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

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Eulerian mass conservation on a stream line to Lagrangian mass conservation

if the density of a fluid particle is conserved on a streamline, $$\frac{d\rho}{dt}=0.$$ Why does this mean $$\frac{\partial \rho}{\partial t}+(\mathbf{v}\cdot\nabla)\rho=0$$ is true everywhere? Why ...
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24 views

How can a rotating cylinder produce lift? [duplicate]

In the air, the velocity and angular momentum that causes a force against gravity is lift. How can a rotating cylinder make lift with angular momentum?
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24 views

Can the fluid volume in a control volume change over time?

For a control volume, am I right in thinking it's just the boundary of the volume that is fixed? The volume of fluid inside the control volume can change, over time?
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26 views

The velocity of air on an airfoil

They say that velocity of the top layer on an airfoil is higher than the lower layer. But, according to the continuity principle of fluid, the velocity of air is inversely proportional to the surface ...
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88 views

Backwards airflow in a Venturi tube

When air is flowing through a Venturi tube, it's speed increases at the narrow section. If the airflow is arranged by moving the Venturi tube through calm air, this means air will momentarily flow ...
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24 views

Does air speed vary in a jet engine axial flow compressor?

Does it get slower and slower after each stage because of the pressure increase? Or does the shrinking of the space after each stage compensate for this and the air speed at the last stage of the ...
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22 views

Using the continuity equation against gravity

Studying Fluid Mechanics right now and in my textbook there is an example of getting water up to a bathroom in a house. We're given the diameter of the inlet pipe and bathroom pipe, but only the ...
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12 views

Viscosity for steam in the Reynolds number

In calculating the Reynolds number for a flow of steam in a pipe, this is the general formula I am trying to use: $$Re=\frac{\rho d v}{\mu}$$ with density $\rho$, pipe diameter $d$, flow steam $v$ ...
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26 views

Expected value, Fluid Mechanics and Momentum balance

I've been doing some problems on Fluid Mechanics involving the balance of Matter and Momentum and I have a question I've been wondering about. Suppose the following: We have a (viscous and ...
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28 views

How to find the force due to fluid pressure over a surface?

The question is about sphere like surfaces, like the hemispherical base of a cylinder as shown. The cylinder is filled with fluid till the given height $h$, and the density of the fluid is $\rho$ ...
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53 views

continuity equation and pressure head in a tank

Consider a tank which is full of water. We connect a horozontal pipe at its bottom. When the pipe is open, water starts flowing through the pipe, then the velocity of water is proportional to the ...
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23 views

How big is the power loss of a downwind wind turbine due to turbulence created by an upwind turbine?

When a horizontal axis wind turbine is placed downwind of another horizontal axis wind turbine (distance between the two is minimal), then the downwind wind turbine has a lower power output because of ...
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28 views

Capillary action and its limitations

From Wikipedia Capillary Action Thus for a 4 m diameter glass tube in lab conditions given above (radius 2 m), the water would rise an unnoticeable 0.007 mm. However, for a 4 cm diameter tube (radius ...
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105 views

Why does it seem as if big vehicles “attract” mine when I drive close to them?

When I drive a car at high speed and when I am near to another big car (like a van, or transport vehicle) I feel an attraction to or something push me toward the other big car . What's the physics in ...
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1answer
70 views

Derivation of Archimedes' principle

It is my understanding that upthrust from a liquid on a body is due to pressure difference on the top of the body and the bottom of the body. How, then, is this fact used in order to derive/work out ...
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37 views

ϕ-component of equation of moition: proving a relationship [closed]

I have the following velocity vector (in spherical polars): \begin{equation} \textbf{v} = u \hat{\textbf{r}} + v_{\phi}\hat{\boldsymbol\phi} \end{equation} Where $u(r) = u$ and $v_{\phi} (r) = ...
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46 views

How can I carry out this force summation? Control volume involved

I have a stationary jet engine on a test stand, like shown in the next figure: The control volume is indicated in the figure as a dashed rectangle, that has its left side far upstream of the ...
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283 views

Physics of how the cochlea isolates frequencies along its length?

