Questions tagged [bernoulli-equation]

This tag is for questions relating to Bernoulli equation [named after its discoverer, the Swiss scientist Daniel Bernoulli (1700–1782)], an equation governing fluid flow for an incompressible steady fluid. It gives great insight into the balance between pressure, velocity and elevation. Bernoulli’s equation is a form of the conservation of energy principle.

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Effect of friction loss on pressure head in horizontal duct

I need to know the effect of friction loss on the decrease of pressure in a horizontal duct (such as in an oil pipeline, with a constant diameter and a high length) and therefore, on the decrease of ...
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Does the flow velocity increase when diameter is halved? PS: Volumetric flow rate changes

Let's assume a flow rate $Q_1$ and a pipe of radius $r$ and length $l$, and the velocity through the pipe is $v_{1(large)}$. We replace half of the pipe length with a pipe of radius $r/2$ and the ...
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Continuity and Bernoulli's Equation in a vertical pipe with different cross sections [closed]

Consider the following situation where the amount of water that goes through a cross section $A_1$ per second is the same as it goes through $A_0$ (just continuity) and is always constant: I setup ...
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How and where does air that is displaced by a constant moving vehicle flow?

How does air that is displaced by a constant moving car move? When a car is driving with constant speed, there is air displaced in front of the car. Let's say the surface of the car view flat from ...
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When using pressure energy to state Bernoulli's Theorem, why do we say it's simply pressure?

I was asked this question in my viva and I couldn't answer. I know there's the whole mathematical explaination of this, when we multiply Force/Area with displacement and convert it into Energy/Volume, ...
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Can a water flow in a pipe be non-turbulent with a Reynolds number greater than 2000?

I have a venturi tube with a narrowing in the middle with 4 manometric tubes and 2 others in the wide part, at the beginning and at the end. I can clearly see that the pressure is no longer conserved ...
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Hole in Bernoulli's theorem

According to Bernoulli's theorem while blowing a paper ball inside the bottle, speed of air at the mouth of bottle is higher and hence creates low pressure relative to inside air, so the air blows ...
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Why is the unsteady Bernoulli equation inconsistent when applying at different points? I've probably misconceptualised the theory

Unsteady Bernoulli equation: $$\frac{P_1}{\rho}+\frac{{v_1}^2}{2}+gz_1 = \frac{P_2}{\rho}+\frac{{v_2}^2}{2}+gz_2 + \frac{f_hg}{\rho} +\int_{1}^{2}{{\frac{dv}{dt}}ds}$$ I've attempted to apply the ...
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Why do we use cubic fluid elements when deriving fluid equations?

Recently I've been delving into fluid dynamics but is frequently troubled by a conceptual issue that I could never get my head around with. To derive fluid equations, we have to separate fluid into ...
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A question regarding fluid flow according to Bernoulli's theorem and equation of continuity [duplicate]

Consider a horizontal pipe with uniform area of cross section at all points kept on the ground.I send water through one end of the pipe at a pressure of around 2atm.Since the pipe is of uniform area ...
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Pressure variation within tank with hole exposed to a known outside pressure variation

I think this is best explained via a diagram, see below. Initial Conditions: Initially, everything is at standard atmospheric temperature, pressure, density etc. Boundary Conditions: Then, a known ...
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Analytical equation for time to empty a pressurized water tank [closed]

I need help determining an equation for time to empty a pressurized tank. I have a sealed water tank pressurized with nitrogen, where the cross-sectional area of the water inside the tank is and the ...
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Can I get more gas pressure then I started with?

The image shows constant gas at 2 psi being released in 55" depth of water. Gas will rise due to it being less dense than water. If gas continues being added into the closed system at 2 psi will ...
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Why is this form of Bernoulli still valid in case of accelerated systems of this type?

Consider a cylindrical container in which water is kept and a hole is made on any point on the curve surface but its at a distance of h from bottom . Water starts leaking out of it . We say we can ...
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Do solar panels help keep roofs on during tornadoes or hurricanes? (does it help at all for pressure equalization on the roof?

further to this previous asked question Why are roofs blown away by wind? do solar panels mounted to roofs "help" at all by keeping roofs in place during wind storms? i.e. if the pressure ...
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Is this definition of streamline motion really correct?

