Questions tagged [fluid-dynamics]

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

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Vorticity: what is the difference between $\nabla \times f$ and $\nabla \wedge f$?

I have always thought that we may obtain information about the vorticity of a vector field $f$ by considering the cross product $\nabla \times f$. In higher level texts on fluid mechanics I see that ...
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What's a good simple model for wind attacking drone?

I'm trying to simulate a drone on https://rapier.rs/. My idea is to do an X shaped object, with a force $P$ on each end of the X, always perpendicular to the drone plane. I want to simulate wind, ...
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Releasing compressed air with the loudest pop [closed]

Due to the dry summer I've been thinking about theory of making cracker/banger without fire. Would connecting a nozzle (de Laval?) to quick release valve from small cylinder with the pressurised air ...
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Kelvin–Helmholtz instabilities - how to solve these questions? [closed]

The Kelvin-Helmholtz problem occurs when horizontal wind and density change at a discontinuity with $U_1,ρ_1$ in the upper layer and $U_2,ρ_2$ in a lower layer. It can be shown that the phase speed ...
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Linear drag for pendulum in air, justifiable or not?

So, when trying to measure the gravity constant $g$ at home through a pendulum I realized I wanted to try to model drag on the pendulum, to get a more accurate result. I am asking how we can justify ...
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What does divergence of scalar times vector vector field physically mean?

We know that: $\nabla \cdot (f \vec{A}) = f \nabla \cdot \vec{A} + \vec{A}\cdot(\nabla f)$ Now divergence of any vector field can be understood in terms of whether the concerning flux is outgoing ($\...
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Surface Tension [closed]

A mercury drop shaped as a round tablet of radius R and thickness h is located between two horizontal glass plates. Assum- ing that h <<R , find the mass m of a weight which has to be placed on ...
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Analytical solution for Navier-Stokes where non-linear term is important [closed]

In general, analytical solution of the Navier-Stokes is difficult to obtain. Simple cases where analytical solutions are known include Poiseuille flow and barometric pressure variation for ...
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Derivation of flow rate and pressure drop

I just read an expression relating to internal flow and pressure drop from here (Derivation of Flow Rate and Pressure Drop Relationships). I am curious about how to derive this formula.
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Incompressible fluid flow in tilted pipe setup - Continuity Equation, Flow Rate, Mass Conservation

Say that we have water flowing horizontally in a pipe of constant diameter. The continuity equation for incompressible fluids, which is a statement of mass conservation, guarantees that the flow rate ...
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Continuity equation for charge density

Let $\rho$ be the charge density and $M_i$ the momentum density. The article I am reading states that the continuity equations for this system are given by, \begin{equation} \frac{\partial \rho}{\...
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Is metaphysics a subject that should replace physics and philosophy? [closed]

I'm really seeking some insight and the following may seem opinionated, but it's really my observations and I could be wrong and I'm completely open to hear thoughts and correction from anyone. If ...
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Conservation of momentum flux

When is momentum flux conserved in a fluid? How do these conditions compare to the conservation of momentum? What is an example when momentum flux is conserved, and momentum not?
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Additional Pressure/Force Impact on a solid body as it moves through a fluid [closed]

I hope you are well. Is there a formula to calculate any (if any) additional force/pressure on a solid body as it moves through a Newtonian fluid? Is this force/pressure a function of the fluid's ...
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What is the effect on fluid shear force by changing the distance between two surfaces?

Scenario… Consider two “drums” of differing diameters, one nested inside another, both centered coaxialy, to form a gap between the two. The outer drum is 60cm diameter and the inner drum is 40cm ...
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Why is the wake of boats leaving a long lasting print on the sea?

