Fluid dynamics Definition and 608 Threads

When we talk about sound waves in a fluid (air, water e.t.c.) we mean that the pressure ##P(x,y,z,t)## satisfies the wave equation, the so called velocity field of the fluid ##v(x,y,z,t)## satisfies the wave equation or both?

Been reading Rocket Propulsion Elements 9th Edition and got approval from my university to design a bi-propellant liquid fuel rocket engine for my senior design project, and I've been understanding everything so far but I haven't quite found an answer to how the pressure works throughout the...

I am trying to mathematically prove the Static Pressure Head equation: H = p/ρg How can I prove this equation and thus determine the nature of the relationship between these variables?

I want to model the advection of debris rock layer with a thickness hd on top of a glacier through ice flow with velocity components u and v. Can anybody explain the physical difference between these 2 equations and which one I should take? Thanks

Hi all, I have some data from an automatic weather station, with recordings of both 2m air temperature and 2m air pressure and also the surface temperature. Is it possible to estimate vertical wind speeds between the AWS and the surface based upon this data? Imagine T_a = 15 degrees and T_s =...

Background A MIDI breath controller converts breathing to MIDI values, which are then used to control a MIDI instrument and produce sound. The ones I'm familiar with work through the use of a pressure chip. For example, the TEC Breath and Bite Controller 2 uses the MPCV5010GP...

Assume that we have a 1.5 km x 100 cm^2 long straight pipe, totally inelastic and full of water. From time t = 0, a pressure of 300 000 Pa is continuously applied to the water with a piston at one extremity. This correspond to a force of 30 000 N on the pipe cross section in the direction of the...

Ocean physics explain cyclones on Jupiter https://phys.org/news/2022-01-ocean-physics-cyclones-jupiter.html Moist convection drives an upscale energy transfer at Jovian high latitudes https://www.nature.com/articles/s41567-021-01458-y...

I saw this in a textbook and I thought it is a corollary of Reynold's transport theorem. Let \mathbf{F} be a smooth vector field Consider the surface integral: \int_{S}\mathbf{F}\cdot d\mathbf{S} and now take the derivative of it, then the expression can be written as...

If one Googles for "laminar flow nozzle", one finds many interesting tutorials on creating a nozzle for a laminar water jet; a stream of water that remains coherent over a long distance without breaking up. These typically consist of a large-diameter tube with regions inside (like sponges and...

According to Cauchy's stress theorem, the stress vector ##\mathbf{T}^{(\mathbf{n})}## at any point P in a continuum medium associated with a plane with normal unit vector n can be expressed as a function of the stress vectors on the planes perpendicular to the coordinate axes, i.e., in terms of...

Hi! Water is flowing in a converging duct, with the angle α, see the figure. My task is to find a real-life phenomenon / application of this model, and later solve it numerically / analytically where this fluidproblem occurs. However, my imagination is kinda slow today, what are some fun /...

I'm currently working on a precise glue/resin dispenser, and I'm trying to derive an equation for the force one must exert on a syringe plunger as a function of the desired flow rate Q, and also accounting for the fluid viscosity and the syringe barrel and needle geometry. I've attached a scan...

Previously, I have seen the derivation of the energy conservation equations for simulation of single phase flow in a porous media (a packed bed). These are the energy equations for the solid and fluid respectively: I understand the derivation, however, these equations will only work when the...

In my first attempt, I started off converting the radii of all three sections from centimeters (10, 8, 6) to meters (0.10 , 0.08 , 0.06), then used the VFR=Av formula to find the speed/velocity of section one. VFR== 0.063 m^3/s A== pi*r^2=pi*(10cm)^2=pi*(0.10)^2=pi*0.01 == 0.031415927 VFR/A=v...

I came across this notation when reading the wiki article on Venturi effect, which baffled me. Can someone please tell me its meaning?

In classical and continuum mechanics if we want to find equation of motion of the body we draw force diagram and apply Newton's 2nd law. In continuum mechanics, equation of motion actually refers to a special point of the body known as center of mass (COM) which can be proven by definition of...

Work - energy principle states that work done by net force acting on the body equals change in kinetic energy of the body. We are talking about continuum mechanics. This principle is usually introduced in mechanics of solid bodies. For us to describe the motion of the body, it is enough to know...

Work - Energy principle states that work of resultant force or sum of work of all forces acting on some system equals change in kinetic energy of the system. For inviscid fluid flowing in a pipe such theorem can be used to derive Bernoulli's equation because as fluid flows it is subjected to...

If I have fluid with area 10 and velocity 10, if the velocity increases to 20 the area will become 5. But if we switch to a reference frame moving at velocity 1 opposite this motion, then it would be 10 and 11 to 5 and 21, violating the continuity equation. What is wrong?

I am trying to calculate the flow rate of O2 from a known volume 25 in^3. The cylinder will fill up to a maximum pressure of 140 psi in 11.26 seconds. Any help to determine the flow rate will be appreciated. Do I use Bernoulli equation to find the flow rate?

Hi guys, I've been doing some light reading on hydraulic jumps. For example: So I've been through the basics, super critical to sub ciritcal etc: https://en.wikipedia.org/wiki/Hydraulic_jump So far I understand that the jump occurs at the two points either side of the critical depth, like we...

When fluid is placed between two parallel plates such that one plate is moving and other is stationary, fluid will start flowing. Between plate and the fluid there is viscous friction given by equation: $$ F = -\eta A \frac {dv} {dy} $$ where $ \eta $ is fluid viscosity, $A$ is area of a plate...