Can anyone explain the separation of frequencies along the basilar membrane of the cochlea please? (equations would be nice) I understand it being related to the resistance caused by fluid in the ...
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44 views

Self-made air pump - What does it take to pump up a balloon?

We are building a simple altitude-controlled balloon (idea borrowed from Google Loons). As part of that, we need an air pump to inflate a balloon acting as ballast (which is called a Ballonet in ...
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20 views

Calculating power in fluid systems with $pQ.$

I was wondering: say we have a fan which is being used to provide lift to some mass, like in a simple air cushion device, where the air has to flow through a chamber beneath the fan. Let's say that ...
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27 views

How are shock waves related to sound, and are there equations describing its density, size, and pressure?

How exactly does one model a shock wave? I've done a lot of searching and have failed to find any equations where we're able to relate things such as its pressure, density, temperature etc. I've ...
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17 views

Roughness of the Surface and the time that a toy hovercraft hovers?

My question is about a toy CD hovercraft. I want to know that how does the time that the hovercraft hovers scale with roughness of the surface? Thanks in advance
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71 views

Water clock in ancient time [closed]

A Water clock used in ancient Greek is designed as a closed vessel with a small orifice O.The time is determined according to the level of the water in the vessel. What should the shape of the vessel ...
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102 views

What's up with my whipped cream? [closed]

I got a latte with whipped cream this morning, and towards the end of the drink I noticed a peculiar effect. Regardless of how I turned the cup and thereby the coffee, the whipped cream pieces ...
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1answer
54 views

The demise of the Tacoma Narrows bridge was casused by aeroelastic flutter. But isn't that just a special case of resonance?

Much of the research I've done on the Tacoma Narrows bridge disaster of 1940 attribute the collapse of the bridge due to aeroelastic flutter - not strucural resonance. But isn't aeroelastic flutter ...
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31 views

Conceptualising the switch from discrete molecules to the continuum (fluid dynamics)

I understand that $\rho(x,t)$ represents the density of the small volume surrounding the point $x$. However what have I done with the discrete molecules in the process of averaging?
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63 views

Deriving an Euler Equation

In this derivation is it necessary to write the triple integral, as I thought that if we are dealing with one fluid particle it only contains one "point" and hence we do not have to take a sum?
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54 views

What does the continuum hypothesis of fluid mechanics mean?

I'm a bit confused by the continuum hypothesis stating that fluid are continuous objects rather than made out of discrete objects. Say for $\rho (x,t)$ (density) is there more than one fluid ...
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31 views

Pressure as the magnitude of the reaction force

Here $\vec{F}$ is the reaction force caused by the interaction of the fluid particle on the surface and another. I don't think the two parts I have highlighted in green tally with one another. If ...
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76 views

Mass flux across a volume

Here mass flux means the mass flow rate, units: kilograms/second This is for a one-dimensional flow Firstly is the reason why the mass flux/ mass flow rate $=$ $\rho(x_1,t)A(x_1,t)u(x_1,t)$ ...
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103 views

Continuity equation in fluid mechanics

The continuity equation in fluid mechanics states that $$ \frac{\partial\rho}{\partial t} + \nabla\cdot(ρ\mathbf u)=0 $$ Can you explain to me what is the physical meaning of each term of the ...
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1answer
35 views

Is the Mass flow rate (Mass flux) a scalar quantity?

Wikipedia states that mass flow rate is a scalar quantity, however Mass Flow Rate= Density x Cross Sectional Area x Velocity and velocity is a vector quantity, so this would imply Mass Flow Rate is ...
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1answer
50 views

Rate of Dripping of tube

My original problem was to discover the rate at which leaking taps dripped, and its relation with the tap's size, radius, etc. However, I have no clue how taps work, so I simplified the problem. ...
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10 views

What to measure for cylinder stiffness/compressibility?

