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

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Fluid mechanics problem

I have a $2D$ fluid parcel with coordinates $(0.5,-0.5), (-0.5,-0.5), (0.5,0.5)$ and $(-0.5,0.5)$ and this parcel is deformed by a steady flow field of $u=ay$ and $v=0$, defined on the basis ${(1,0), ...
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Vorticity and circulation in fluid mechanics

Given a fluid element whose circulation was determined counter-clockwise, how can I calculate the Vorticity of the element? The circulation is $$\Gamma = (\frac{\partial u_2}{\partial ...
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2answers
342 views

Why does tea rises in the pot but water don't?

I was wondering when I boil water in a pot it only shakes too much while boiling. But I could not figure out why tea rises in the pot when we boil it. it is also a liquid but it starts rising up till ...
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1answer
57 views

Relationship between Connection and Material Derivative

Suppose $D\subset \Bbb R^3$ contains a fluid and that $f : D\times \mathbb{R}\to \mathbb{R}$ is a time dependent function defined on the fluid region. In that case, the material derivative is defined ...
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48 views

Weight held by jet stream of water

Consider a bucket of weight $W$, held in air by a jet stream of water from the ground (moving vertically upwards) at height $h$. The water is fired from the ground at the rate of $\mu$ (units ...
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114 views

Why viscosity is diffusive?

I'm studying fluid mechanics in more depth during my Ph. D. and there is something related with the diffusive term that has been bothering me for a long time. Looking at the convection diffusion ...
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1answer
63 views

Why do we need the material derivative?

I'm studying fluid mechanics, and I got the impression that the material derivative is nothing more than "differentiating along a path" and so I got confused on why do we need it. Basically, let ...
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How far can water rise above the edge of a glass?

When you fill a glass with water, water forms a concave meniscus with constant contact angle $\theta$ (typically $\theta=20^\circ$ for tap water): Once you reach the top of the glass, the water-air ...
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32 views

How to find the required inlet velocity/pressure to achieve 0.5 m/s in one part of the underground tunnel? [closed]

I have this problem here related with tunnel and ventilation. As you can see at the picture below, it is a top view of the tunnel. The tunnel has an inlet and an outlet. The air flows from the inlet ...
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118 views

Transport theorem derivation question

I am trying to rigorously go through some fluid mechanics proofs and theorems. I am currently going through a proof related to the transport theorem and I am having trouble with a step. The steps in ...
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191 views

Absolute Viscosity of Water at certain temperatures

I just started my class on fluid mechanics. There's a problem that requires absolute viscosity $u$ of water at 25C. I looked up my table in the book and I only have it for water at 20C and 30C. I ...
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54 views

Bulk Modulus, How are these formulas equivalent?

Bulk Modulus is defined as $$ B = \frac{VdP}{-dV}$$ Where $V$ is volume and $P$ is pressure. It is also defined as, $$ B = \frac{\rho dP}{d\rho}$$ Where $\rho$ is density. Question: How are these ...
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70 views

Mathematical model of a fluid: which viewpoint is the standard one?

I've been studying fluid mechanics and I have some doubts on the mathematical model of a fluid. First we let $D\subset \mathbb{R}^3$ be a region in three-space filled with a fluid. This region has as ...
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2k views

What does the Reynolds Number of a flow represent physically?

What does the Reynolds Number of a flow represent physically? I am having trouble understanding the meaning and the utility of the Reynolds number for a certain flow, could someone please tell me how ...
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56 views

What forces of stress really represent?

I'm studying fluid mechanics and the book says the following: For any continuum, forces acting on a piece of material are of two types. First there are forces of stress, whereby the piece of ...
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221 views

Branching lemon drop “smoke rings”

This might be hard to ask, but here goes nothing. I recently poured a cup of water into a black coffee cup. There was a light source--not very bright--above the cup. Anyways, I was squeezing a ...
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470 views

Sixth Power Law

The Law: The size of a solid material that can be carried by a (water) stream is proportional to the sixth power of its velocity. I have just discovered that I read this law long time ago (it has ...
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73 views

Intuitive explanation of Poiseuille's law — why $r^4$?

According to Poiseuille's law, the effective resistance of a tube is inversely proportional to the fourth power of its radius (as given by the following equation). $$R = \frac{ 8 \eta \Delta x}{\pi ...
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375 views

How to calculate pressure loss due to water leakage from a hole in a pressurized unit

I am trying to develop a method for calculting the rate of pressure loss from a small hole in a pressurized vessel full of water (small air pocket likely at top of vessel). I've found a formula for ...
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29 views

Flow past a parabolic lamina submerged in a tube. Please see the attached figure

How do I compute the velocity field around the parabolic body using Navier-Stokes? I want to solve it like Poiseuille's law. I have no slip at the wall boundary and a free shear layer at the ...
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2answers
7k views

Does pressure drop across pipe affect flow rate?

Let's say there is a main pipe containing $100\: \mathrm{m^3/hr}$ a fluid of density $750\: \mathrm{kg/m^3}$ and it's gonna be branched into 2 pipes (Pipe A and Pipe B) of the same diameter. If Pipe A ...
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138 views

Integrating the divergence of a velocity field (Fluid Mechanics)

I'm looking more for verification of my answer as I'm not 100% sure how valid my integration is here: If I have a 2-D incompressible fluid velocity field given by ...
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1answer
58 views

What is the physical basis of the $\rho \bf{u} \times \bf{\omega}$ force on a fluid vortex line?

In fluid dynamics, the force density on a vortex line is $\bf{f} = \rho \bf{u} \times \bf{\omega}$. In Faber, Fluid Dynamics for Physicists, ch. 4, this is "derived" by analogy with magnetostatics, ...
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26 views

Variable area manometer duct

How does one measure the pressure at the end of the manometer tube when the manometer tube itself is having a variable area?
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245 views

Why is this the volume flow rate per unit area?

