What is Fluid dynamic: Definition and 90 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. Seyn

    A Question about Kelvin’s circulation theorem

    In Currie’s fluid mechanics textbook, there is a statement “the vorticity of each fluid particle will be preserved.” as the result of Kelvin’s circulation theorem. Kelvin’s circulation theorem claims that For inviscid flow, constant density or barotropic fluid, conservative body force, the...
  2. Seyn

    A Stress tensor and pressure relationship

    I'm studying with Currie's Fundamental Mechanics of Fluids, Fourth edition. I'm confusing with the above statement; the force acting in the x2 direction is P2=s12n1 which is n1 direction. Is there anybody help me to understand this subject?
  3. R

    I V * grad(V) = grad(V^2/2) - rotor(omega)

    Hi, while studying for my aerodynamics class, I encountered this equivalence that my professor gave us as a vector identity: $$ \mathbf{V} \cdot \nabla \mathbf{V} = \nabla\left(\frac{V^{2}}{2}\right)-\mathbf{V} \times \boldsymbol{\omega} $$ where ## \boldsymbol{\omega} = \nabla \times \mathbf{V}...
  4. E

    Biology Equations governing cavitation, flow speed, and delta vapor pressure...

    Looking for the flow speed for cavitation to occur
  5. tracker890 Source h

    Q2: In a relative non-inertial reference frame, why is fluid velocity zero?

    Q： Referring to the solution of this problem, why does the equation (eq) hold true? $$ \frac{\partial}{\partial t}\int_{CV}^{}{u_{xyz}}\rho d\forall =\frac{\partial}{\partial t}\left( u_{xyz}\cdot M \right) =M\left( \frac{\partial}{\partial t}u_{xyz} \right) =M\left( \frac{\partial}{\partial...
  6. tracker890 Source h

    Q: In a relative non-inertial reference frame, the fluid velocity is zero?

    Q： Regarding item (4), my understanding aligns with (eq_1), where M is a constant. However, why does ##\left( \frac{\partial}{\partial t}u_{xyz} \right)## in (eq_1) equal 0? $$ \frac{\partial}{\partial t}\int_{CV}^{}{u_{xyz}}\rho d\forall =\frac{\partial}{\partial t}\left( u_{xyz}\cdot M...
  7. tracker890 Source h

    Confusion in using the continuity equation here

    Q： Why does assuming "Properties in the tank are uniform, but time-dependent" lead to the validity of (DmDt)sys=0? Doesn't the mass within the system change over time? reference.
  8. tracker890 Source h

    Why can a fluid that satisfies the continuity equation for mass conservation cross streamlines?

    reference reference_2 Q： Why can a fluid that satisfies the continuity equation for mass conservation cross streamlines?
  9. tracker890 Source h

    Q: The instantaneous gas discharge of the system and the C-E

    Q： Why is air expelled from the system, yet the system's mass remains unchanged? Isn't mass related to volume?
  10. I

    I Compressed air Pushing a Column of Water

    Greeting, I have been noodling on this problem for a bit and was hoping to have some input from this form. what volume of compressed air, at 200 PSI, will it take to push lets say 30 gallons of water 8 feet up a 3/4" pipe at a minimum of 8 gpm with a minimum pressure of 8psi at the top if...
  11. D

    Creating turbulence in a small tube

    I have an odd question or a project I have been bouncing around in my head and I want to make sure that I am understanding the science of it all correctly. My question is will this cause turbulence in the larger chamber so that the air from the Yellow Question mark area is being pulled and mixed...
  12. URIA

    Help with fluid dynamics problem

    Dear All, I tried to solve the attached question. it's about Couette flow, where the 2 plates move. in fact, I have to find the stability condition. is someone familiar with this and can help? many thanks, uria
  13. tracker890 Source h

    Why Is Taking Moments at Point A' Incorrect in Rotational Balance Problems?

    Please help me to understand why it is wrong to take moment for point ## A’ ## , because I think static equilibrium should be static equilibrium for any point in space. Method 1： $$ \sum{M_A=0:} $$ $$ F\cdot R=\left( F_p \right) _x\cdot \left( R-y_p \right) +\left( F_p \right) _y\left( x_p...
  14. tracker890 Source h

    Q：Hydrostatic Pressure vs. Energy Conservation Equation

    Please help me to understand which ans is correct. To determine the ##P2##. $$ h_{LM}\ne 0 $$ Method 1： $$dP=\frac{\partial P}{\partial x}dx+\frac{\partial P}{\partial y}dy+\frac{\partial P}{\partial z}dz$$$$\phantom{\rule{0ex}{0ex}}\rho \overset\rightharpoonup{a}=-\triangledown p+\rho...
  15. K

    Engineering Hydrodynamic force on hinged flap gate

    I have attempted to use the law of conservation of momentum. The Areas are the lengths marked with the red striped line times the length into the paper, and the Forces F1 and F_hydro are the hydrostatic pressure and hydrodynamic forces respectively (acting on the plate) (The x y components is...
  16. tracker890 Source h

    Question about source flow rate across line AB.

