Questions tagged [bernoulli-equation]

An equation governing fluid flow for an incompressible steady fluid

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1answer
806 views

How is the pressure energy term equal to atmospheric pressure here?

I was looking up at the derivation of Torricelli's law in my textbook: $$P_a + \frac{1}{2}{\rho}v_1^2 + \rho gy_1=P + \rho gy_2$$ This is the equation representing one of the steps for its ...
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2answers
607 views

Bernoulli equations when different fluids and volumetric flow rates are involved

I have doubts on the use of Bernoulli equation when multiple volumetric flow rates are involved. Consider for istance the device in picture. Water flows in the main tube, while in the tank below ...
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1answer
2k views

Why decrease in velocity will increase pressure?

According to the Bernoulli's equation, if velocity decreases, then pressure increases. I am trying to understand the Bernoulli's effect based on a situation. Suppose we have a stream of water. Let'...
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1answer
428 views

Water container on a balance and Bernouilli's principle

Consider a cylindrical water container on a balance. Suppose the water surface is initially at level $h$ above the balance. The pressure at the bottom of the container is then $$p_i = p_0+\rho g h,$$ ...
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1answer
2k views

Bernoulli equation and pumps [closed]

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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2answers
2k views

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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1answer
1k 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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3answers
776 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
240 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
77 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
63 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
641 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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606 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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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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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
285 views

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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2k 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
132 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
949 views

Bernoullis in Parallel pipes

Im having trouble with a scenario where a flow 𝑄𝑆𝑡𝑎𝑟𝑡 splits into two parallel pipes 𝑄𝐴 and 𝑄𝐵 then rejoins 𝑄𝐸𝑛𝑑 before exiting the control volume what makes this scenario difficult is ...
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345 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
436 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
219 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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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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Does continuity equation hold if the flow is accelerated?

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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300 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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2answers
4k 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
380 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
139 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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1answer
195 views

Reconciling $Q=PR$ and $Q=vA$

Say we have a closed loop system, where the flow $Q$ is constant through a pipe. Then, at one segment of the pipe, we make the radius smaller. This causes the resistance $R$ to be greater, so the ...
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4answers
10k 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
553 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
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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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1answer
2k 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
103 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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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 this ...
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1answer
470 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 what ...
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3answers
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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
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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
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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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1answer
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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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8answers
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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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2answers
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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
571 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
650 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
227 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
353 views

Bernoulli equation as an energy conservation equation

I don’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 ...