Questions tagged [flow]
The motion of fluids (gases, liquids and granular material).
1,533 questions
2
votes
1
answer
63
views
Trouble understanding the boundary conditions for the Blasius boundary layer equation
In Section 7.2.1 of Bergman's Fundamentals of Heat and Mass Transfer, there is a derivation of the Blasius equation
$$ 2 \frac{\mathrm d^3 f}{\mathrm d \eta^3} + f \frac{\mathrm d^2 f}{\mathrm d \eta^...
- 137
1
vote
1
answer
75
views
How to find pressure in pipe contraction for compressible high speeds flow?
Air with density ρ, absolute pressure P1 flows through a pipe with velocity v₁ and cross-sectional area A₁, and then enters a contraction with area A₂. A1/A2=10. We need to determine the pressure P₂ ...
- 1,004
0
votes
2
answers
115
views
Does the no-slip boundary condition contradict Bernoulli's equation here?
Imagine inviscid, incompressible steady-state fluid flow around a cylinder like in the diagram below so that it flows around the cylinder symmetrically about the x-axis:
According to the no-slip ...
- 121
0
votes
2
answers
501
views
Which orientation of a truncated cone will drain faster?
A container is shaped like a truncated cone (frustum) as in cylinder-like shape where one end has a larger radius than the other. Both orientations contain the same volume of water, and the outlet ...
- 11
2
votes
3
answers
91
views
Velocity of efflux when the area of hole is equal to the cross-sectional area of the container
From the equation of continuity and Bernoulli's theorem a formula can be derived for the velocity of efflux when it flows from a hole of area $a$ such that the cross-sectional area of the container is ...
2
votes
1
answer
237
views
Alternate statement for Liouville's theorem: Can you say that the relative velocity between any two representative points is zero?
So Liouville's theorem basically says the local density of representative points stays constant or that the flow of representative points resembles that of an incompressible fluid. Can you then say ...
- 31
0
votes
0
answers
27
views
Regarding movement of representative points in phase space (Liouville's theorem)
Okay, so I'm studying statmech from Pathria.
Liouville's theorem talks about the flow of representative points in phase space. These representative points represent each and every microstate ...
- 31
3
votes
0
answers
76
views
Squire’s article “The Round Laminar Jet”
I was reading the article "Round Laminar Jet" by H.B. Squire about the Landau jet (for which I can't provide free access, sadly). It models a fluid being discharged into a space containing ...
- 31
-1
votes
1
answer
68
views
Does it make sense to open both windows if outside airflow seems to be moving in one direction?
I am trying to figure out if it makes sense to open both of the bedroom windows in the below scenario. Both windows swing out from the center and stand perpendicular to the wall. Other rooms in the ...
- 1
3
votes
1
answer
82
views
Low Mach number expansion
I'm reading the article "Lattice-Boltzmann Simulations of Particle-Fluid Suspensions"
by A. J. C. Ladd and R. Verberg.
In section 5.4 ("Limiting Cases"), the authors note that in ...
- 69
2
votes
0
answers
79
views
Do fluid streams attract each other ("pinch" or bundle together)?
Do fluid streams (air coming out of two jet engines, one on each wing; hot gas coming out of multiple rocket nozzles, etc.) attract one another ("pinch" or bundle together)?
cf. History of ...
- 2,221
0
votes
2
answers
95
views
Pressure conflict when priming a siphon: 1m water column vs. 20cm tank level
I have a question about fluid dynamics that is causing some confusion for me. It relates to the pressures at play when priming a siphon.
The Setup:
Imagine two identical tanks, Tank A and Tank B.
...
- 111
1
vote
0
answers
84
views
Confusion in Pitot stagnation pressure $(½)ρV²$ with momentum-flux pressure $ρV²$: control-volume derivation and instrumentation implications [closed]
When a Pitot tube faces a uniform incompressible flow we obtain the usual Bernoulli result for stagnation pressure:
$p_{0} - p_{\infty } = (1/2)\rho v_{\infty }^{2}$
so the Pitot gives the dynamic ...
- 41
0
votes
0
answers
49
views
Continuity equation vs Poiseuille's law [duplicate]
In a pipe of diameter 10cm that narrows into a pipe segment of diameter 5cm, my understanding with the continuity equation is that flow remains constant in both segments of the pipe. However, ...
- 61
1
vote
3
answers
268
views
Understanding flow rate with equations
I am having trouble understanding the continuity equation alongside Poiseuille's law. I would like to mention a scenario of a syringe with diameter 4cm pushing saline solution into a tube of 1mm ...
- 61
3
votes
3
answers
1k
views
Why does a free-falling liquid jet contract while an upward jet expands, from a molecular perspective?
I’m trying to understand this strictly from the atomic/molecular level, without relying on equations of continuity. Consider this situation:
A vertical water jet is released in free fall (downward).
...