    Q：Please hlep me to understand which ans is correct.To determine the flow rate in Line AB. $$\mathrm{Known}：V_A,q,r_A = constant.$$ so/ select：## A,{B}^{\text{'}},B,A,## is control volume $${Q}_{AB}={Q}_{A{B}^{\text{'}}}=\iint _{A}^{}({V}_{A})dA={\int }_{{\theta }_{A}}^{{\theta...
  17. jackkk_gatz

    How far will the bottom gate of a reservoir open?

    <Moderator's note: Upload images to PF. Do not use an external image server.> I got an expression for the angle taking that initially the gate is closed, so the gate has h, W and L as their dimensions. So there is a surface integral to find the resultant force applied on the gate, using the...
  18. samy4408

    I Relationship between viscosity and velocity in fluid mechanics

    hello, I read in a lecture paper about fluid mechanics that velocity is not related to viscosity, i found this odd and i think it is an error , can someone confirm that?
  19. wessholders

    I Water flowing through a funnel

    Will water flowing through a funnel be accelerated more by a "curve-walled" funnel rather than a "straight-walled" funnel?
  20. P

    I Compressed gas energy storage formula

    Hi, I’m looking for formula to find the energy stored in a compressed gas for non ideal gases, for example, argon. The formula should also include the thermal energy caused by compression. Thank you in advance.
  21. R

    Real-life phenomenon/application of this fluid dynamics model

    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 /...
  22. K

    A Thermal shock wave question from my hydrodynamics simulation

    This is a fluid dynamic simulation. The top area has 100 degrees Celsius. The bottom area has 0 degrees Celsius. And both are filled with an ideal gas which is 1-atmosphere pressure. Two areas are connected through the left small line. Another part is blocked. So heat transfer can only happen...
  23. Angelo Pascal

    Geophysics: Fluid Dynamics Problem

    (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) +...
  24. bjarke

    Hagen-Poiseuille vs Bernoulli

    I am trying to calculate the exit velocity of a nozzle (0,25Ø) that is connected to a high pressure syringe (10 BAR), however I cannot understand why Hagen-Poiseuille will have a higher exit velocity then Bernoulli when HP take viscosity into account.
  25. W

    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)...
  26. Tymofei

    Pressure Differential in Fluid Dynamics: Why More on the '+s' Side?

    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...
  27. Amitayas Banerjee

    How does water rise along a glass plate? (surface tension question)

    So, I was studying about general properties of matter and topics like surface tension. I came across the phenomenon of water rising along a glass plate like in the picture. I looked for some mathematical interpretation of this on the internet and in some books. [![enter image description...
  28. nohappy

    The Venturi Effect cannot explain how an eductor works

    I've google all the keywords like "eductor", "ejector", "Venturi pump". All of them are the mechanism or applications that utilize "Venturi Effect". All of them are trying to explain the "suction effect" by saying that restriction area makes the fluid's velocity higher and hence lower pressure...
  29. Geith

    (Fluid mechanics) How to find the flow rate of a gas from a vessel

    I am working on a project where I have to calculate various results relating to the motion of a water bottle rocket being launched. I am currently stuck on trying to find how long the thrust period of the rocket is. The model for the rocket is as follows: It is a 2L (0.002m3 bottle filled with...
  30. O

    I Force on a rigid body inside a liquid flow

    Hi, I am trying to find out Force on a rigid body when it is completely inside a fluid with density p, i.e. the body is completely drowned in the liquid and then another liquid is pushed into the container with different density 'r' (such than r > p). Thanks.
  31. X

    Measure flow rate with a manometer (pressure gauge)

    Hello! I have a volume of 50 liters which I pressurize with air so that I read 1 bar on the manometer. But there is a leakage in the volume so after 30 sec the manometer shows 0,5 bar. What is then the air flow ( liter / min) of the leakage?
  32. Kaushik

    B Uncovering the Complexities of Streamlined and Steady Flow in Fluid Dynamics

    What is the difference between streamlined and steady flow? Is unsteady streamlined flow possible? If yes, could you please explain what are the characteristics of unsteady streamlined flow?
  33. yash_it_is

    Gauge pressure in Momentum conservation of fluids.

    I want to ask why is it that we use gauge pressure instead of absolute pressure in CV analysis for momentum conservation of fluids. I did read that because P(atm) would be present everywhere so it won't have a net effect on the CV but it's highly non intuitive as I can't apply force balance on...
  34. ValeForce46

    Is the balance of forces equation correct for a tube immersed in alcohol?

