Questions tagged [bernoulli-equation]

An equation governing fluid flow for an incompressible steady fluid

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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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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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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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Bernouli equation on streamline

I made my first point at the free surface of the water and my datum to be the very bottom. Part b of the question asked to find the velocity of the water in the pipe. I set my second point to be at ...
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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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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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67 views

Limitations of converting pressure into kinetic energy

Bernoulli's principle states that an increase in the kinetic energy of a fluid occurs simultaneously with a decrease in pressure for isentropic processes. What then limits us from converting all of ...
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57 views

Why that Bernoulli function contains many streamlines and vortex lines but not only singular streamlines?

I know that for a stream line inside the gradient part equal to a constant. But when we consider the fluid is rotational which the velocity cross product vorticity not equal to zero. So how can we ...
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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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141 views

How to find velocity of water flow and $Q$ if I know static pressure at the end of the pipe of known diameter?

I have a pipe. At its end I have mounted pressure meter. Of course there is no circulation. Water pressure meter is a kind of stopper for water. I know diameter of the pipe, and I know its pressure in ...
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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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Doubt in derivation of Velocity of efflux (Torricelli's theorem)

To find the velocity of efflux of fluid from a hole in a simple cylindrical container we use the Bernoulli's equation. $$P + ρv^2/2 + ρgh= constant$$ For our specific case we take the pressure at ...
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246 views

Mathematical description of Bernoulli equation and transition from laminar to turbulent flow

I am very interested in the mathematical description of the next topics: 1. Bernoulli equation 2. Transition from laminar to turbulent flow Could you help me ...
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818 views

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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134 views

Why is that? repulsive forces and attractive forces

These are the upper and lower discs A and B. There is a small hole in the center of A, and a pipe is connected to the small hole. The pipe is connected to compressed air. We use B to approach A. ...
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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 ($A$) ...
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215 views

What happens if a helicopter's propeller spins in reverse?

I know airplanes and helicopters fly thanks to the same principle, the Bernoulli Principle. The wings and blades are designed so that the air travels faster across the up side than it does on the ...
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212 views

Question about Airy wave theory

I have a fundamental misunderstanding about Airy wave theory. All the texts that derive the dispersion relation for gravity water waves use as a final step the unsteady Bernoulli equation: $$\frac{\...
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z in incompressible flow equation

I'm trying to calculate the flow rate out of my water tank. On Wikipedia one can find Bernoulli's incompressible flow equation as: $$\frac{v^2}2 + gz + \frac p \rho = \mathrm{const}$$ With $p = \rho ...
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What is the value of the constant on the right hand side of Bernoulli equation?

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 ...
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Which equations recommend to model a flux through a Bernoulli tube?

Which equations recommend to model a flux through a Bernoulli tube? The velocity of the flow varies very little along the tube, in addition the tube has different transverse areas. I am doing a ...
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383 views

Mass Flow with Stagnation Pressure/Temperature

I saw in many papers and books that when a compressible gas flows through an orifice, the mass flow is calculated using the stagnation pressure and temperature. That is, $\dot{m} = \frac{P_o \cdot A \...
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237 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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41 views

Liquid Flow Over Object

When there is a large object in the bottom of the ocean of height h, the surface of the ocean rises by a height less than h. In fact, if the ocean depth >> h, then the surface will rise negligibly. (...
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112 views

Tank draining with piston

I am trying to solve a problem which is close to the tank draining (as here Fuel tank draining) but with a piston a the top of the tank which means $p_A$ different of $p_B$. I search the velocity $...
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75 views

Does using Bernoulli's equation for a region of zero mean flow violate mass conservation?

Let's say I have a pressure reservoir with zero mean flow connected to a pipe with mean flow. So for the reservoir we have $p_1>0$ and $v_1=0$. For the pipe we have $p_2,v_2>0.$ Bernoulli's ...
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How does this spray gun work?

This is the critter spray gun. The liquid in the jar is at atmospheric pressure (there's a vent hole connecting it to the atmosphere). A fast jet of air flowing right over the end of the pickup tube ...
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403 views

Outflow from a tank

Consider a tank with an outflow a the bottom: with the unsteady Bernoulli equation:$$\int_S \frac{\partial v}{\partial t} \ dS+\frac{v^2}{2}+\frac{p}{\rho}+gz=0$$where $s$ is the path between $S_1$ ...

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