This is the definition that I have got in my textbook regarding streamline motion Streamline motion is the motion of fluids where particles flowing through a specific point have the same velocity at ...
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All conditions for a siphon to work?

I am struggling a bit with the concept of siphon. Firstly, if we consider a pipe filled with water, the inlet is in a tank of water at the altitude $z_I$, and the outlet is in the air at $z_O$. Here ...
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Flow on an inclined plane and Bernoulli's principle

I've stumbled upon the following question: Consider a steady, incompressible and viscous flow on an inclined plane with an angle $\alpha$. The surface is in contact with air (which can be assumed to ...
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How high can water rise up your arm hanging in the water from a moving boat? (Bernoulli's principle)

I have the following problem where you have to apply Bernoulli's principle, which asks: How high can water rise up one's arm hanging in the river from a boat moving at $u_1 = 1 \text{ ms}^{-1}$? (That ...
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Question about fluid in free fall flow

Some time ago i saw this question Why does water falling slowly from a tap bend inwards? Which explains why the water flowing from a tap bend inwards while falling, using an inviscid flow model. ...
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Pressure required to create enough suction to pull water up height h

I am trying to find out how much pressure needs to be added to a system to draw up water. The system is essentially a 5-gallon water bottle with a manual hand pump, like this: https://www.terapump.net/...
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What is the maximum height that a siphon can work?

Here is a photo from an article on siphon in Wikipedia My first question is what does maximum height of siphon mean? I mean which part of the siphon in below the photo would represent maximum height. ...
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Will the equation of continuity be applicable when there are more than one path where the liquid may flow like in a junction?

Consider a situation of a container having cross-section A and two holes of area "a" are at some point on the sides of the container diametrically opposite to each other . If fluid is filled ...
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Viscous liquid flows through a horizontal pipe of varying cross-section

Question: A viscous liquid flows through a horizontal pipe of varying cross-sectional area. Identify the option which correctly represents the variation of height of rise of liquid in each vertical ...
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Pressures in Bernoulli's equation

Let's say a pipe runs along the seafloor with velocity $v_1$, then exits at the surface with velocity $v_2$. I want to use Bernoulli's equation to find $v_2$, but I am confused about the pressures in ...
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Would pressure decrease if I added a tesla turbine to the pipe system?

There's constant 2 psi of gas in my pipes. Once I open the valve the gas begins to spew out. Would psi decrease if I added a few tesla turbines connected to a generator in the pipe system? I added a ...
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Calculat Specific Gravity (SG) using pressure differential

Can anyone help me to calculate SG in an open tank of fermenting juice? I have two pressure sensors mounted a metre apart. The juice height above the top sensor can vary. The pressure sensors are ...
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Does the pressure in dynamic fluids depend on speed or cross sectional area?

I have encountered this question in my Giancoli Physics textbook, and I am pretty convinced that the answer should be A and E. But the solutions manual has neglected E as a potential answer and ...
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How to derive Bernoulli's equation in steady irrotational flow?

Condsider an incompressible, inviscid, irrotational fluid with constant density $\rho$. Let $\overrightarrow u$ be its velocity field, $p$ its pressure field and $\overrightarrow F$ be an external ...
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Axial compressor stage pressure gain - Diffusor vs. flow area reduction

I've been diving into fluid dynamic machinery and I've come to what seems like a paradox to my half-knowledge. Namely, on 2d or 3d schematics on the internet, you can see an axial compressor has an ...
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Suction caused by an open window of a plane

So I know this question has been asked before, and I have seen other posts. The reason I want to post a new one is because there is something about the Bernoulli's principle I want to understand. Is ...
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Conservation of momentum of ideal gas in pipe

I was reading this question Pressure drop in a pipe due to cooling and have a follow up question. Please note that the question is about an ideal frictionless pipe. In the question, it is stated $$ \...
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Pitot tube airflow speed measurement

how pitot tube can specify the airflow at aircrafts. according to formula airflow speed is related with fluid density. when aircraft passes through clouds it meets different density of fluid than ...
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Does this simulate fluid dynamics well?

