An equation governing fluid flow for an incompressible steady fluid

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A few questions related to bernoullis principle & fluid dynamics in a pipe

I've been struggling with a few things as i've been introduced to bernoulli's principle, hopefully someone can help me clear things up(in somewhat plain, easy to understand language) In the examples ...
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56 views

Bernoulli equation and pumps [on hold]

I have a doubt on the use of Bernoulli equation for pumps. Consider the situation in the picture. I marked different points: $1$ on the surface of first tank, $2$ in the exit from first tank, $3$ ...
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Static vs Dynamic pressure

According to Bernoulli's law, the narrower the tube where the fluid is flowing the lower its static pressure and the higher its dynamic pressure. Does this make any difference? If the dynamic pressure ...
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Rate of air release from bladder with compression to avoid rupture

I need to know the maximum compression speed that can be applied to a rectangular bladder which has a open air port that will avoid rupturing the bladder. The bladder is 40" wide, 100" long, and 10" ...
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1answer
33 views

Matching Bernoulli equation and Hagen Poiseuille law for viscous fluid motion

I thought that Bernoulli equation could be used only in the case of non viscous fluid. But doing exercises on 2500 Solved Problems In Fluid Mechanics and Hydraulics (Schaum's Solved Problems Series) ...
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72 views

Pressure just before the hole in a draining tank

I get extremely confused in fluid dynamics problem where the pressure in some points is required. Consider the ideal fluid in the tank in the following picture. I would like to understand what is the ...
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2answers
58 views

Pressure due to weight of the fluid in fluid dynamics

In Bernoulli equation, the only term which corresponds to what one usually calls "pressure" is $p$, the other are still pressures dimensionally but their meaning is linked to kinetic and potential ...
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3answers
27 views

Application of Bernoullis identity for problem concerning hole in a container

Consider the following problem: We have a container of water with a hole on the side, and we want to determine the velocity of the stream coming out of the hole (at $S_2$): If we suppose $S_1>&...
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2answers
41 views

Different locations of a pump in a tube

I'm confused about pumps in fluid dynamics. As far as I understand, the basic effect of a pump which deliver a power $\mathcal{P}$ can be described with modified bernoulli equation between a point $A$...
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1answer
67 views

If the pressure between the cross-sections of a pipe is equal, will $P_1$ and $P_2$ be cancelled out of Bernoulli's Equation?

a). Water is flowing through a pipe of two circular cross- sections area $A_1$ and $A_2$ lying horizontally as shown in figure below. The pressure difference between the cross-section $A_1$ and $A_2$ ...
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37 views

Conditions of validity of basic fluid equations

I easily get confused about the conditions of validity of basic fluid equations. I list the conditions for these equations to hold true, as I could understand them. $\rho v S=\mathrm{constant}$: ...
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1answer
45 views

Inverted U manometer

I have some doubts on inverted U manometer. In the picture there is one U inverted manometer, the space above the liquid in the manometer is filled with air which can be admitted or expelled through ...
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3answers
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Tank draining derivation: is it correct to use Bernoulli and continuity equations?

I'm confused about a classical exercise on tank draining, which asks to find the time requested for empty the tank. I'll put here the derivation I found on textbook and on the web, which I'm not ok ...
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2answers
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Conversion of pressure energy into kinetic energy

So we have Bernoulli's equation which tells you about the change in different types of energy when fluid flows from one point to another. I can understand the conversion between kinetic and potential ...
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3answers
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Why does Bernoulli's equation only apply to flow along a streamline that is in viscid, incompressible, steady, irrotational?

I am learning about hydrofoil on this website. In a later video I watched, I learned that in the process of deriving Bernoulli's equation, $$constant=P/d+gh+1/2v^2$$ has to multiplied through by ...
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1answer
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How can I determine the height in this fluid dynamics problem? [closed]

Here's the problem: I used Bernoulli's Equation and tried to make the height the subject: The tricky thing about the problem is that the initial height is not given. Checking by dimensional analysis ...
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2answers
49 views

Application of Bernoulli's equation to siphon

I'm trying to understand how to use Bernoulli's equation in practice. So I will make an example of where is my confusion. I found this great explanation on Wikipedia about the siphon, but there is a ...
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1answer
11 views

How come in these Bernoulli problems, the Pressures on both sides cancel?

