# Questions tagged [bernoulli-equation]

An equation governing fluid flow for an incompressible steady fluid

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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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 ...