An equation governing fluid flow for an incompressible steady fluid

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1answer
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How can I determine the height in this fluid dynamics problem? [on hold]

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
32 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
10 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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1answer
73 views

Bernoullis in Parallel pipes

Im having trouble with a scenario where a flow ๐‘„๐‘†๐‘ก๐‘Ž๐‘Ÿ๐‘ก splits into two parallel pipes ๐‘„๐ด and ๐‘„๐ต then rejoins ๐‘„๐ธ๐‘›๐‘‘ before exiting the control volume what makes this scenario difficult is ...
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69 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
42 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
36 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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42 views

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
60 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 ...
2
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0answers
24 views

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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0answers
24 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
310 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 ...
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9answers
500 views

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 ...
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0answers
34 views

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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1answer
94 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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0answers
62 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 ...
2
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0answers
48 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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1answer
48 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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4answers
511 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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1answer
69 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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2answers
225 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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0answers
31 views

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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1answer
84 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 ...
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0answers
93 views

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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0answers
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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34 views

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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1answer
87 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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2answers
75 views

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
208 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
179 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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61 views

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 ...
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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} = ...
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2answers
120 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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3answers
127 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 ...
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2answers
146 views

Simple cylinder fluid mechanics, draining from hole on bottom

So my professor is having us work on an assignment where there is a cylinder full of water with a hole in the side near the bottom. Given the use of stopwatch, balance beam, beakers, etc, how can we ...
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2answers
68 views

Bernoulli principle and particle

Bernoulli principle describes the flow of a fluid for steady, incompressible flow along a streamline. But it is said for a particle of a fluid along a streamline. My question is a particle of fluid ...
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2answers
105 views

Bernoulli equation as an energy conservation equation

I donโ€™t want to learn and apply Bernoulli's equation. It is complicated and you need to remember a lot. I instead want to apply energy conservation. But I don't always find it easy. For example, when ...
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2answers
321 views

Bernoulli's equation and pressure in a (mostly) sealed container

Let's say that I have a large soda bottle. I drill a small hole through the side of it, put my finger over it to seal the hole, and fill the bottle up with water. When I let go of the hole, water ...
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1answer
406 views

Bernoulli's Equation for flow of gas and changing area

My task is to determine the size of piping needed in a system. In this system, hydrogen gas flows horizontally in a $\frac{3}{4}\,\mathrm{inch}$ pipe and into a vertical pipe of a larger diameter. My ...
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1answer
161 views

Forces of reaction and torque of water flowing out of a vessel

Consider the problem wherein we are told to find out the force of reaction of water flowing out of a vessel through an orifice. I attempt to compare it with a shotgun and a bullet as a conservation ...
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3answers
311 views

Question Regarding torricelli's theorem/Law

I recently studied about bernoulli's equation/principle. After the derivation of the said equation , my book gave some applications of the principle, which include torricelli's theorem/law. In ...
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1answer
84 views

volumetric flow rate due to Bernoulli's principle

for calculating the volumetric flow rate of a liquid coming out of a tube, I know that If the pipe is too short, the Hagenโ€“Poiseuille equation may result in unphysically high flow rates; the flow is ...
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47 views

Measuring Steam Flow with Venturi Effect?

I understand steam is a compressible fluid and that the Bernoulli effect has been generalised for compressible fluids but I'm struggling understand how the Venturi effect can be generalised to allow ...
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On deriving a fluid flow pressure drop model using either physical theory or empirical methods

I'm trying to derive a model from physical principles of fluid flow, a simple quadratic model that tends to well fit actual pressure-flow data. For (real) subsonic air flow (ideally adiabatic) ...
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1answer
129 views

Flow in diverging channel is unstable according to Bernoulli's equation

So let's say we have a circular pipe with a variable cross section with an inviscid incompressible fluid flowing through it. The areas of the two ends are $A_1$ and and $A_2$. Let's say we also ...
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17 views

Bernoulli's principle in moving car not works [duplicate]

According to Bernoulli's principle, an increase in the speed of the fluid occurs simultaneously with a decrease in pressure. As I understand that also applies to gas or air. Ok, so when I open a ...
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1answer
122 views

What is the best way to calculate speeds at other points in a venturi-tube when knowing one?

I and a friend have made a venturi tube trough which water flows at a low speed. The flow is therefore laminar. We measured the static pressure using some piรซzometers at the points 1,2 and 3. We know ...
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1answer
80 views

Finding the expression for the time it takes for a water tank to be half empty

The problem is to find an expression for the time it takes for a cylindrical water tank is half empty. I am given that the water tank has a diameter of $D_0$ and a hight $H$. The water outlet is ...
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3answers
994 views

Is Torricelli's law “wrong” for big holes? - Tank draining problem

Consider a tank full of water with a constant cross-sectional area A1 placed vertically on the ground. Now someone drills a hole of an area A2 in the bottom of the tank, and the liquid starts escaping ...