Questions tagged [fluid-dynamics]

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

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Is dropping water from a cup in a dry bucket an incompressible flow?

I'm learning hydrodynamics by googling stuff so forgive me if the question is super simple. Imagine that I'm holding a cup of water, which I proceed to drop in a bucket laying next to my feet. The ...
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Pressure increases with increase in depth

Confusion in law of liquid pressure . Pressure increases with increase in depth from its free surface. So , does it mean that $h_0$ increases or h increases(Height of the body ).Not sure which height ...
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Is this correct for pressure exerted by a liquid?

$P_0$ is atmospheric pressure and $P_1$ is height×density×gravity. So , is the diagram correct for saying that Total pressure in the liquid = $P_0+P_1$. Since the direction of $P_0$ vector is ...
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Why isn't the capillary tube displaced downward by the column of water?

Water moves upward in a capillary tube due to intermolecular forces between water and the glass wall of the capillary tube. If those forces act on water pushing it up, why don't we see the opposite ...
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What is the work done to pull up a cylinder out of water? [closed]

What is the work done to pull up a cylinder out of the water if it is situated at the bottom 1m below the surface? Mass of cylinder=35kg, Radius of cylinder=10cm, Height of cylinder=60cm.
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Beaker and suspended ball weight measured by spring balance

Can someone explain to me why when we suspended a ball with a density greater than that of water in water by the help of a string why is the weight measured by the spring balance=Weight of beaker + ...
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Sum of Stresses in a Control Volume along $x$-axis

We were looking in class at the sum of forces, acting on surface $x$, of a control volume $dV$. I see from the equation, the first term is the normal force, and then the rate of change of the force ...
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Why does uniform flow become unstable when the Seddon celerity is greater than the Lagrangian celerity?

Uniform flow down an inclined open channel becomes unsteady under certain conditions. Vedernikov's number > 1 is a generally accepted necessary condition for this type of instability. Vedernikov's ...
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Volumetric Dilatation Rate, Material derivatives, and Divergence

in class we derived the following relationship: $$\frac{1}{V}\frac{dV}{dt}= \nabla \cdot \vec{v}$$ This was derived though the analysis of linear deformation for a fluid-volume, where: $$dV = dV_x +...
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Traffic flow problem: the length of merging lanes, finding an equilibrium situation - fluid dynamics

Lane A and B merge in one lane, and later on lane C merges in this lane aswell. A zipping system is used at each of these points (the cars from each of the traffic streams merge in turn.) Suppose that ...
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Swimmer in pool - Fluid dynamics

I think the main mechanisme for the question a) is dead water but I dont know how to solve the following questions b and c. I tried to look at the internal waves but i was not sure how to use them ...
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Traffic flow problem: does zipping shorten waiting time - fluid dynamics

Zippers shorten the length of traffic jams. Does it also shorten the waiting time? To calculate this we assume that there is a blockage on the road causing maximum $q = \epsilon \ll q_{max}$ cars per ...
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Doubt regarding SHM in a U-Tube using energy conservation

While finding the SHM equation for liquid in a U tube using energy conservation, we have:$$E=K+U \tag{1}$$ $$K=\frac12Mv^2$$ where $v=\dot{y}$ For claculation of $U$, it is given in "Vibrations ...
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Question on Goldstein's propeller solution

In 1929, Goldstein derived an exact solution for the flow field of a propeller with rigid helcoidal vortex wakes in uniform translation. My question is - Is this solution valid for a static propeller ?...
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Can a Mach number be defined for a hot gas fluid element using its own temperature and velocity?

I know that the ratio of an object's speed to the local sound speed is called the Mach number: $$M = \frac{v}{c_s}$$ where $$c_s = \sqrt{\frac{\gamma kT}{\mu m_p}}$$ I have always thought of the Mach ...
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How might one design an infinity balloon without an appropriate material

A while ago, I was working on a idea I had. I wanted to design a hypothetical sail that was effectively weightless. Why I wanted a 'weightless' sail is a rabbit hole that I'm not going to get into but ...
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What's the difference in force between lifting an object out of a viscous fluid (like honey) versus air?