    This is a problem from a past exam. For point a) the balance between force should be given by the following equation $$M*g+p_0*A=ρ*g*(A*d)+p*A$$ But I still have two unknown values... I know that pressure outside the tube at depth d is $$p(d)=p_0+ρ*g*d$$ and this has to be equal to the...
  35. J

    Sinking Object Motion Equations

    Hi guys! I am currently learning about fluid dynamics, and I am stuck on a certain equation derivation. It's about sinking motion which considers only gravity force, buoyant force, and viscous resistance. The link attached has the details...
  36. tjholi

    Derivation of the Emptying Time for a buoyant box to drain

    Problem Statement: I am having trouble deriving the expression from the initial equations. (Calculate the emptying time considering Volume conservation) Relevant Equations: Q=A*sqrt(b(H-h(t)) And we have dh/dt =Q/S (conservation equation) and we have to obtain h/H = 1-(1-t/te)^2 with te=...
  37. schang04

    Calculate the time it takes for gas to fill a chamber (high P -> low P)

    How do you calculate the time it take a high pressured gas to fill a chamber? I have a gas in a chamber that is at 600psi and then another chamber at atmospheric pressure. When the valve between the two chambers is opened, how do you calculate the time it would take to fill the chamber? Are...
  38. WhiteWolf98

    Fluid Dynamics - Mass Conservation, State Equation for an Ideal Gas

    I understand that ##\dot m=\rho Q## and ##{\dot m}_{in}= {\dot m}_{out}## . So one can say that ##\rho Q_1 = \rho Q_2##. But I'm not sure if that equation is correct. I don't know if the density remains constant, or the volume flow rate. And then how I'm also supposed to tie a state equation in...
  39. B

    I Analytical Open Channel Rectangular Fluid Flow

    Hi All, I'm looking for an analytical solution to the open channel rectangular fluid flow profile. The flow is bounded by three walls but the top is open to atmosphere. Assume steady state flow that is parallel and incompressible.I've already found information involving a rectangular flow...
  40. E

    Pressure in Forces on Submerged Surfaces

    Why does the pressure we take into account is the gage pressure and not the absolute pressure? Reading Fundamentals of Momentum Heat and Mass transfer by Welty in chapter 2 it says "the magnitude of the force on the element dA is PgdA ,where Pg is the gage pressure" my question is why the gage...
  41. LordGfcd

    A fluid mechanics problem -- Shape of a falling water drop

    Homework Statement A drop of water fall towards the ground with initial mass [m][/0] and radius [r][/0] (assume the initial shape of that water drop is sphere). the air resistance is F=½.ρ.A.[v][/2].C (C is the drag coefficent, A is the area that the air contact with the water drop and ρ is the...
  42. T

    Calculating the drag force on a spherical object with holes

    I am looking for a bit of guidance on how one could calculate the drag force of a sphere with holes in the sphere falling through a fluid, in my case water. So I know for a low Reynolds number the drag force on a sphere is given by stoke law, but what I would like to do is calculate the drag...
  43. EastWindBreaks

    Why does this solution assume it's a steady-flow system?

    Homework Statement Homework Equations unreliable source of solution: The Attempt at a Solution [/B] I came across this problem while practicing for the final exam in thermodynamic,my attempt: i recall this type of problems are not steady-flow system. Since the change in kinetic and...
  44. P

    Is this kind of pressure chamber design possible?

    Hi! Given that the chamber is airtight and no air leakage occurs, is the design in the picture below possible? Can the pressure inside the chamber cause the button (black part at the top) to be "pushed"? https://imgur.com/a/wOSD30D Obviously the temperatures are over-exaggerated, but the...
  45. Arslan Siddique

    Calculation of Velocity and Shear rate in rectangular channel

    Hi everyone, I would like to know the formula for calculation of velocity and shear rate in my rectangular fluid channel. Here are the important values regarding my rectangular channel. W= 2.5 mm, H=3 mm, L=35 mm. Fluid: Diluted Bacterial suspension derived from wastewater. Flow rate: 0.125...
  46. S

    Calculating Air Speed Diff. of Plane Lifts

    Homework Statement We have a plane which lift area is A=500 m2 and weight of plane is m= 540 000 kg. That the plane can stay in air the pressure difference between top and bottom of the lifts have to be: B>G --> Δp= (m*g)/A = 10 594.8 Pa. Homework Equations Bernoulli equation The Attempt at...
  47. V

    Calculation of pressure variation due to fluid discharge

    Dear all, I have a headache and I need you help, with the following problem. I need to create excel sheet for the calculation (estimate) of the size of the orifice on the orifice plate that will produce a pressure reduction rate in pipeline at 0,5 bar per minute. It is not important to...
  48. A

    Calculating the velocity and pressure profiles across an axial fan

    Hi, This is my first post on the PhysicsFormus I am trying to design an inlet and outlet for an axial fan and calculate velocity and pressure profiles in the duct. See the sketch attached. The ultimate goal is to carry out a CFD study but I was wondering if there is an analytical solution for...
  49. T

    How to find the velocity of air flow around the aerofoil?

    Homework Statement How to find the velocity of the air flow around the aerofoil? Homework Equations U - freesteam velocity β - angle of wing camber The Attempt at a Solution To find the velocity of the air flow at each section of the aerofoil, am I right to say that the horizontal velocity...
  50. T

    FEA for Water Tank: Weight & Pressure Analysis

    Hi, I'm trying to do some stress analysis on a tank filled with water, I have split the walls into sections and applied the appropriate pressures. However, I'm confused as to whether I apply the weight of the water+pressure at that height difference to the bottom of the plate; or will the...
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