- 486
0
votes
3
answers
134
views
Pressure gradients vs. Bernoulli: what drives blood flow through a stenosis?
In a vessel stenosis, the static pressure drops locally (e.g. from 100 mmHg to 60 mmHg) and then rises again downstream (e.g. to 80 mmHg). Intuitively, this looks as if fluid should flow backward from ...
- 647
2
votes
2
answers
421
views
Compressibility in Stoke's work of Navier-Stokes equations?
Can you explain is equation (12) compressible? Isn't compressible flow when we have term $dρ/dt$?
Here is full Stoke's work: link
photo of equations (12) and (13)
Compressible N-S equations:
- 1,004
6
votes
2
answers
344
views
Pitot Tube vs Bunsen Burner
In a pitot tube, the holes to the static pressure chamber are perpendicular to the flow of the surrounding air. In a bunsen burner, the air supply holes are perpendicular to the flow of gas.
From what ...
- 63
1
vote
3
answers
519
views
Are compressible Navier-Stokes equations valid in the incompressible regime?
Are compressible Navier-Stokes equations valid in the incompressible regime or I must use strictly incompressible version of N-S to get correct result?
Original N-S equations works only for ...
- 1,004
0
votes
0
answers
80
views
Has the kinetic energy of falling into the water also been transferred to the water in the pool?
The water falls vertically onto a thin and lightweight iron disc, and then flows horizontally in all directions on the disc. However, the disc does not sink to the bottom of the water. My question is, ...
- 2,338
0
votes
0
answers
121
views
Is it possible to construct Smooth solutions for the unsimplified version of the viscid and incompressible Navier-Stokes eqs.? Smooth is essential
There are many exact solutions to the simplified Navier-Stokes equations. However smooth and 3d solutions do still remain elusive.
Is there a way to construct an exact 3d smooth solution generator of ...
- 1
3
votes
1
answer
109
views
Where are the round shadows coming from?
The gif shows a shallow stream and the picture is taken from a small bridge.
Even though it is completely impossible to see anything in the water from the side, on the ground you can see round shadows....
- 193
1
vote
3
answers
276
views
Can the speed of the wind be determined from a photo or video of a flag?
When a flag moves around in a wind of constant speed can we determine wind speed from the flags distorted shape or angle it is flying at?
Perhaps this video of a flagpole vortex can help
Flagpole ...
user439184
3
votes
2
answers
696
views
What is the physical meaning of surface integral when the vector field is not velocity?
I understand that if the vector field is a velocity field, then the surface integral means volume rate, because the product of velocity v and area A is dimensionally volume over time V/t.
But what if ...
- 137
6
votes
1
answer
381
views
Zero vorticity for ideal flow
My notes state that the given the vorticity equation:
$$\frac{\partial \boldsymbol \omega}{\partial t} + (\mathbf{v} \cdot \nabla)\boldsymbol\omega = (\boldsymbol\omega \cdot \nabla)\mathbf{v} + \nu \...
- 79
1
vote
0
answers
120
views
Force density for a moving fluid
I know very little about fluid dynamics.
I wonder what the consequences of a moving fluid would be on the density force equation :
$$\mathbf{f} = - \nabla P$$
With the total force :
$$ dF=\mathbf{f} ...
0
votes
0
answers
107
views
What is density and flow of a fluid in general theory?
Picture below is from Dirac's general theory of relativity. I want to understand the red line.
The author use:
$t=x^0, x=x^1, y=x^2, z=x^3$
$\surd = \sqrt{-g}$
I treat the fluid as analogue of ...
- 471
2
votes
1
answer
96
views
How is flowrate affected with pressure drop? [closed]
Assume $50\text{ gpm}$ at inlet of a pipe with pressure drop as $10\text{ psig}$. Will the flow at outlet still be same $(50 \text{ gpm})$?
Will a larger pressure drop will decrease the flow rate at ...
- 21
3
votes
2
answers
265
views
From the Poisson bracket equation to the Euler equations in fluid dynamics
In the book Introduction to Mechanics and Symmetry (Marsden, 1998, pp. 20–21), it is stated that the Euler equations for an incompressible, ideal fluid:
$$
\frac{\partial \mathbf{v}}{\partial t} + (\...
- 1,586
1
vote
1
answer
174
views
Will the water in the garden hose move closer?
I use a garden hose to water the garden. Assuming that when I am stationary, the horizontal distance of water movement is 3 meters, but when I move horizontally at a constant speed perpendicular to ...
- 2,338
1
vote
0
answers
149
views
The validity of "added mass" calculations for real fluid
When a body moves with a constant speed $U$ through a fluid, it experiences constant drag due to the fluid viscosity $\mu$, and dynamic pressure $\frac{\rho_f U^2}{2}$. The question which type of drag ...
- 557
0
votes
0
answers
74
views
Can a normal (transverse) velocity perturbation affect local mass flux in a flowing fluid?
