Questions tagged [bernoulli-equation]

An equation governing fluid flow for an incompressible steady fluid

68 questions
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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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Deriving the expression for the height of liquid in a cylinder spinning on a turntable using Bernoulli's principle

When a liquid in a cylinder is spun on a turntable, it will experience a vortex or whirlpool effect, as shown below: I have seen and understood a proof for the value of $h$ by taking the motion of a ...
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Flow through a hole in a sphere

I have a sphere of diameter $D$ (radius $R$) with a small hole of diameter $d$ (radius $a$) in it, with air flowing through the axis of the hole: I am trying to estimate the drag force due to ...
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Bernoulli's theorem in water flow through a burette

Consider a burette (like the one in a chemistry lab) with uniform cross-section and open at both ends so that they are exposed to the atmosphere. Once we open the stopcock/plug (P in the diagram) the ...
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Increase Air Speed at outlet

I have a set up that inflates a rubber jacket in order release the metallic rings from underneath it. I am currently having issues with not having enough pressure (force) at the outlet to inflate the ...
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If the difference in pressure is zero between two points of a horizontal constant radius pipe, why isnt flow rate zero?

In a straight pipe of uniform cross-sectional area filled with a nonviscous, incompressible fluid, the pressure at one end is equal to the pressure at the other end. Which of the following statements ...
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Water in the bunker problem

We have a bunker(Like a Cylinder), full of water with height $H$ initially, there is a whole at the bottom of the bunker. The pressure of the air outside is $P_0$. The surface of the bunker is $A$ and ...
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Does air with zero viscosity has effect on the motion of a top-spin ping-pong ball?

Normally (in air with a non-zero viscosity), when I give a ping-pong ball top-spin, the air above the ball tends to decrease in velocity while the air on the downside tends to decrease, resulting in a ...
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Static Pressure in a Venturi vs a Free stream

We seem to have two conflicting measures of pressure in a Venturi siphon open to the atmosphere,$\hspace{100px}$. Bernoulli's principle says that, by energy conservation for a steady flow $Q$, the ...
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How to explain rise of the disk?

The situation is as shown above. Now, to explain why the bottom disk rises, I applied Bernoulli's Equation at a point just below and just above the disk.The pressure difference hence obtained should ...
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Do viscous and inviscid flow have opposite effects on pressure?

Consider flow through the converging and diverging portions of a tube with varying radius: In inviscid flow, Bernoulli's equation states that velocity at the throat will be the highest, so this area ...
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Bernoulli Principle at a Microscopic Level

Good evening, kind forum users. I'm trying to understand the microscopic mechanisms that justify the Bernoulli principle. I found an interesting discussion on the site of NASA that tries to describe, ...
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Height of Fluid in circular motion

I have a question regarding the the height of a fluid spinning due to a drain in a sink. We are following Feynmans Lecture of physics. It should be "easy to see" that, that the height is something ...
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Can you explain the perfume bottle with the Bernoulli effect?

Someone explained the perfume bottle with the Bernoulli effect: squeezing the bulb over the fluid creates a low pressure area due to the higher speed of the air, which subsequently draws the fluid up. ...
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Proof that pressure rises in a fixed control volume

I am looking for a proof using Bernoulli's equation that that for $Q=(Area)(Velocity)$, $Q_{in}>Q_{out} \Rightarrow P_{inside}>P_{outside}$. I read that for a computer, if the case fans blow a ...
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Why water doesn't drop down from a hole when a stream of water travels fast over it?

why water doesn't fall down from hole on the roof when its raining heavily (water moves fast on the roof) ? Can I know the theory behind this and the factors affecting?
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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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How do you determine the pressure of water at the surface?

Using Bernoulli's equation, how would you determine the pressure of the water at the surface in a vacuum? I have tried figuring this out and I believe it would be 0pa due to the height of water ...
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What is the physics behind lifting a submerged bucket out of water?

When you submerge a cylindrical bucket into the water and let all the air out, trying to lift the bucket back out is particularly difficult if we keep it vertical to the surface. In order for the ...
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Bernoulli equation

Can we apply Bernoulli equation to a closed system the same way we apply it to an open system? In an open system increasing the speed of the fluid implies that either the pressure or GPE should ...
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Bernoulli's principle and gases: not matching real-world experience

Bernoulli's principle is said to be applicable to compressible fluids at low mach numbers, with the pressure substituted by pressure potential, which is linear with temperature (http://www.cns.gatech....
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The use of Bernoulli's equation with a siphon and similar problems?

There are a variety of problems in fluid mechanics that involve the flow out off, for example, a beaker. A typical example is that of a siphon shown below: (From wikipedia, by Tomia, CC BY 2.5) ...
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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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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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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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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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I've been reading on wikipedia that the Bernoulli principle is often incorrectly applied to the example of blowing on pieces of paper because A third problem is that it is false to make a ...
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How do I apply Bernoulli's equation in a rotating frame of reference?