If you have an open tank filled with water, and you poke a hole half way down the tank, you can solve for things like the speed of the water coming out of the hole with the Bernoulli's equation, $P_1 +...
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82 views

Bernoullis in Parallel pipes

Im having trouble with a scenario where a flow π‘„π‘†π‘‘π‘Žπ‘Ÿπ‘‘ splits into two parallel pipes 𝑄𝐴 and 𝑄𝐡 then rejoins 𝑄𝐸𝑛𝑑 before exiting the control volume what makes this scenario difficult is ...
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76 views

Intuitive explanation for lower pressure above airfoil

From Bernoulli's principle we know for an incompressible fluid (constant density $\rho$) in a gravitational potential $\psi=gz$, that we can state the equation along a streamline from point 1 to point ...
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2answers
46 views

Hourglass fluid mechanics issue with Bernoulli's equation

I know that I'm thinking about this problem wrong, but I've been pondering it for a while and can't understand something. On my fluid mech. exam I had a problem that asked to determine the radius of ...
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1answer
43 views

How is the Bernoulli's Principle related to a campfire blowpipe?

My uncle recently told me that a campfire blowpipe (It is used to blow air into the fire so that it continues to burn) works on the Bernoulli's Principle. How is it so?
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Bernoulli principle and falling object

Consider the following situation, also depicted in the picture bellow (and please excuse my lack of Paint skills): A helicopter is flying at a constante altitude, and hovering the same ground spot. ...
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2answers
65 views

velocity of water exiting a 20 m hole at the bottom of water column 5000 m in height

What would be the velocity of water exiting a tube that has a height of 5000 m from a hole with a diameter of 20 m at the bottom, if the height of the water remains constant at 5000 m? Would it be ...
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Ratio of Stagnation to Normal Flow Properties in Incompressible Flows

I know in compressible flows the ratio of stagnation to normal flow variables is a function of the Mach number and usually the specific heat ratio. Does this ratio mean anything for incompressible ...
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25 views

Bernoulli principle and viscous loss

Imagine I have a fluid flowing at a rate Q in a closed circuit with no viscous losses (Bernoulli's principle applies + total energy is equal to the kinetic energy). Now, I add a resistor with ...
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2answers
334 views

Does continuity equation hold if the flow is accerelated?

I'm Studying the streamline flow, specifically the continuity equation Bernoulli's Principle. Consider the following system where a liquid flows through the pipe of a uniform area of cross section A,...
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9answers
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Are eductors working on the Bernoulli principle?

This is a picture of an eductor. The wikipedia article claims that it works on the Bernoulli principle. The Bernoulli principle is famous due to the misconception about how aeroplanes fly and because ...
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Isentropic flow through nozzle

I've a question concerning the use of the Bernoulli principle. Let's say I have a pipe filled with air at atmospheric pressure, with a constricting section ala the figure below. The volume before the ...
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2answers
118 views

Why does pressure decrease as velocity increases?

Bernoulli's principle states that as velocity increase pressure decreases. But higher the velocity, greater is the temperature and pressure must be high. Can you explain the situation in both the ...
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66 views

Flow in a cylindrical pipe

A cylindrical pipe is, at the left of section A, divided by a plane passing through its axis. The upper half is supplied with water at a velocity $V_1$, the lower half is supplied with water at a ...
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54 views

Origin of spin and direction in the magnus effect

If you solve the Bernoulli equation: $$p=p_0-\rho_0{v^2 \over 2}$$ using a complex flow potential for a flow around a cylinder: $$W(z)=v_0 z + {v_0 R^2 \over z} - {\Gamma \over 2 \pi } \ln(z)$$ you ...
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55 views

Pressure gradients at two different sized holes separating 2 chambers at different pressures [closed]

Why is the pressure gradient by the simplified Bernoulli equation higher at the smaller hole?
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590 views

Why does moving air have low pressure?