Roughly, how much more force does it take to lift a stick out of a viscous fluid (like honey) than the same object the same distance in air? I'm not looking for a hard number- more like a back of the ...
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What quantity of freezing water could generate 300,000 joules of mechanical energy from expansion - enough to boil an electric kettle? [closed]

When water freezes, it expands with considerable force - enough to break glass and burst through copper water pipes. If this material expansion was harnessed - e.g. liquid water placed in a container ...
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Pitot tube accuracy in high temperature flow

It seems that Pitot tubes are employed regularly in measuring velocity in high temperature flows (at least several hundred degrees, e.g. industrial gas stacks). However, the associated pressure ...
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Solving unsteady flow in a syringe

I want to solve the problem of unsteady flow in a syringe. The piston as shown in the below figure is pushed by some force $F$, resulting in flow velocity $u_0$ from the orifice. The flow velocity ...
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Is the pressure of an incompressible fluid discontinuous or continuous across an aperture, like the nozzle of a hose?

Is the pressure of an incompressible fluid discontinuous or continuous across an aperture? E.g. inside the fire hose water is at high pressure, outside of it it's at 1atm, but what does the transition ...
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Energy lost due to air drag of a varying velocity object [closed]

How do we calculate total energy lost of an object due to air drag which is moving with varying velocity (from $v_1$ to $v_2$ m/s with an acceleration $a$ and over a displacement $s$) in air? Assume ...
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How to determine the derivative of velocity with respect to height? [closed]

I have a question on fluid dynamics which requires to find the derivative of velocity with respect to height. It was solved by my teacher but I am not able to grasp the solution. Here is the question: ...
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What is the derivative of velocity with respect to height?

I have a question on fluid dynamics which requires to find the derivative of velocity wrt to height? It was solved by my teacher but I am not able to grasp the solution. Here is the question: - A tank ...
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How do I know pressure is equal in a static fluid in connected tubes?

This is from knight. What I don't get is why $p_1=p_2$. I don't think we can use the hydro static pressure formula because the top and bottom of a cone are not identical. I get why pressure at the top ...
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Solution for Inviscid Flow in a Moving Corner

I am considering the below situation (taken from page 26 of Fluid Mechanics by Landau and Lifshitz) where an inviscid fluid flows into a corner and is then turned back around. The corner is the ...
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Is the velocity of a fluid in a vertical tube constant? [closed]

Here is how I concluded that: Let there be two points $A$ and $B$ in a tube, $B$ being a little higher up. Using the Bernoulli's equation: $$P_B+\frac{\rho v'^2}{2}+\rho gh=(\rho gh+P_B)+\frac{\rho v^...
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Can a high density of particles simulate fluid dynamics?

There are different ways to simulate fluids, some involve numerical solutions to PDEs. I was wondering if these PDE formulations can be thought of as an a infinite limit of a collection of particles? ...
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Understanding water flow in a fertilizer injection system

I recently set up a small EZ-Flo fertigation system. This is a tank full of fertilizer solution that you attach to a pipe that you are using for a sprinkler or irrigation. As water flows down the pipe,...
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Pressure drop on diver and airplane against acceleration

I'm curious about the relationship between the pressure drop an object is experiencing and the acceleration it is experiencing. From book Frank 8ed Fluid Mechanics, this equation show that sum of per-...
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Shear Stress at Boundaries of two Infinite Parallel Plates

This is a worked example on a book I am reading (Fundamentals of fluid Mechanics). They calculate the shearing stress in the top layer, bottom layer and middle layer. The calculate 𝜏 > 0 (in the ...
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Does unity drag coefficient have special meaning?

gives examples of drag coefficients of assorted shapes from 0.045 to 1.28. I understand that $C_D=\large{\frac F{\frac 12Av^2\rho}}$. Does a drag coefficient of exactly one correspond to any ...
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How to simulate or solve $n$-legged manometer without solving Euler's equations?

