Questions tagged [flow]

The motion of fluids (gases, liquids and granular material).

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1answer
42 views

How does a viscous fluid flow?

In all problem involving viscosity, while applying $f=nA \frac{du}{dz}$ why do we consider velocity of the bottom layer to be zero?
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Fluid mechanics

I have seen the following equation of continuity for fluid dynamics for compressible as well as incompressible fluids $$\rho_1V_1A_1 = \rho_2V_2A_2,$$ and it is derived from conservation of mass ...
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121 views

Airflow velocity and volume loss due to friction

I have a vacuum that the manufacturer claims capable of moving 20,000 cfm of air. In my application we often connect 150 feet of 6 inch diameter, smooth bore, flexible tubing to the vacuum. I know ...
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1answer
326 views

What is the physical meaning of irrotational flow?

I am studying fluid dynamics and while searching on the internet, found many videos explaining the mathematical aspect of rotational and irrotational flow, but i need more clarity on what actually it ...
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230 views

What happens to the fluid flow velocity and concentration in a tube that branches out

Suppose that liquid is flowing through a tube with a constant velocity of, say 10 m/s. Within the liquid, there is a constant concentration of some substance, [S], lets say of 20 uM. Then, at some ...
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1answer
210 views

Why textbooks use geometric center/centerline of the pipe when calculating/measuring pressure?

Studying Fluid Mechanics, I started to notice that almost every textbook/website uses a specific point to make calculations about the pressure in a liquid at a given depth (hydrostatic pressure): the ...
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182 views

Transitioning between Lagrangian and Eulerian fluid variables

I'm having trouble understanding the motivation between wanting to transition between the two descriptions. I figure that switching from Eulerian to Lagrangian fluid variables is useful if we want to ...
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211 views

Why using average pressure in calculations gives the most accurate results?

In the saga of trying to answer the question that came into my mind while studying the basic concepts of Fluid Mechanics, "Why textbooks use geometric center to calculate hydrostatic pressure when ...
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279 views

Does the drag equation only apply to turbulent flow

I am doing an analysis of the motion of an object in air and so I'm first finding whether the flow is laminar or turbulent. From my research, I'm still a bit confused as to whether the drag equation ...
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230 views

How to calculate the power required by a fountain pump?

How can I calculate the power required by a fountain pump, if just the efficiency of the pump, the height of the fountain and the diameter of the water jet is given?
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1answer
496 views

Continuity equation in the Lagrangian flow picture approach

In deriving continuity equations using Lagrangian. We consider the element of fluid which occupied a rectangular parallelopiped having its centre at the point $(a,b,c)$ and its edges $\delta a$ , $\...
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301 views

How is the power of water flowing through a pipe directly proportional to $v³$ and not $v²$?

How is the power of water flowing through a pipe directly proportional to $v^3$ and not $v^2$? (Where $v$ is the velocity of water) I have been trying to write power in terms of $v^3$ but I'm ...
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Introducing stream function with given velocity equation

Bit information about the problem We are dealing with the slide coating process - where basically a polymer is being put onto a slot, which is moving in the $x$-direction with velocity $v_0$. The ...
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126 views

When exactly can the concept of stagnation pressure be applied?

Although I've attached a homework problem here, I'm only using it for reference for a conceptual question on stagnation pressure. From my understanding, in the photo attached above, the pressure at ...
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33 views

Grounded Circuit Electricity Flow

Yesterday I watched a video "How to connect LED strip to your car" in which one of the LED powering cable wires was connected to the body of the car(grounded) and the other one to a fuse. My questions ...
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49 views

Why that Bernoulli function contains many streamlines and vortex lines but not only singular streamlines?

I know that for a stream line inside the gradient part equal to a constant. But when we consider the fluid is rotational which the velocity cross product vorticity not equal to zero. So how can we ...
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Computing the velocity of fluid along the length of a cylinder

I am modelling the flow of fluid through a cylinder of length L.The cylinder is divided into three segments(each segment of length L/3), there are four nodes(i=0,1,2,3). I'm trying to compute the ...
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231 views

Why does Pascal's principle apply to a Hydraulic jack but not to stream lines in a stream tube?