In fluid mechanics we consider a fluid filling a region $D\subset \mathbb{R}^3$ together with a function $\rho : D \times \mathbb{R} \to \mathbb{R}$ called the mass density such that for any ...
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47 views

Effect of Reynolds number on wake region

For a flow over a smooth sphere, does the wake region increases with increase in Reynolds number? And if so, then why?
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Is the flow in a ducted fan really incompressible?

I have a long duct with a fan in the middle of it. The fan causes a steady airflow in the pipe which is at low speeds (incompressible) the mean flow in the pipe is about 10 m/s. However the fan blades ...
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85 views

Titanic Question

I was reading this question: Was Titanic's captain's decision correct? @oakad commented about a Russian vessel keeping itself afloat by going in reverse, using hydrodynamic pressure to keep ...
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1answer
66 views

A way to track a gas's expansion

I was wondering if there is a way to see, empirically, how a gas behaves. Perhaps the most natural way is to use fumes with color, but they quickly disperse, rendering partially useless. Are there ...
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79 views

Can we 'see' the Kolmogorv microscale

My understanding of Kolmogorov Microscale is that in a turbulent fluid, smaller eddies tend to be similiar to larger eddies - until you arrive at the microscale. My understanding (that may be wrong) ...
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101 views
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37 views

Heat transfer to a cube from one of the faces [closed]

Heat Flux= 10 MW Inlet water temperature = 28 degree centigrade for cooling purpose through a tube passing through the centre of retangular block of length 50 mm,height 30 mm and width 30 mm inner ...
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1answer
83 views

Simple expression for transitional pressure force

Consider a simple, circular orifice with an upstream, high gas pressure and downstream, normal atmospheric pressure. Consider also a flat circular plate that can be positioned anywhere along the ...
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225 views

Analogy between fluid dynamics and electromagnetism

I've been reading a set of notes (Chapter 13 of Caltech Ph 136 notes from 2004, by Blandford and Thorne) that draw an analogy between fluid dynamics and electromagnetism, identifying the magnetic ...
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98 views

The Spinning Log “Perpetual Motion” problem, and my attempt at a solution

So I was introduced to this "perpetual motion" riddle a few weeks ago. The problem goes like this: we all know perpetual motion machines are not possible, but this riddle seems like it should work as ...
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72 views

Milk-First School

I have always been struck by the huge amount of different arguments about the issue: When you make a cup of tea, the milk should be poured first or added to the cup after the tea? Wikipedia, ...
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1answer
276 views

Calculate flow rate of air through a pressurized hole

I was wondering about this: If there is a pressurized container, like a tank of compressed air at some pressure that is greater than the ambient air pressure, and this tank of air has a hole in it, ...
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1answer
47 views

Pressure at a bend in a pipe

This is a question from a study guide for a military officer exam: I have fluid flowing through an elbow in a pipe (the elbow is in the shape of an upside down and backwards "J") and the flow goes ...
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1answer
34 views

Modelling the fluidity of a fluid (grease) based on temperature

I am trying to create a statistical model of a lubrication system. A central grease pump takes grease from a tank and injects it into some cavities (via grease lines) until a pressure set-point is ...
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1answer
108 views

help with absolute pressure to gauge pressure derivation steps

I would like some help with the explicit math steps to go from equation 2 to 3. These equations are presented in a paper that I am reading. I will show where these equations came from and my attempt ...
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Water pump with a tap connected at its opening not pumping water when water is drawn from the pump before starting the pump [closed]

Please give your explanation in layman terms, without throwing any complex equations at me. We have a 5000 liter tank dug in ground and a water pump connected to this tank that draws water from it ...
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5answers
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How effective is speeding?

At a simple level, speeding in a car attempts to minimize the time required to travel a distance by utilizing the basic relationship: $$d=st$$ So for a given distance, time should be inversely ...
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1answer
76 views

How can I see this equation describes advection?

My notes say that this is the equation for the "advection of a quantity A at speed v": $$ \frac{\partial \mathbf{A}}{\partial t} = \nabla\times(\mathbf{v}\times\mathbf{A}) .$$ Is this true? How can ...
3
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1answer
33 views

Are the cylindrical and spherical form of Jeans' equations equivalent?

The question kind of says it all, what I really want to know is are the differences in their forms only due to the co-ordinate transform? And as such should a suitable spherical system satisfy ...
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How is viscosity described on the molecular level?

What is the 'molecular' origin of the viscosity? The molecular origin of elasticity is almost clear for me: at the very bottom the 'elasticity' comes from the attraction and repulsion between atoms ...
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2answers
104 views

Question on using Leibniz formula to derive thin-film equation from Navier-Stokes

I actually posted this to math.stackexchange.com a few months ago but never got any answers. I am trying to work through the derivation in this paper by Petr Vita, which derives a thin-film ...
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2answers
2k views

How do we calculate the speed of an air bubble rising in water?

We all know that an gas bubble expands as it rises through a liquid due to decreasing pressure.But at what speed does it rise? if we make a bubble of unit volume filled with a gas of given density at ...
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200 views

How does a hinge affect the amount of a submerged material?

Suppose I have a rod that has a density of $X <1$. If I were to submerge that rod in water (density 1), I would expect $X$ of the rod to be below water and $1-X$ of it to be above water (simple ...
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What does centre of lift depend on?

I've read in many places that centre of lift is about quarter chord of the wing and that post-stall lift (the part developed on lower surface) has centre midchord. The later makes sense; the pressure ...
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499 views

How do rudders work?

It is possible for a boat to use rudder to make a U-turn while coasting (moving by inertia), although it would lose some speed. How exactly do boats trade a portion of magnitude of the initial ...