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

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Why do we use time-dependent regions in this derivation?

I'm studying fluid mechanics and I have the following doubt: on the book, the author first deduces the differential form of the equation of balance of momentum. First he argues that if the fluid is ...
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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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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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64 views

No-slip boundary condition for viscous fluids

When dealing with fluid mechanics of viscous fluids, both theoretically and numerically, I've always been told that the boundary condition applied at solid walls has to be a no-slip one. My teachers ...
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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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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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402 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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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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35 views

Liquid film in a narrow slit

If a thin sheet of some material in which a slit is cut is immersed in a liquid and removed, a liquid film (bridge) stays in the slit. Is it possible to calculate the shape of the film if the ...
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246 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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60 views

Liquid Column “Recoils” in a Sealed Cylinder When Hit by a Piston — Is it Possible?

Consider a cylinder filled partially with a liquid (e.g. water). The cylinder is sealed, and is at held at room temperature (e.g 298K). At equilibrium (or when no external disturbance is imparted to ...
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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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57 views

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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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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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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103 views

Mixing mild and cold water, which one to pour first?

Suppose for example that a person like me likes his water in-between. A bit colder than the room temperature but not very cold. If you have a water dispenser that pours rtp water and cold water, which ...
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101 views
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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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99 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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1answer
84 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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73 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
296 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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53 views

Flow velocity out of a pipe

For a compressible homoentropic gas is the flow velocity out of the pipe the same as the velocity into the pipe?
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48 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
35 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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34 views

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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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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108 views

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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53 views

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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83 views

Integrating pressure over a surface

Consider the 2D airfoil below. In engineering (and maybe physics) you will often see something like the following as an expression for the pressure force acting on a surface (in this case a curve ...
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27 views

Can pressure in bars be equated to flow in litres per second? [duplicate]

I have a 160 mm water pipe at 5 bar pressure.What is the flow in litres per sec? I want to fit a hydro turbine to the outlet.
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504 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 ...
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2answers
106 views

Confused about the theoretical origin of quadratic air drag [duplicate]

Though the mathematical concepts underlying quadratic air drag are quite straightforward (a single variable differential, just like the linear drag equation), my text book (and online text books) ...
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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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Vanishing viscosity in eqn. of heat transfer for free convection: on what argument?

In Landau's and Lifshitz' Fluid Mechanics on the derivation of the equation of heat transfer for free convection p. 218, they write In the thermal conduction equation (50.2), the viscosity term ...
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88 views

Shallow water wave question from Acheson's book

I am learning Fluid mechanics by reading Acheson's book entitled "Elementary Fluid Dynamics". Below is from problem 3.1. Consider the Euler equation for an ideal fluid in the irrotational case. We ...
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49 views

Steam Turbine Inlet Velocity

Consider an ideal steam turbine. The power generated by a steam turbine comes down to the torque and the angular velocity, which is ultimately dependent on the velocity at which the flow enters the ...
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68 views

What is the difference between 'flow' and 'move'?

I just met with a very basic question.(Might even sound silly!) My textbook kinda says(not exactly), 'Whatever flows is a fluid'. That got me wondering because we are creating a whole category of ...
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51 views

Fluid flow at mach 1

fluid-dynamics is not my preferred discipline, yet I have been landed with this problem and just seeking some clarification. I have a nozzle at the end of a tube, with 8 holes in it, and we are going ...
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Is this really a golden ratio spiral?

In this blog post, I found this picture: Does the water really form golden ratio spiral in such cases? Or is the photo just a provocative example, without physics grounds for claims about ...
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45 views

Flow rate is calculated only using the parallel component of the velocity vector

Flow rate is calculated using only the parallel component of the velocity vector to the area vector. Why is this? How can I mathematically prove this? Namely, how do I prove any perpendicular ...
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173 views

Analytical solution of transient barometric formula for fluid in one dimension

Consider a column of fluid of length $L$, with initial density $\rho_0$ and initial velocity ($u_0 =0$) everywhere. Now at time $t=0$ gravity is switched on. No-slip boundary conditions are assumed at ...
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111 views

Help with ideal gas law manipulation

Equation 1 represents an improvement over the intial assumption of constant mass velocity (i.e., $\rho v=\rho_o v_o$). We can now improve Eqn. (2) to get to Eqn. (3). My question is: what are the ...
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2answers
109 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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4answers
934 views

Calculate water flow rate through orifice

I'm not very good with fluid physics, and need some help. Imagine the following setup with water contained in-front of a wall with an opening on the bottom: How do I calculate the water flow $Q$?. ...
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34 views

Macro-Level Explanation of Fluid Heat Transfer

Here's something I've been struggling with for a while. Say you have a hot fluid and cold surface (or the reverse, so long as there is a temperature difference) where the fluid flows over the ...
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2answers
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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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63 views

Reference Request: Fluid dynamics/Elasticity via Lagrangians

Would there be a book that does what Landau does in Fluid Mechanics and Theory of Elasticity using Lagrangian's/Action-principles, analogous to the presentation in Landau's mechanics? I have only ...
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Viscous Burgers equation physical meaning

The viscous Burgers' equation: $$ q_{t}+q\:q_{x}~=~\nu\:q_{xx}, \mbox{ where } \:\:\nu >0, $$ combines the nonlinear propagation of $q(x,t)$ and the diffusion. What is this equation for? (in ...