A picture is better than a long explanation. The boat is long gone but its wake is visible for a very long time and forms a pattern looking like a trail on the sea. The two lines are not even ...
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How to dampen or prevent tsunami before shoreline? [closed]

Tsunami waves break before shoreline and change to horizontal destructive flow. There is two types of shoaling dry bed and wet seabed flow. During tsunami dry bed flow Froude number could be much more ...
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Simple Waves In Context of Riemann Invariants for One Dimensional Gas Flow governed by Euler Equations

I'm struggling to understand why in a simple wave, where one Riemann invariant is constant, why the characteristic curves along which the other Riemann invariant remains constant can't intersect? My ...
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Why is the pressure inside a fluid is equal in all directions? [duplicate]

Actually, I am thinking that the fluid pressure occurs as the result of the forces acting on each molecule from each other. If it is true, then why should the horizontal force be equal to the vertical ...
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What is the relationship between the falling acceleration of a tank of water with a spout, and the displacement of the water efflux from the spout?

I conducted an experiment, where I changed the falling acceleration of a tank of water with a spout, and measured the displacement of the water from the spout. I knew that in free fall, none of the ...
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Can Mach number be greater than 1 if mass flow rate is decreasing?

Here is the mass flow rate equation from the NASA site(enter link description here). According to this the maximum mass flow occurs at Mach number M = 1, which I can understand. But I can substitute ...
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Why flapping rudder produce net thrust if one half-stroke produce thrust and second half-stroke drag?

In small sailing boat like optimist is well know technique when there is no wind, rudder pupming which push boat forward.You just need push-pull rudder stick left to right with fast movement. Rudder ...
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Propagation Of Error Calculation Of Incompressible Continuity Equation

Hello I am having trouble deriving the correct equation for error in vertical velocity from the incompressible continuity equation. We are trying to estimate vertical velocity ($w$) from the ...
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1 vote
1 answer
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Comparison of 2 fans [closed]

I have 2 20" box fans. The first fan draws .65 Amp and claims 1780 CFM. The second fan draws .45 Amp and claims 2300 CFM. The fans are new, and the electric motors are of similar design, so I ...
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Why does a stream of falling water get narrower at the bottom? [duplicate]

At first glance, I thought that the flux of the velocity field, $\mathbf u$, should be constant. The velocity of the water increases due to gravity, hence the imaginary area the velocity field is ...
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3 answers
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What is the $P_o$ or $P_i$ in Bernouilli's equation?

I've been learning about Bernoulli's equation: $$P_i + pgh_i + p\frac{v_i^2}{2} = P_0 + pgh_0 + p\frac{v_0^2}{2}$$ but am confused about what $P_i$ and $P_0$ truly represent. Sal from Khan Academy ...
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Water flowing around cylinder exciting circular waves of which wavelength?

I am dealing with the following setup: Imagine an upright, fixed cylinder in flowing water of constant and homogneous velocity. "Behind" the cylinder one can imagine ship-like wakes to ...
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1 answer
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Propagation velocity of circular gravity-capillary surface waves in shallow water

My question deals with the general dispersion relation for gravity-capillary surface waves in shallow water. I stumbled across the follwing two dispersion relations: $w^2 = gk + k^3 \sigma/\rho$ (from ...
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Averaged null energy condition for a perfect fluid

The energy momentum Tensor for a perfect fluid reads $T^{\mu\nu}=(\rho_0+P)u^\mu u^\nu+Pg^{\mu\nu}$. I should apply now the averaged null energy condition to this energy momentum tensor and derive ...
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What is the speed of the information transmission between water molecules?

What I would like to know is if for example I move a molecule in water how fast this information will reach the neighboring molecules
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$\Delta P=QR $ in fluids

Seems like a stupid question but I think that how delta p can be negative?! Both Q (flow) and R(resistance) are positive and also for flow we need pressure gradient which means the second pressure ...
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3 votes
2 answers
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Would water flow from the higher container to the lower one? [closed]

Two identical open-topped containers contain identical amounts of water, and they are connected by a tube at their bases. Container A is higher than Container B. How much water, if any, will flow from ...
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Conflicting result for velocity and radius in physiology

My problem is that we say V = Q/A (V velocity, Q flow, and A area of pipe) in haemodynamics. Based on this formula, the velocity ​​is inversely related to the second power of the radius. Combining ...
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Microscopic description of drag

It is well known that a fluid opposes the motion of a moving object and we can represent this resistance in motion with a force, which we call it drag. Different fluids exert different drag forces ...
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How to model increased volume but constant energy density

I'm looking to model a system, where the volume of the system increases as a function of time, but the energy density remains the same. How do I do this? The way I'm thinking about it is a container ...
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11 votes
2 answers
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How far should I spread my fingers when swimming?