I have a empty bottle and immersed it into the water, where the pressure inside the bottle is equal to air pressure. If I want to make a hole on the bottle, how big is the hole to prevent the water leak into the bottle at different depth? what kind of parameter is involve in this phenomena? can...

Consider a manometer as shown above with different widths W and w. If we take a mass (red) that is frictionless and does not allow water to leak of mass M, then I would like to calculate the height of water H in the narrow tube of width w. I arrive at a non sensical answer of H = 0 in one...

Hello all, I am trying to understand how a force at the opposite wall from water entering a pressurized air (atmospheric pressure) tank, and for this discussion it is rigid, with no relief valve to displace the compressed air can be deduced. I have created a simple illustration and believe this...

(a) Write down an expression for the velocity field corresponding to uniform rotation. Find the vorticity corresponding to this flow. (b) Consider a small perturbation u' to the state of uniform rotation with angular velocity Ω, which has the form of a plane harmonic wave u'= A exp i(k·x−ω t) +...

Greetings, I am about to start experimenting with misnamed rocket stoves and rocket mass heaters. I say misnamed because I think the velocities are too slow to be rocket science. (Why would I experiment with these? Because I have cement, perlite, and reinforcement materials at hand and I just...

Does anyone know of any good papers/lectures/textbooks/etc that discuss the physical and mathematical principles that explain the structure and motion of clouds? Thanks.

The attachment below describes a tank, hollow pipe and two flexible (balloon like) bags forming one body of weight W_tank. My two questions are what are the downward forces acting on the submerged body in both cases.

Hello, The question will probably be related to mechanical engineering / chemical engineering / aeronautics. I come from the field of optics and have no background at all on fluid dynamics. I'm trying to calculate the dependence of pressure on distance, i.e. P(x) in a gas flow problem: I...

Typical box fan+air filter setups use axial consumer-grade fans designed for providing maximum air flow at low power consumption. These fans do not provide sufficient air flow at the high static pressure requirements typical of air filters. The air filters DIYers use are high Merv(e.g Merv 13)...

v1- velocity of water at the top of the barrel v2- velocity of water at the the pipe (bottom of cylinder) p + (⍴ *(v1)^2)/2 + ⍴gh=p + (⍴ *(v2)^2)/2 + ⍴gh atmosferic pressure cancels out (⍴ *(v1)^2)/2 + ⍴gh = (⍴ *(v2)^2)/2 + ⍴gh density doesn't affect the result(cause its in every term)...

The problem states: Two parallel plates separated by distance h, the plate at the top moves with velocity V, while the one at the bottom remains stationary. My initial approach was: I considered, ##du/dy = V/h## and for the shear stress ##\tau = \mu \frac{\partial u}{\partial y}## For...

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: $$dV = dV_x +dV_y + dV_z$$ I understood the derived relation as: 1/V * (derivative wrt time) = div (velocity)...

What is best theoretical shape of undertray for maximum downforce , maybe wing shape or venturi shape? classic "venturi shape" with diffuser "wing shape"

Can someone please tell me a basic and easy-to-understand example of Residual in CFD? Thank you

why is ro = 0.2255? Thank you

Earlier today I realized that, when a strong gust of wind would blow through my area, it would pick up leaves off the ground and typically blow them in circular patterns, and typically the leaves would go in at least several complete circles before coming to rest back down on the ground. Why is...

So, it's a long way to the solution, but I'm finding it difficult to find a starting point. I'm going to say that as a first step, I should find what the value of the stream function ##\psi## is, at the surface. In order to do this, I need to use the following equation: ##F=\phi+i\psi## If I...

Let's start with a horizontal tube with a constant diameter. I'm not sure if it's important, but let's assume it's frictionless. I will have some fluid flowing in this tube and if it's important, we can make the fluid incompressible, inviscid, irrotational, etc. To create a flow in the tube...

I hope you guys don't mind a bizarre question from a novice. I've learned just enough about fluid dynamics to be dangerous. Assume that we have a straight, rigid tube with a constant inner diameter. It's not long, let's say it's around a foot (in case that matters). We cut a chunk out of the...

hi guys I'm really struggling to get the expression for average speed in turbulent flow The book explains absolutely nothing about how the integration is carried out, in addition to the fact that the logarithmic term becomes undefined when r = R what I did was carry out the integration up to...

I have a problem with plumbing in the bathroom at my condo (quite old) that I am living. The plumbing inside the walls of my bathroom make this whistle noise always and it goes away when I flush the toilet. And then it comes back again after sometime. Do you know what could be happening here?

I am a layman with very little experience in math and physics and recently I became curious about how to analyze dampened oscillations occurring in fluid mediums, such as those following a disturbance in a pool of water. What sort of math and physics is required to understand this phenomenon and...

I have few conceptual doubts in fluid mechanics. Here is the one I will ask first. I want to understand the force direction acting on the solid liq interface during fluid flow, Let's say a fluid is flowing in a pipe. Now the fluid applies a shear stress at the walls of pipe in the direction of...

With the assumptions of Inviscid flow, no pressure gradient and no body force terms in 1-D Navier Stokes becomes 1-D nonlinear convection equation; And if we assume velocity of wave propagation is constant value c, equation becomes 1-D linear convection equation; This is online derivation and...

Here i added a page from my fluid dynamics book where it shows particle model for deriving the equation. My question is why pressure is more at stream side aka 'positive "s" direction'.I would expected more pressure on the other side because for example when you trying to push a rigid object or...