Fluid dynamic Definition and 93 Threads

Hello everyone, I’m working on a project where I need to use a cylindrical tube with a vacuum pump to suck in mechanical parts. The tube approaches the part, and the vacuum generated by the pump draws the part into the tube. I want to understand how to link the key parameters of the system: the...

First of all I have this system $$\begin{pmatrix}\tau_{xx} \\ \tau_{yy} \\ \tau_{zz} \\ \tau_{xy} \\ \tau_{yz} \\ \tau_{zx} \end{pmatrix}=\begin{pmatrix}C_{11} & C_{12} & C_{12} & 0 & 0 & 0 \\ C_{12} & C_{11} & C_{12} & 0 & 0 & 0 \\ C_{12} & C_{12} & C_{11} & 0 & 0 & 0 \\ 0 & 0 & 0 & C_{44} & 0...

To find the potential function, I'm starting with the laplace equation ##\Delta \phi = 0 ## In cartesian coordinates the solution is ##\phi = \sum_m (A_m e^{mx} + B_m e^{-mx}) (C_m sin(my) + D_m cos (my))## Using the first boundary condition. ## u = \Delta \phi = -u_0 \hat{y}## The gradient in...

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...

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?

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}...

Looking for the flow speed for cavitation to occur

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...

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...

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.

reference reference_2 Q： Why can a fluid that satisfies the continuity equation for mass conservation cross streamlines?

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

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...

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...

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

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...

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...

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...

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...

<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...

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?

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

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.

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 /...

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...

(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) +...

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.

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)...

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...

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...

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...

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...

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.

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?

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?

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...

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...

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...

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=...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...