I intend to apply Bernoulli's equation in an annular swirl flow where v_z is constant, omega_z is dependent on radial location. I need to apply the Bernoulli's equation in a reference frame rotating ...
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If a gas in a pipe is travelling from a large cross sectional area to a smaller cross sectional area, will it cool down?

So in a problem like the one in the link below: https://www.youtube.com/watch?v=5W2JgWKiYoU Velocity increases, so pressure must decrease, thus the pressure at the small part of the pipe will be ...
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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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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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What is the lift coefficient of human body?

Assuming we can change angle of attack by changing our hands orientation what is the maximum aerodynamic lift coefficient of human body?
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Can Bernoulli's theorem be applied to laminar flow?

Since in streamline flow the velocity of a particle at any point is same, Bernoulli's theorem can be applied to streamline flow, but could it be applied to laminar flow?
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Velocity of a leak in a cylindrical water tank that spins with constant angular velocity

We have a cylindrical water tank that spins over its axis of symmetry. Here's a diagram: The objective is to find: $1$ - The tangential and radial components of the velocity of the water as it ...
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If Bernoulli's Principle may leads to a collision between two ships, then will it happen in a multi-ship situation?

I mean several battleships sailing on a sea towards the same direction. Some of them are parallel with short distances between each other. Could the pressure difference be cancelled out?
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Should I use a barometric pressure sensor (BME280) or a differential pressure sensor (MPXV7002DP) to measure the airflow and pressure in an open tube?

I'll elaborate more on my set-up. I have a an acrylic tube and inside the tube is a ball one side has a dC fan to output air and the other side is a small cover just to not let the ball escape from ...
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Measure static pressure with measuring tubes of different diameter

Assume you have a horizontally placed cylindrical pipe with constant diameter. There is a flow of water, through this pipe. You want to measure the static pressure inside the tube, which should be the ...
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Material Derivative in Fluid Dynamics and Bernoulli Flow

If a fluid flow, such as water, is incompressible then the convective derivative term in the material derivative is equal to zero. How then, in a Bernoulli flow where there is an increase in velocity ...
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Does bernoulli's principle explain the suction by an emerging air stream?

Consider flow exiting a nozzle into atmosphere, its static pressure will decrease through the nozzle as the molecules vectors align with the direction of the exit. However, as soon as it exits the ...
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How does a sonic jet attenuate a sound wave?

Let's assume air flows through a pipe and exits into free atmosphere. The atmospheric pressure is below the critical pressure of the flow, hence the gas is accelerated and a sonic jet forms at the ...
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Couette Flow encountering an airfoil obstruction

Im interested in what would happen to an airfoil place within a Couette type fluid flow bounded between a fixed and moving boundary plate If we say the plate is infinite to establish a steady state ...
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Do the height of the water columns decrease when we push pistons with constant speeds in this venturi pipe?

Let say when the pistons are kept stationary the height of the water columns are h. And we start exerting extra force on the left piston in figure, and the pistons are moving with constant speeds. ...
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Bernoulli's principle for a liquid with non uniform density

Consider a cylindrical container (section $S$, height $H$) which contains a liquid with non uniform density. Let $z$ be the axis along the height of the container ($z = 0$ indicates the top of ...
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Venturi effect on molecular level

Is there a good explanation why the pressure becomes lower on the narrow part of the venturi pipe? I'm not interested in the newton explanation or pressure differences explanation. I want to ...
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Eulerian approach to control volume and energy conservation equations

After refreshing/researching the Eulerian approach to conservation equations for mass, energy, momentum I am struggling with understanding the partial derivative term that I believe represents ...
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What is the maximal velocity of air blown through a straw?

If an adult can buildup a pressure of 9kPa when blowing air through a straw then the pressure drop will be 0.5*1.25*v^2. But if I want to compute the air volocity in the straw how can I know the ...
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How to apply Bernoulli's equation on an experiment of rising water with a straw?

Consider the following experiment: Rising a water in a straw. For the sake of simplicity, let me assume that there is no air in the straw by redefining the height h...
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Wind Power in a Wind Tunnel

Two questions in one day! What? Okay, so the power equation for air flow is as follows: $$P = 1/2 \cdot \rho \cdot A \cdot V^3$$ In a wind tunnel due to the Bernoulli principle as the area ($A$) ...
I've never used that constant in solving problems. In the questions in my book, I just equate $P_1+\frac{1}{2}pv_1^2+pgh_1$ to $P_2+\frac{1}{2}pv_2^2+pgh_2$ to get the unknowns. But what is the value ...