Consider a typical manometer tube but with $n$-legs, different heights at the initial time. Is there any way to solve it numerically or analytically without solving NS or Euler's equations? For ...
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Surface tension and capillary rise intution

I am high school student I am very confused in "surface tension", My confusion is that: 1) In this image I have shown that, In some books the reason for this shape of meniscus is explained ...
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Derivation of general equation of heat transfer & entropy

In Landau & Lifshtiz Volume 6 on fluid mechanics we derive the general equation of heat transfer by starting with the expression $$ \partial_t \left( \frac{1}{2} \rho v^2 + \rho \varepsilon \right)...
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How much work could be got from temperature differences during a rocket's descent from low earth orbit?

It strikes me that there is a lot of energy dissipated during a typical rocket's descent from Low Earth Orbit. How could that energy be captured and used? I wonder whether it might be possible to ...
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Continuity equation, why doesn't it apply here?

In this question above, I am confused with why the continuity theorem do not apply here. Since I think this is still a laminar flow of incompressible fluid. What do I not understand about the ...
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Uniform / rigid rotation in fluids, velocity gradients and resulting friction

In the derivation of the Navier-Stokes equation e.g. in Landau & Lifshtiz Volume 6 on fluid mechanics it is stated that the viscous stress tensor $\sigma_{ij}^{\prime}$ must also vanish when the ...
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Euler equation in comoving coordinate

I have the following cosmology exercise : I found many hints on internet : first source, second source But I still can't figure it out. If we is start from \begin{equation} \frac{\partial \vec{v}}{\...
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2 connected tubes filled with water, placing a stopper in one and raising the other, how can I determine pressure exerted onto the stopper?

If I have two 20ml test tubes connected at the base via a thinner flexible U-shape tube and I pour a set amount of water (40ml) into one test tube whilst both are at level height, the water ...
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Raoult's Law and Boiling Point Elevation

Raoult's Law states that vapor pressure decreases when a non-volatile solute is present. Boiling point is when vapor pressure = ambient pressure. Since vapor pressure is less, shouldn't the energy ...
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At what speed will a gas exit a vacuum?

I have limited knowledge about vacuums and fluid dynamics. Question: Let's say that I have some hydrogen inside of a fully sealed container at low pressure and I unseal it. At what speed will the ...
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How does increased fluid velocity give rise to low fluid pressure at a point?

Pressure difference is inversely proportional to velocity. But how is it valid at a point? Can you also include the example when we squeeze a pipe in which water is flowing, the velocity increases? ...
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Viscocity and exchange of material between different mediums

In the book of S. Vogel, Life in Moving Fluids, at page 29, it is stated that Lower viscosity at higher temperature implies steeper velocity gradients and thus thinner gradient regions on surfaces. ...
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Does turbulence increase with radius or decrease

IV lines must be regularly ‘flushed’ to avoid infection and line occlusion. More turbulent flushing better removes any particles attached to a catheter wall, which decreases chances of complications. ...
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Wind turbine in water

I have a 3D printed wind turbine (I got the design from a research paper). If I conduct a particle image velocimetry experiment in a water flume instead of a wind tunnel, what should I expect as the ...
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Locality of the Turbulent Energy Cascade

Locality appears to be an omnipresent feature of physics, including within turbulent fluid dynamics. In 1941 Kolmogorov postulated that the turbulent energy cascade is driven by scale-local ...
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Understanding conditions for a choked nozzle

I am interested in knowing if a nozzle (Convegent-Divergent) is choked (sonic state at the throat). I have read that the nozzle is choked if : the static pressure $p_t$ at the throat is equal to the ...
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What causes water droplets to drop in periodic, but not uniform time intervals?

A little while ago I noticed water droplets forming from a slightly overflowing reserve in my sink. They dropped in a special periodic time pattern, which was not uniform. Instead two droplets would ...
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Does ∇⋅τ = μΔv in the Cauchy Momentum Equation?

I find two versions of the Cauchy momentum equation (1, 2): $$ \rho \frac{D\vec{v}}{Dt}=\rho\vec{g} - \nabla{p} + \mu\nabla^2\vec{v} $$ $$ \rho \frac{D\vec{v}}{Dt}=\rho\vec{g} - \nabla{p} + \nabla \...

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