According to Wikipedia lift in an aircraft is due to an area of low pressure formed above the wings of an aircraft due to the fast moving air there. So why exactly is an area of low pressure created ...
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74 views

Rate of flow of water fluid mechanics

If we have a cylindrical tank of area $A$ which has a small outlet of area $a$ at the bottom of the surface . And the container starts filling with a constant rate $k [m^3/sec]$ . Now the max. level ...
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246 views

Torricelli's speed of efflux law

Torricelli's law states that if we make a hole in a container of fluid open to atmosphere, then the speed of the fluid spouting out is: $$\sqrt{2gh}$$ Does this velocity correspond to the horizontal ...
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Pressure Variations due to Flow in an Inviscid Fluid

Let's say we have an irrotational, inviscid fluid with steady flow. Then the Bernoulli function (ignoring gravity) $$H=\frac{p}{\rho}+\frac{u^2}{2}$$ is constant everywhere. My notes then make a jump ...
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88 views

How to calculate the speed of a jet of liquid coming out of a nozzle? [closed]

I'm working on a project and i need to calculate speed of a jet falling from a nozzle. But my question is that, is it correct to use $$v=\sqrt{2gh}$$ Or should the speed of the jet be independent ...
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1answer
68 views

Application of Bernouli's Theorem

We have to calculate the velocity of efflux in this problem. My issue is, when I apply Bernoulli about the open end of the fluid and a point just outside the orifice, I seem to get a different answer ...
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Pressure inside tank while discharging water

I have two tanks, one initially fully filled with water (large tank) and the other one (smaller) is empty and has low pressure (say 0.5 bar) and the two tanks are connected from the bottom with pipe ...
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27 views

Lift provided to an aeroplane [duplicate]

We say that aeroplanes find lift due to an effect explained by Bernoulli's theorem. But isn't newton's third law of motion applicable along with Bernoulli's theorem? otherwise, an aeroplane wouldn't ...
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How does Bernoulli's principle produce wing lift? [duplicate]

In the Ray Kurzweil's book How to create a mind is said that: The mathematics of how Bernoulli's principle produces wing lift is still not yet fully settled among scientist [...] What does ...
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92 views

Bernoulli Principle and pressure function

I have read in several places now that for compressible flow the Bernoulli equation $$ \frac {v^2}{2}+ P\ + \Psi = \text{constant}$$ requires: $$P=\int {dp\over \rho(p)} $$ But I don't get ...
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Conflicts between Bernoulli's Equation and Momentum Conservation?

The well known Bernoulli's equation states that $P+\frac{\rho V^2}{2}=c$ However, a simple momentum conservation considering $P_1$ and $P_2$ acting on two sides, and velocity changes from $V_1$ to $...
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1answer
230 views

Relation between pressure and velocity of a fluid

What is the relation between pressure and velocity of a fluid in a closed pipe flow? I used the Bernoulli equation in case of a pipe having non viscous fluid. The pipe is say tilted at an angle and ...
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1answer
207 views

How to calculate leakage flow in a horizontal pipe?

Consider the picture below: The microcontroller takes care of maintaining the pressure $P_1$ constant. In addition, the flow $F$, the area of the pipe ($A_p$) and the area of the hole ($A_h$) are ...
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Bernoulli's Equation for Barotropic Flows

I'm trying to understand a derivation of Bernoilli's Equation and I'm having a hard time understanding the math behind this indentity $$ \frac{1}{\rho} \nabla p = \nabla \int \frac{\textrm{d}p}{\rho}....
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What is Pressure Energy?

While deriving Bernoulli's Theorem, our teacher said that the sum of KE, PE and Pressure Energy per unit volume remains constant at any two points. $$P + \rho g h + \frac{\rho v^2}{2} = \text{...
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129 views

Air flowing through a duct (pressure drops)

Let's say that I have a duct with the length $ l $ that is connected to a fan, and through the duct there is air flowing with the velocity $ u $. Moreover, let's say we install a manometer right after ...
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134 views

Can Bernoulli fly a car?

I need to settle an argument. How much influence, if any, does the Bernoulli principle have in sending a stock car traveling at 200 MPH sailing through the air when the air pressure unexpectedly ...