Pascal's principle says that the pressure applied at one point in an enclosed fluid under equilibrium conditions is transmitted equally to all parts of the fluid and thus the pressure in e.g. ...
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Flow rate and pressure of air in a constant diameter hose vs. flow rate and pressure of air in a hose of varying diameter

Say we have Hose A, a straight hose with constant diameter D. Also we have Hose B, a hose with a varying diameter, but whose average diameter throughout the length of the hose is D. (diameter of hose ...
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127 views

(Fluid Dynamics) Euler's equation including gravity

In fluid dynamics, we can write down the Euler's equation as $\dfrac{\partial \mathbf{v}}{\partial t} + ( \mathbf{v} \cdot \mathbf{\text{grad}} ) \mathbf{v} = - \dfrac{\mathbf{\text{grad}} \; p}{\rho}...
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How do “pouring spouts” prevent liquid from escaping through the air intake?

You may be familiar with the types of pouring spout found in many professional cocktail bars, similar to the following: The hole on the top of the spout is an air intake, which connects to the narrow ...
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50 views

Can all 2D solenoidal fluid flows be given in terms of a stream function?

Is it true that for any 2D solenoidal fluid flow $\mathbf{u}$ ( i.e one with zero divergence, $\mathbf{\nabla\cdot u = 0}$ ), that $\mathbf{u}$ may be obtained from a stream function? I had always ...
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Minimal drop size

I am trying to do something that requires very high precision, so I got stuck in a question: What is the lower bound of a size of a water droplet (and what is the equation, I want to use different ...
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2answers
147 views

Density of particles in the Lagrangian description of fluid flow

I am trying to learn about the material (or particle) derivative in fluid dynamics. I was looking through this explanation, and they mention things at the beginning and the end that confuse me. ...
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25 views

How to get constant water pressure in a circular distribution pipe?

I have a circular 3/4" pipe( 62" in diameter). It has 11 tee outlets, 3/4"x3/4" to 1/2", which each have a 1/2" hose that funnels the water downward. The pump(400gph) is pumping the water vertically ...
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Does molten solder flow towards a heat source?

When soldering both plumbing and wiring I have heard the advice that you shoulf apply solid solder opposite to your heat source, since the solder "will flow towards the heat" once it melts. Is this a ...
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214 views

Bernoulli's Effect on Blood Pressure [closed]

What is the impact of height, let's say being on top of a 4,000 m high mountain, on blood pressure / flow velocity given Bernoulli's Equation?
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Bernoulli principle

I've been trying to deduce the Bernoulli's theorem but i have a few problems Why is it restricted to a streamline? Thank you very much
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Fluid Pressures at the End of the Pipe

Consider the very standard pipe problem used to calculate the force required to hold a pipe with a bend that has some fluid flowing through it, as shown in the image. We use Newton's second law of ...
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1answer
118 views

Mass flow rate of evaporating water in a vacuum

I'm melting ice in a vacuum using a heating plate, and attempting to condense any water vapor evaporated from the melted water onto a cold plate. Is there a way to describe the mass flow rate of the ...
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1answer
95 views

Hydroponics Recirculating water flow [closed]

I hope this is the right place to post this, and help would be appreciated. I've have been working on a multi tower hydroponics system for the past couple of weeks. I'm currently trying to figure ...
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1answer
37 views

What is the force being applied? (Water Pump Problem)

Lets talk about the water pump problem where you must pump water up and out of a tank and figure out how much work was needed to accomplish this. So assume we have a cubic container with length 1 on ...
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1answer
63 views

Confusion on flux definition

In the context of fluid mechanics, flux is the quantity per time per area and one could calculate the total movement of that quantity per unit of time through a control surface by $$\iint{}flux(S,t)...
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Proof regarding curl of a vector [closed]

I'm stuck in this problem where we need to prove that the curl of the velocity vector is twice the angular velocity of a rigid body in circular motion. How do I prove it? I am very new to the concepts ...
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275 views

