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

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Boundary Conditions for axisymmetric stream functions in a pipe

I'm solving the equation $$ \frac{\partial^2 \psi}{\partial r^2}+\frac{\partial^2 \psi}{\partial z^2}-\frac{1}{r}\frac{\partial \psi}{\partial r} =-\omega_\phi $$ in a cylindrical pipe, where ...
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26 views

Rigorous definition of pressure in a fluid

We briefly introduced some terms at the start of my Fluids class, and one of them was pressure. I'm looking for a rigorous definition of pressure. Wikipedia gives this definition for pressure: $p = ...
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1answer
40 views

Physical Meaning of Divergence of Convective Velocity Term

When taking the divergence of the convective velocity term, I get the following: \begin{align} \nabla\cdot\left[\mathbf u\cdot\nabla\mathbf u\right]&=\frac{\partial}{\partial ...
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21 views

Question on pressure required on a fire hose pump [on hold]

Not entirely sure of how I transfer a pressure value to speed to reach the top of the building and also unsure of how the height of the fire hose affects the question. At the moment I am ...
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3answers
102 views

Why does a bubble take a spherical shape?

I suspect this has something to do with thermodynamics and the isoperimetric inequality and I'm interested in a mathematical derivation of this result.
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1answer
33 views

Position based dynamics constraint scaling factor

Reading through Müller et al., Position Based Dynamics, 2007 I got lost when passing from equation (5) $$\Delta p = \frac{C(p)}{|\nabla_pC(p)|^2}\nabla_pC(p)$$ to equation (6) (and applying the ...
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3answers
55 views

How long does it take to equalize pressure of two gas containers?

I'm looking for an equation that will tell me how long it takes for two gases at two different pressures to equalize their pressures. As a more concrete question, Container 1 has gas at pressure P1. ...
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42 views

Particle based fluids

I am reading through this paper (pdf) which talks about particle-based fluid dynamics based on SPH. I can understand the idea behind SPH and how the particles' positions are to be updated, however, in ...
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46 views

meteorite-like impact of a drop of yogurt

When I throw a drop of Yogurt (through spoon) into a dish of Yogurt, it caused something like a meteor hitting the earth and something occurs similar to the place a meteor hitting the earth(Barringer ...
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1answer
66 views

Bernoulli Equation Paradox

Imagine a funnel with an extremely wide mouth, filled with water. Attached to the stem is a water pump that pumps water upwards (into the funnel). Water is being pumped in at the rate of Q. The cross ...
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230 views

How does train back draft work

Quoting platforms and stations : Fast trains can create a vacuum called a ‘back draft’ that can blow you over or suck you under a train. How does that work ? I thought that the volume of air ...
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20 views

Equation of acoustic pressure in moving fluid: derivation

I'm looking for a detailed derivation of the equation of acoustic pressure with harmonic time dependence (of type $p(t,{\bf r}) = \psi({\bf r})e^{i\omega t}$) in moving fluid and under assumptions ...
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2answers
55 views

Time for water levels to equalize

Suppose that someone dumps some quantity of water into the ocean somewhere. Also, assume that no other water level changes are occurring. How long does it take for the change in water level to ...
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17 views

Fill and drain tank (same time) [closed]

Consider an open tank with cross section area A, into which liquid can enter at the top through one pipe and leave at the base through another. If the liquid enters at the constant rate of a volume of ...
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65 views

Can one model a spiral galaxy with a similar manifold to one for a whirlpool?

My question is more of a phenomenological question than literal, since the forces involved are very different. When one looks at the distortions (or wrinkles or whatever you wish to call them) in the ...
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0answers
23 views

What is the relationship between the angular speed and the diameter of the eye of a water vortex?