I have 2 cylinders made from different polymers. Both cylinders are made to 'accept' the same volume of water. When I fill cylinder 1 it is subjectively stiff while cylinder 2 is subjectively floppy. ...
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107 views

How to calculate liquid pressure regardless of the gravity?

Assume we have a balloon in a tank filled with a liquid , without any gravitational forces: We just know the Temperature, V0 and V1 I want to calculate the pressure exerted from the liquid on the ...
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Where can I find a table for NIST standards on temperature and pressure?

The Wikipedia article Standard conditions for temperature and pressure notes that IUPAC and NIST are two of the most common standards for temperature and pressure in use. Even if I could have gotten ...
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55 views

Why is mass per second constant in the Equation of continuity?

Why should the mass per second be constant in the equation of continuity? Why can't the mass accumulate inside a tube?
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75 views

Walking on water

I was wondering about walking on water. I wonder if we can use surface tension to do this. Lets say I make a pair of shoes in shape which has infinite perimeter (e.g a koch snowflake) with glass. Now ...
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36 views

What will happen to this fan in this situation?

Lets say I have a pipe with a fan at the end of it and it is drawing ambient air from the other end of the pipe. Once I account for some blockages and looking at the fan curve, it was found the ...
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2answers
88 views

By what mechanism is lift produced on a rotating cylinder in an inviscid flow?

I am taking some introductory fluid dynamic classes, and have become very confused by the Kutta-Joukowski theorem. One of the conclusions that can be derived by applying Kutta-Joukowski is that a ...
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1answer
52 views

Why does a propeller suck in air from the front?

A rotating but fixed propeller sucks in air from the front. What is the cause for this acceleration of air particles? Since propeller blades act like rotating wings, my best guess is that the blades ...
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1answer
99 views

Is Magnus effect a corollary of Bernoulli principle?

Magnus effect is commonly explained using Bernoulli principle. However, taking the lift on a rotating cylinder as an example, the velocity difference is caused by the extra work done by the rotating ...
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39 views

Superfluids (meaning, properties)

I am curious as to what a superfluid is? I have seen videos that say that they have zero viscosity, and I know that it means that there is no friction between the layers of the fluid. But what is its ...
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28 views

Microscopic definition of dynamic pressure of fluids

So we have a moving fluid and we know from Bernouli's equation that there is a term called dynamic pressure(not to be confused with the hydrostatic pressure of the fluid). So,what exactly is it and ...
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33 views

What is the difference between high speed water supply and high pressure water supply coming out of a hose?

According to Bernoulli's principle, $P + \frac{1}{2} d v^2 + dgh = constant$ where, P is pressure, d is density of water, v is velocity and h is height. Assuming that height of a plastic pipe is ...
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1answer
31 views

Tsunami effects of a nuclear explosion

Sea surface nuclear explosion arouses a tidal wave of water. How does this kind of wave compare to naturally occurring tsunamis? E.g. what would be the potential of a 100KT bomb 100km away the from ...
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44 views

Why does this capillary action generator not work?

So I was doing a bit of reading. Apparently the the obstacle to generating energy from the forces driving capillary action is breaking the surface tension at the top of a capillary tube. It is just ...
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Practical nozzle question / mass of finger?

A spray bottle i own broke off its compressor tip so i fashioned another one from a rubber tube, a pen lid, an ear plug and a 1 mm radius tube from a computer cleaning duster. The opening of the ...
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How to obtain this equation for skipping stones over water?

I think I have a decent conceptual understanding of the forces at work when stones are skipped over water. My question pertains to the equation found in this [source][1]. Reproduced in Latex this ...
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boundary layer pipe

What is the shape of fluid(say water) on exiting a pipe due to boundary layer formation?Since the velocity decreases as we move from centerline of pipe to boundary along the radius(say fully developed ...