# Fluid dynamics Definition and 333 Discussions

In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including aerodynamics (the study of air and other gases in motion) and hydrodynamics (the study of liquids in motion). Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space and modelling fission weapon detonation.
Fluid dynamics offers a systematic structure—which underlies these practical disciplines—that embraces empirical and semi-empirical laws derived from flow measurement and used to solve practical problems. The solution to a fluid dynamics problem typically involves the calculation of various properties of the fluid, such as flow velocity, pressure, density, and temperature, as functions of space and time.
Before the twentieth century, hydrodynamics was synonymous with fluid dynamics. This is still reflected in names of some fluid dynamics topics, like magnetohydrodynamics and hydrodynamic stability, both of which can also be applied to gases.

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1. ### A Converting this vector into polar form

In the following%3A%20https://pubs.rsc.org/en/content/articlehtml/2013/sm/c3sm00140g?casa_token=3O_jwMdswQQAAAAA%3AaSRtvg3XUHSnUwFKEDo01etmudxmMm8lcU4dIUSkJ52Hzitv2c_RSQJYsoHE1Bm2ubZ3sdt6mq5S-w'] paper, the surface velocity for a moving, spherical particle is given as (eq 1)...
2. ### B What is Knudsen flow?

I am a high school student trying to carry out an experiment about fluid. Thus I am studying Knudsen flow and come up with following questions. 1. How can a Knudsen flow occurs? 2. Can I simply dig a small hole on a board and make Knudsen flow? 3. What the difference between viscous flow...
3. ### B Is blood a rheopectic fluid?

Hello everyone, I need your help. A teacher once told me that blood is a non-Newtonian, rheopectic, pseudo plastic fluid. I get the non-Newtonian/pseudo plastic part, but I can't understand why blood is rheopectic...is it or not? Thanks
4. ### Need help coming up with ideas (bachelor's thesis)

TL;DR Summary: Need help coming up with ideas to present a current thesis in terms of qualitative and quantitative ideas. Hey! I have a problem. I have picked up on a project for which I am planning on doing my bachelor's thesis on. The guy behind the project is not a physicist, per se, as he...
5. ### Volumetric flow of a overflowing cone

I solved the case where m=0.99999. Then the height at which it overflows can be obtained with the equation, when points on the liquid surface are chosen. Then the cross-sectional area is given by the circumference of the circle times the height that the parabola reaches, that cross-sectional...
6. ### I Fluid flow through a pin-hole of x diameter in a closed container

Greetings, I've come across lots of exercises regarding Bernoulli's equation. However, never seen one where the top of the vessel is closed, and fluid flow exists via gas (air) going in. Has this problem been studied in the past? Assume a cylindrical vessel filled to the maximum with a D-sized...
7. ### I Momentum of a Water Jet Impacting Plate

Suppose you have a jet of fluid (say water) traveling vertically upward at a constant velocity. It impacts a stationary horizontal plate and so moves radially outward in all directions. Assume that there's no energy loss during the impact, so the speed of the fluid remains constant. Is momentum...
8. ### Bernoulli equation and parallel pipe branch

Hello! I have a question regarding the application of the bernoulli equation and calculation of the flow through a parallel pipe branch. It's more the basic understanding how the flow will establish. You can find a sketch attached to follow my explanation. Let's assume I have a pipe with...
9. ### I Physics of paper absorbing Water -- Doesn't this decrease Entropy?

Summary: doesn't this decrease entropy ? Cellulose is known for its hydrophilic quality, which can be explained from the polarity of its hydroxyl groups. We all know water can overcome the force of gravity through a piece of paper you put in the water. Correct me if I'm wrong but this is a...
10. ### I Sound waves in a fluid

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?
11. ### Bi-propellant Liquid Fuel Engine Pressures Before Thrust Chamber

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...
12. ### Engineering Fluid Dynamics: Proof of the Static Pressure Head equation

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?
13. ### A How can I interpret the 2D advection equation?

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
14. ### I Can you estimate vertical wind speed based upon temperature difference?

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 =...
15. ### Audio/Video Fluid Dynamics—Building a better MIDI Breath Controller

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...
16. ### B Propagation speed of movements of a fluid in a pipe

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...
17. ### A The kinematic equation'' of fluid flows

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...

19. ### B Beam of air: Extending the range of a fan

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...
20. ### Dependence of the stress vector on surface orientation

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...
21. ### Calculating force on a syringe plunger for a viscous fluid?

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...
22. ### Modelling of two phase flow in packed bed using conservation equations

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...
23. ### Speed/Velocity and Volume Flow Rate of Viscous Fluids

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...
24. ### I Work - Energy Principle Application to Fluid Flow

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...
25. ### I Work - Energy Principle Application to Fluid Flow

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...
26. ### I Bernoull's Equation Derivation From Work - Energy Principle

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...
27. ### B Fluid Continuity Equation in different reference frame

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?
28. ### Fluid flow rate calculation

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?
29. ### A Hydraulic jumps: Why do they occur when/where they do?

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...
30. ### I How Does Fluid Viscosity Determine Viscous Friction Between Fluid and Moving Plates?

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...
31. ### I Maximum hole diameter to prevent water leakage

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...
32. ### B Manometer with a twist

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...
33. ### Force from Water Entering a Pressurized Tank with No Relief Valve

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...

35. ### Vortices and turbulence in square vs round pipe

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...
36. ### Resources for the physics of clouds

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.
37. ### I Neutrally Buoyant Bodies

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.
38. ### Pressure profile of a gas flow through an orifice

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...
39. ### Comparetto type Air Cleaner/Filter: What causes its increased airflow?

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)...
40. ### Slip Conditions for flow between Parallel Plates

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...
41. ### Relating volumetric dilatation rate to the divergence for a fluid-volume

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)...
42. ### Help with best aerodynamic shape of undertray for maximum downforce?

What is best theoretical shape of undertray for maximum downforce , maybe wing shape or venturi shape? classic "venturi shape" with diffuser "wing shape"
43. ### I Why does wind blow leaves in circles?

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...
44. ### Surface Pressure Coefficient Distribution of a Doublet in a Uniform Flow

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...
45. ### Sorry, another Bernoulli equation paradox

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...
46. ### Flow of air through an open tube with a balloon

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...
47. ### Average velocity in a turbulent flow tube

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...
48. ### I A real life problem with plumbing at my house

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?
49. ### Classical Oscillations in Fluids

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...
50. ### Some questions about Friction in fluid flow

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...