In a water vortex formed in a plastic bottle, what is the relationship between the angular speed of the water and the diameter of the hole in the cap? I would have expected that according to the ...
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0answers
9 views

How to determine the pressure of the moving water at the bottom of a vertical pipe [closed]

Water is flowing upwards in a vertical pipe with an inside diameter of 0.06 m at a velocity of 0.0152 m/s. The length of the pipe is 0.5 m. What is the pressure at the bottom of the pipe? Density of ...
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21 views

The shape of water column flowing from tops [closed]

My question is what are the useful to study about the shape of water column flowing from tops?
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29 views

Estimate the maximum distance of water spatter

There is a faucet dripping water from height $H$ onto a smooth, horizontal ceramic surface, and I need to give a upper bound of the maximum distance between the water spatter and the point directly ...
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20 views

flow through an orifice [closed]

The surface area of a first orifice with 2 mm diameter is 3 mm$^2$. The surface area of a second orifice is 5 times bigger from the surface area of the first orifice (15 mm$^2$). How much would be ...
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40 views

Isn't it impossible to make a theoretical model to describe the behavior and the statistics of a turbulent flow? [closed]

Why mathematicians are interested to smooth solutions of Navier Stokes equations? For the three-dimensional system of equations, and given some initial conditions, mathematicians have not yet proved ...
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3answers
77 views

If a body is floating in a static fluid, then the volume of the displaced fluid equal to the volume of the inmerse part of the object (proof)

Suppose an arbitrary body is floating in a static fluid, either totally or partially immersed in it, then the volume of the displaced fluid equal to the volume of the immersed fraction of the object. ...
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1answer
41 views

How to design windy area - what variables?

When you're walking around malls or parking structures, or a building corner, you'll sometimes notice areas with consistent windiness. I was wondering what positions, angles, wind direction, ...
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72 views

When I dissolve sugar in my cup of tea/coffee, does it become a liquid or gas, or neither? [migrated]

When I dissolve sugar in my cup of tea/coffee, does the sugar go from being a solid to being a liquid or a gas, or neither? Related: What keeps the sugar suspended in the tea?
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33 views

Calculate surface pressure due to forced vibrating plate using wavenumber space [closed]

My problem lies in the field of acoustics. I have a given complex velocity distribution. The velocity is the velocity in the normal direction to a rectengular simply supported vibrating plate. I now ...
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4answers
356 views

Is a causal relationship implied by Newton's 2nd Law?

Throughout my time learning physics I have been imbued with the notion that forces cause accelerations, period. Accelerations don't cause forces, and they aren't merely correlated phenomena. By ...
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3answers
47 views

Propellers and the Speed of sound

I was reading this website that described a novel wind turbine technology and it has this quote: In the mid-20th century, open propeller-driven planes with piston engines reached performance ...
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13 views

What is “full clutching flow” in fluid-dynamics with regards venturi design?

As the title says, what is "full clutching flow" in fluid-dynamics with regards venturi design? I came across this reference a few times and can not find any further info on it, I'm currently ...
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1answer
87 views

How fast would a bullet travel through liquid air?

According to Wikipedia, a bullet from a .22 Long Rifle travels at a speed of 320 m/s and the density of liquid air is 870 kg/m3. What equation would calculate the speed of a bullet fired into liquid ...
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18 views

Velocity of a fluid in presence of sphere [closed]

Consider the following problem: A rigid sphere of radius $a$ is placed in a stream of fluid whose velocity in the undisturbed state is $V$. Determine the velocity of fluid at any point of the ...
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22 views

Notation regarding the continuity equation for conservation of mass [migrated]

I have the following equation for the net mass flow out of a control volume through a surface $S$ - $$\int \int_S p \overrightarrow{V} \cdot \overrightarrow{d}S$$ (Actually there should be an ellipse ...
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1answer
57 views

Movement of a cylinder filled with water

Not long ago I was pretty bored at a dinner and I started playing with a water bottle that was not empty: I've been quite interested in its behavior when putted on its side and pushed: the bottle of ...
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1answer
73 views

At what speed would you die upon impact with water?