Non-dimensionalization of Navier-Stokes equations multiphase flows

I am currently dealing with multiphase flows and have to use the non-dimensional form of the Navier-Stokes equations (NSE). In the scientific literature I found various formulations (and almost no ...
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1answer
527 views

3D Stream function in fluid mechanics

The 3D stream function ${\bf \Psi}$ for a steady flow field can be defined as: $\rho{\bf u}={\bf \nabla}\times {\bf \Psi}$. Where, ${\bf u}$ = velocity, $\rho$ = density. Now, this ${\bf \Psi}$ can ...
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Anomalous dimensions and RG flow - Polchinski 1984

While defining a renormalizable field theory in the UV, we can assume it to have a simple form, i.e only containing a few operators(the relevant and marginal ones). Now, as we start flowing along the ...
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2answers
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Creating a constant flow system [closed]

I've been asked to create a system that will output a constant flow of liquid (water) even when the input pressure is variable. I can't use gravity filtration because the system is for a straw filter ...
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1answer
105 views

How to find velocity of water flow and $Q$ if I know static pressure at the end of the pipe of known diameter?

I have a pipe. At its end I have mounted pressure meter. Of course there is no circulation. Water pressure meter is a kind of stopper for water. I know diameter of the pipe, and I know its pressure in ...
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2answers
314 views

Is equation of continuity valid even against gravity?

Consider a tube having variable cross section and is placed vertically. The upper part it has a cross section of $4\ \mathrm{mm^2}$ and the lower part has a cross section of $2\ \mathrm{mm^2}$. If ...
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1answer
65 views

What should be the characterisitc dimension for angled entry of cylinder in water?

I am working on problem for angled entry of cylindrical object in water (30 degrees and 60 degrees), for that I need to calculate the characteristic dimension of the cylinder to calculate the impact ...
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1answer
104 views

Deriving the variable area flow equation from the differential form of continuity equation

Following is the differential form of continuity equation for a steady in-compressible flow $$ ∂u/∂x+ ∂v/∂y + ∂w/∂z = 0$$ Now can we obtain the variable area flow equation A1V1=A2V2 by solving ...
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Is it possible to calculate natural gas (i.e. methane) flow in pipe based on temperature and pressure?

Given a known pipe diameter, pressure, and temperature, is it possible to calculate the flow rate of natural gas (i.e. methane et al) in the pipe? To me, this doesn't seem possible without some sort ...
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1answer
131 views

Why is the contour of a stream function the same as the streamline?

I am studying acoustic streamlines. As this paper Singular points of intensity streamlines in two-dimensional sound fields says the level curves or contours of stream function represents the ...
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2answers
1k views

Zero velocity divergence for incompressible flow is derived from conservation of energy equation or conservation of mass equation?

I'm a bit confused about incompressible flow definition. In many textbooks or scientific articles, they simply claim that the incompressibility condition for Navier-Stokes equation is: $\nabla \cdot \...
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290 views

Intuitive explanation of supersonic flow behavior?

It is well known that once the flow of a gas becomes supersonic, it behaves very differently to subsonic flow: Velocity increases as flow area increases. Velocity decreases along a pipe with friction....
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93 views

Buoyancy: integrating over a region where the fluid isn't?

On both ProofWiki and Wikipedia, the article's respective authors manage to arrive at Archimedes' principle by applying the Gauss theorem to the surface integral of the fluid's stress tensor $\sigma$: ...
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Why does compressible flow never choke in a thin-plate orifice?

According to this Wikipedia article on orifice plates: ... the flow of real gases through thin-plate orifices never becomes fully choked. Further to this, there is a reference given, which states ...
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Are there any fluids that flow slower in a constricted region, unlike water?

It is well known that when water flows through a tube you can make it flow faster by making the tube narrow. Now consider what happens when a group of people are moving and the space becomes narrower....
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a flow through a pipe submeged in a moving fluid

There is a classic problem by which a fluid having a uniform velocity profile enters a tube. The pressure at the outlet is atmospheric, and the dimensions of that tube (diameter and length) are known. ...