One way to improve efficiency of swimming stroke is to increase area of the stroking surface - for example wear fins on hands. But what if we increase drag of the palm? If we spread our fingers then ...
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Derivation of Flow Rate and Pressure Drop Relationships

In fluid mechanics, I consistently see two different types of expressions relating internal flow and pressure drop: $$ \Delta P = \frac{k}{2} \frac{\rho}{A^2} Q^2 $$ which is based on Bernoulli's ...
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Navier-Stokes Equations in Einstein Notation and its relation to Poisson's Equation

The Navier-Stokes equations are: $$\partial_t v + v \cdot \nabla v = - \nabla p + \nu\nabla^2 v, \quad v \in \mathbb{R}^3\\ \nabla \cdot v = 0$$ I have seen that, using Einstein notation (which I am ...
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Galilei transformation of mass flux

Is it possible to perform a Galilei transformation of a flux without additional information? Say we consider a flux $q = \rho v$ that can be written as the product of density $\rho$ and a velocity ...
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How to model a vector field with positive divergence everywhere?

If I wanted to construct a 3D vector field where each point has maximum divergence, meaning the vectors point radially outwards from each point, and a constant magnitude of, say, 5, how would I do ...
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Intervals between the last drops of liquid

When a bottle is nearly empty, the remaining liquid would come in the form of drops, which are becoming less and less frequent. I am wondering, if there is distribution describing the intervals ...
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Rule of thumb for estimating settling of colloid particles based on size vs $g$ force?

It is generally accepted that once undissolved particles in a solution see one of their dimensions fall below ~1 mcm zeta potential makes them reppel each other more than gravity helps them coagulate ...
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What is the intuition behind the ${\nabla u^T}$ term of the stress/strain tensor for a Newtonian fluid?

$$\epsilon=\frac{\nabla u+ \nabla u^T}{2},$$ $u$ is vector displacement, and $\nabla u$ is the gradient matrix of $u$. Now for a Newtonian, incompressible fluid, this describes the shear stress forces ...
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If an airfoil had a hole going through it, would it create more lift and reduce drag?

To visualize what I'm asking, imagine the side view of an airfoil. Then make a hole that goes all the way through the airfoil that runs along the mean camber line (or had some sort of camber to it). I ...
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1 vote
1 answer
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Bernoulli's equations on a falling (not freefall) bucket of water

If a bucket of water with a tiny spout at the bottom (allowing the water to jet out) is falling (not at freefall due to a pulley system), will the air pressure above the water level in the bucket be ...
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1 vote
1 answer
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Mass flux in a multicomponent mixture with a concentration-dependent density

This question concerns how to properly calculate the change in mass in a multicomponent mixture when the mass density is concentration-dependent. For a 1D rod of length $L$ that has a mass density $\...
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1 vote
1 answer
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Velocity at a place for fluid with a given pressure gradient?

In a spherical coordinate system, the origin is a sink with fluid extending to infinite distance. The pressure gradient generated in the fluid is: $$\nabla P \alpha \frac{1}{r^2}$$ where $r$ is the ...
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2 votes
1 answer
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Does the Continuity Equation Imply it's Zero for Incompressible Flow?

This might be an incredibly simple question, but I haven't been able to figure it out on my own. I'm an engineer by trade, so please forgive my unfamiliarity with vector calculus. I'm interested in ...
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-1 votes
1 answer
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Reducing yawing in a kayak with a rudder

Disclaimer I would first like to thank in advance the people for taking the time to read this question. Please, note that this is not either homework or an open question: I just wondered about the ...
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1 vote
2 answers
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Navier-Stokes Equation Derivation in "A Mathematical Introduction to Fluid Mechanics" (Stress Tensor)

My question relates to the attached pictures, which contain text from the book noted in the question title. In particular, my question is related to the first assumption made in the text (See bottom ...
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