Find the speed of fluid using bernoulli

In summary, the conversation discusses finding the velocity (v) using the Bernoulli equation. The individual applied the equation using the surface of water and the right-end of the pipe as reference points and simplified the equation to find v. After discussing the steps, it is confirmed that the answer is correct with a degree of confidence of 0.5%.
  • #1
songoku
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Homework Statement


untitled-7.jpg


Find v


Homework Equations


Bernoulli


The Attempt at a Solution


Here's what I've done

I took the surface of water as first reference and the right-end of the pipe as second reference, so:

P1 + 1/2 ρV12 + ρgh1 = P2 + 1/2 ρV22 + ρgh2

P1 = P2 = Patm and I assumed v1 = 0 and h1 = 0, then the equation became:
0 = 1/2 ρV2 - ρgh
v = √(2gh) ---> ta daa, I'm finished with degree of confidence 0.5 % that my answer is correct.

Do I get it right? Thanks
 
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  • #2
It is 100% correct.

However to build up your confidence let's just clear up how we got here.

After applying the equations, we realized two things.Pressure at surface and Pressure at exit are same as they are open to atmosphere.

Then we made velocity zero.
That was using equation of continuity as surface area of water is much greater than that of pipe.
 
  • #3
Ah I get it. Thanks for the help :smile:
 

FAQ: Find the speed of fluid using bernoulli

What is Bernoulli's equation and how is it used to find the speed of fluid?

Bernoulli's equation is a fundamental equation in fluid dynamics that relates the pressure, velocity, and elevation of a fluid along a streamline. It states that the total energy of a fluid system remains constant. To find the speed of fluid using Bernoulli's equation, we equate the total energy at two different points along a streamline and solve for the unknown velocity.

What are the assumptions made in Bernoulli's equation?

Bernoulli's equation assumes that the fluid is incompressible, inviscid, and irrotational. In other words, the fluid has a constant density, there is no friction between fluid layers, and the fluid particles do not rotate as they flow along a streamline.

How is Bernoulli's equation applied in real-world situations?

Bernoulli's equation is used to understand the flow of fluids in pipes, airfoils, and other systems. It is commonly used in the design of aircraft wings, turbines, and pumps. It is also used to explain phenomena such as lift and drag forces.

Can Bernoulli's equation be used for all types of fluids?

No, Bernoulli's equation is only applicable to ideal fluids that follow the assumptions mentioned earlier. Real fluids, such as gases, have additional factors that need to be considered, such as compressibility and viscosity.

What are the limitations of using Bernoulli's equation to find the speed of fluid?

Bernoulli's equation is based on ideal conditions and does not take into account factors such as turbulence, boundary effects, and energy losses due to friction. It is also only applicable along a streamline, so it cannot be used to determine the overall flow behavior of a fluid system.

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