If we hit the water at great speeds, we die. This is because the water has no time to "move out of the way" and acts as a "solid" surface. At what falling speed can we consider the water as a ...
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2answers
61 views

Is it possible to limit water flow this way and how is this effect called?

I needed to propose a mechanism to store water and keep water flow at the same level with 100% passive equipment. Here's what I came up with. If you turn a water reservoir upside down and put in ...
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1answer
56 views

Can we measure the depth of water by scattering water?

Suppose we release an object and make it fall on the surface of water, then the scatter of water is recorded, Taking some observations, can we calculate the depth of the water by analyzing the ...
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1answer
56 views

What are the principles behind foam formation?

We know that while pouring water in a glass, there is close to no foam, but if pouring beer, there is much foam (unless pouring "slowly"). So, can the most prominent factors that contribute to foam ...
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1answer
57 views

Definition of pressure in Bernoulli's principle

I have a difficulty to understand Bernoulli's Principle which states increased fluid speed decreases the pressure. But in a wind tunnel when we measure the pressure with a pitot tube, both the ...
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1answer
14 views

Electrohydrodynamics: How will electric potential develop in a fluid when potential is applied from ends

Lets say, I have a fluid in a rectangular enclosure (2D). I apply electric potential $U=U_1$ at left boundary and $U_2$ at right boundary. In the lower and upper boundaries, the potential varies ...
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1answer
42 views

Orientation of large water drops break-up

I have observed that if you pour small globs of water from a considerable height (let's say more than 20 meters), the globs will break up. This is not surprising at all since the amount of water ...
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1answer
32 views

What is the difference between a vortex ring and a circular line vortex?

Can someone explain the difference between a vortex ring and a circular line vortex? Or are they the same?
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49 views

Flow from the bottle

I made some calculations about flow from the bottle, but problems occured when the experimental data came back. Need to refine calculations, but problems occur when trying to link the angle to the ...
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1answer
52 views

How a fan moves air? [duplicate]

How does a fan moves air towards you (I mean in 1 direction). Also propeller and fan have different shapes, does it mean they work different?
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2answers
43 views

U.S. Standard Atmosphere

My textbook states that "Ideally, we would like to have measurements of pressure versus altitude over the specific range for the specific conditions (temperature, reference pressure) for which the ...
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3answers
2k views

What is going on in front of and behind a fan?

Why is it that when you drop paper behind a fan, it drops, and is not blown/sucked into the fan, whereas if you drop paper in front of a fan, it is blown away?
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2answers
54 views

Basic understanding of stress tensors in a fluid

So, after having spent the last 9 hours attempting to understand the basic tenets of stress tensors in fluids, I can honestly say that I think I know less now than when I began. My questions are ...
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0answers
11 views

Basic understanding of stress tensors in a fluid [duplicate]

So, after having spent the last 9 hours attempting to understand the basic tenets of stress tensors in fluids, I can honestly say that I think I know less now than when I began. My questions are ...
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1answer
31 views

Feeling the Breeze

This question is based on an odd phenomenon I noticed last week. Since then, I've been collecting more data to try to get an accurate picture of the facts. Each morning, I go to my bus stop. It's on ...
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0answers
48 views

How do I enforce the no-slip boundary condition in time dependent incompressible pipe flow?

This is a technical problem which must have been solved already. It won't be in beginners textbooks but there should be a solution somewhere. I welcome reading suggestions. Maybe someone with ...
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51 views

Derivation of the equation of motion of a viscous fluid by Landau & Lifshitz

I am trying to follow Landau and Lifshitz, from the Volume 6 (Fluid Mechanics) of the Course of Theoretical Physics, on their derivation of the momentum equation for a newtonian viscous fluid, but I ...
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1answer
78 views

Why Are Normal Shock Waves Unstable in a Converging Channel?

While learning about shock waves in an introductory Gas Dynamics course, it was revealed that normal shocks are unstable if formed in a converging channel. Even if the local conditions ostensibly ...