Consider a 2d simulation which consists of thousands of tiny circles bouncing off each other in elastic, frictionless collisions. Particles are thrown into the simulation from the left side of the ...
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How pressure force is doing work on tapered sides in inertial moving frame but not in rest frame?(

While trying to understand Bernoulli application in inertial moving frame i tried watching this video https://youtu.be/CT4H3Xt84ZE but i dont understand few things from 7:04 to 7:42 : Sir told that ...
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How to use Bernoulli equation in a rotating frame and is it always true that bernoulli will work?

Lets say a fluid is rotating in a cylindrical shape container with every circular fluid streamline rotating with same $w$ by some external mechanism, now imagine asking for pressure difference between ...
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Why is Bernoulli equation applicable here eventhough we can see that streamlines would be like curve not straight? Also at orifice speed is not steady

Consider the famous setup of Toricelli ones where a cylindrical container of large area $A$ and a very small hole of area $A'$ is there at the bottom (in the curve side of the container ), now due to ...
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Flow rate of Venturimeter $v=\sqrt{\left(\frac{2\left(P_{1}-P_{2}\right)}{\rho}\right)}\left[\left(\frac{A}{a}\right)^{2}-1\right]^{-\frac{1}{2}}$

How to derive $$v=\sqrt{\left(\frac{2\left(P_{1}-P_{2}\right)}{\rho}\right)}\left[\left(\frac{A}{a}\right)^{2}-1\right]^{-\frac{1}{2}}~?$$ I came across it while studying fluids mechanics in medicine ...
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Shower power -- I can get a more effective rinse by removing a flow restrictor. Have I increased water pressure? What principles apply here?

I watch a plumber on social media; he explains how to do simple fixes. Sometimes his customers want more "pressure" coming from the shower head; when they feel like it's just a "trickle&...
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Bernoulli Equation Application - Water Spray into the air & Siphoning Gasoline out

The following images show the application of the Bernoulli Equation in a variety of cases. First, spraying water into the air. State 1 is where water exits the hose; State 2 is where the water jet ...
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Which is correct related to lift: Bernoulli's theory or Newton's theory? [closed]

I was trying to find out how exactly is lift generated. I came across Bernoulli's theory and Newton's theory. But I no where found which one is correct. Can someone help me out with this?
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Continuity equation for non-viscous fluids through a tube

In basic textbooks, the equation of continuity for non-viscous fluids through a pipe is usually written as $$ \rho_{2} A_{2} v_{2}=\rho_{1} A_{1} v_{1} \tag{1} $$ with $\rho$ and $v$ being the density ...
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Which direction will a truncated cone be pushed by airflow?

Consider the shape below, with the bottom and top faces being holes. Imagine we hold the shape in place and blow a wind into the big hole. The air will exit the small end at a higher velocity due to ...
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What exactly is $h$ in the bernoulli equation?

I've started with some very basic fluid dynamics, basically what's in Khan academy. The Bernoulli equation, from what I know, relates the pressure to velocity at two different cross-sectional areas of ...
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Analyzing Magnus effect from ground frame

How can we explain Magnus effect to the path deviation of a spinning ball assuming the air is still (looking from ground frame)? I understand that we can use bernoulli principle from ball's frame, but ...
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What causes the Venturi Effect (the pressure of a fluid decreases when its velocity increases)? [duplicate]

In class I learned about the Venturi Effect, how when a pipe constricts the fluid traveling through it travels at a faster velocity than when the pipe was wider, but with less pressure. This was ...
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1 mile high tube

It is pretty well known that the atmospheric pressure reduces with altitude. What happens to the airflow if we anchor an imaginary one mile tube near the sea level that has a hole near its base? Does ...
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3 votes
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Why does gas that's been choked accelerate when the area it's passing through increases? [duplicate]

The throat of a rocket engine gets it up to sonic flow, and the bell of the engine gets it flowing even faster. But why does this happen? In subsonic flow the gas would slow back down, so why does ...
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Work - Energy Principle Application to Fluid Flow

Work - energy principle states that work done by net force acting on the body equals change in kinetic energy of the body. We are talking about continuum mechanics. This principle is usually ...
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What is the cause and what is the effect in the Bernoulli effect?

There is widespread confusion (among learners) about the Bernoulli effect, and I think a large part of this confusion is owing to muddling up cause and effect. So I am providing this question and ...
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