Consider a steady, unidirectional flow—for example, a river flowing in the x-direction with velocity v. Suppose I apply a localized velocity perturbation in the normal direction (say, in y-direction),...
- 51
2
votes
1
answer
243
views
How to model flow of gas through "large" hole into vacuum?
I have a chamber with a gas at an initial pressure of $P_0$. A hole of diameter $d$ is opened in the container, into another chamber with a constantly working vacuum pump, such that $d > \lambda$ (...
3
votes
1
answer
151
views
Korotkoff sounds and turbulent flow
In Physiology the traditional way of measuring the blood pressure is cutting off the blood flow by applying pressure with a handcuff and slowly lowering the pressure to hear the Korotkoff sounds.
My ...
- 247
0
votes
0
answers
77
views
How do I check the stability of a fluid velocity distribution?
Suppose we have a unidirectional velocity field, $\vec{u}=\left<0,u_\theta,0\right>$ in
cylindrical coordinates, whose azimuthal velocity is found by Navier-Stokes (negating advection, $\vec{u}\...
- 161
2
votes
2
answers
197
views
Are there any exact examples of non-laminar flow?
All the example solutions of the navier stokes equation I have seen have assumed laminar flow. I understand that the general solution to the NS equation has not been found, however are there any ...
- 2,115
0
votes
0
answers
55
views
Total pressure for a compressible, isothermal and stationary flow
I was asked to determine the total pressure in the case of a compressible, isothermal and stationary 1D flow. The hypothesis of perfect gas is valid.
The idea was to start from the momentum equation ...
2
votes
1
answer
164
views
How do flows accelerate around curved surfaces?
I am currently struggling to understand boundary layer separation, specifically in the case of a flow around a sphere.
I understand that an adverse pressure gradient is required - this causes the flow ...
- 23
3
votes
2
answers
138
views
Deriving Bernoulli along a streamline from the energy conservation equation
Good evening, I'm trying to figure out how could I derive the Bernoulli equation along a streamline $h + \frac{1}{2} u^2 + g z = \text{constant}$
starting from the energy conservation equation. This ...
- 31
0
votes
0
answers
139
views
What is the Pressure Across Streamlines?
If you have a flow with uniform streamline entering a bend in a pipe, is the pressure on a streamline near the outside of the bend larger than the interior of the bend if the flow is irrotational? I'...
- 131
8
votes
0
answers
2k
views
Why do traffic jams happen even on a highway?
I was surprised to find myself in a traffic jam on a highway (it's a densely populated city). If we think of vehicles on a highway as particles flowing in a pipe, when the inflow exceeds outflow the ...
- 13.5k
2
votes
1
answer
168
views
How do people verify if two points are on same streamline when applying Bernoulli?
I know that Bernoulli's equation only holds between two points if they lie on same streamline however i have often seen people use Bernoulli's equation without proving that the two points they are ...
- 271
1
vote
0
answers
62
views
Equivalence of pressure gradient term in core-annular flow
I'm trying to figure out if it is correct or incorrect to assume that the pressure gradient in a core-annular flow system is the same in the core and the annulus (steady state, vertical flow, annulus ...
- 149
1
vote
4
answers
380
views
Why can't internal forces do work in proof of Bernoulli equation?
So i was reading the proof of Bernoulli equation specifically this one
My doubt is why we didnt include the net work done on the fluid due to the internal forces in the fluid.
So far i got the ...
- 271
3
votes
0
answers
152
views
Shape of a rope in steady flow [closed]
I want to measure flow speed in an exotic way: with a hanging inelastic rope/thread/string/chain.
Assume we have a cylindrical, flexible thread, hung from one end in a steady flow. I assume inviscid, ...
- 33
1
vote
0
answers
60
views
Doubt regarding seepage pressure in flow net
The seepage pressure at an intermediate point of a flow net in many books, is given by the formula
$$p=(H-nh)Y.$$
Here, $H$ is the total head at the upstream side of the flow net, $n$ is the number of ...
- 51
1
vote
0
answers
32
views
High pressure pulsed flow through a heated tube [closed]
I am working on an engineering problem as part of a private research project. The problem is out of my field of expertise and need some help.
The purpose of the question:
To determine if a metallic ...
- 11
24
votes
1
answer
2k
views
Why does a mosquito net block the breeze even though its mostly porous?
When my window is fully open, I can feel the breeze from outside. But when I put on my mosquito net, the breeze gets blocked almost completely. Why does mosquito net block the breeze, even though its ...
- 13.5k
1
vote
0
answers
89
views
Explain reduction in air pressure over wing at molecular level, for case where density and temperature is constant? [duplicate]
Pressure is caused by bouncing molecules at the surface.
Air over wing reduce static pressure, for low subsonic flow, up to 0.3 Mach density(very small change) and temperature are constant, how then ...
- 1,004