 views

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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0 answers
11 views

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 ...
15 votes
1 answer
967 views

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 ...
1 vote
2 answers
216 views

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 ...
1 vote
1 answer
20 views

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) ...
2 votes
1 answer
3k views

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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1 answer
476 views

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 ...
2 votes
1 answer
1k views

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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3 answers
906 views

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 ...
1 vote
0 answers
26 views

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 ...
0 votes
1 answer
980 views

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 (...
1 vote
2 answers
646 views

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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2 answers
627 views

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'...
3 votes
0 answers
82 views

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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1 answer
3k views

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 ...
0 votes
1 answer
54 views

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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2 answers
696 views

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 ...
1 vote
2 answers
68 views

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 ...
1 vote
2 answers
144 views

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 ...
1 vote
0 answers
34 views

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 ...
1 vote
1 answer
867 views

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 ...
0 votes
1 answer
1k views

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'...
1 vote
0 answers
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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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48 views

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'...
4 votes
2 answers
831 views

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 ...
1 vote
2 answers
2k views

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 ...
0 votes
0 answers
34 views

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?
0 votes
1 answer
45 views

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 ...
1 vote
0 answers
33 views

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 ...
2 votes
0 answers
43 views

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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2 answers
778 views

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 ...
0 votes
3 answers
796 views

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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0 answers
19 views

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 ...
1 vote
1 answer
65 views

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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0 answers
44 views

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 ...
-1 votes
2 answers
49 views

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 ...
0 votes
1 answer
68 views

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 ...
1 vote
2 answers
136 views

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, ...
1 vote
0 answers
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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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0 answers
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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 ...
0 votes
2 answers
622 views

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. ...