Problem with Bernoulli's equation

In summary, the person is having trouble with part (b) of a problem that involves the equations x=vt, the x(t) kinematics equations, and Bernoulli's equation. They are trying to set equations for the distance as equal and solve for y1', but are unsure how to use the quadratic equation in this situation. They eventually find the answer with the help of someone else's advice.
  • #1
Loopas
55
0
(1)

Hey everyone,

I'm only having trouble with part (b) of this problem. I attached a picture of the problem and its diagram.

(2)

x=vt
the x(t) kinematics equations
Bernoulli's equation

(3)

I set the equations for distance as equal:

2√(y1(y2-y1))=2√(y1'(y2-y1'))

But I don't think this can be solved for y1'. I also have a feeling that I may have to use the quadratic equation but I'm not sure exactly how.

Thanks for the help.
 

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  • #2
mathematically you should just be able to distribute the y1 through the parenthesis, then get rid of the radical(provided that is what that symbol is), then solve the quadratic problem. but I cannot tell you if your physics formula is correct. I've not worked with bernoullis other than conceptual problems.
 
  • #3
Loopas said:
(1)

Hey everyone,

I'm only having trouble with part (b) of this problem. I attached a picture of the problem and its diagram.

(2)

x=vt
the x(t) kinematics equations
Bernoulli's equation

(3)

I set the equations for distance as equal:

2√(y1(y2-y1))=2√(y1'(y2-y1'))

But I don't think this can be solved for y1'. I also have a feeling that I may have to use the quadratic equation but I'm not sure exactly how.

Thanks for the help.

The leading 2's cancel on each side. Then square each side. Should make life simpler for you.
 
  • #4
That simplifies to:

y1y2-y1^2=y1'y2-y1'^2

Now here is where I'm stuck. I'm not sure how to use this with the quadratic equation or solve for y1'.
 
  • #5
Well, everything but y1' are constants. Move everything to one side and sort it into the standard form of a quadratic.
 
  • #6
Found the answer, thanks for the help!
 

What is Bernoulli's equation and what does it explain?

Bernoulli's equation is a fundamental equation in fluid mechanics that describes the relationship between pressure, velocity, and elevation in a fluid flow. It explains the conservation of energy in a steady flow of an incompressible fluid, where the total energy remains constant along a streamline.

What are some common problems with Bernoulli's equation?

Some common problems with Bernoulli's equation include the assumption of an ideal fluid, neglecting viscosity and turbulence effects, and the difficulty of accurately measuring all the variables in a real fluid flow.

How can the assumptions in Bernoulli's equation affect its accuracy?

The assumptions made in Bernoulli's equation, such as the ideal fluid assumption and neglecting viscosity and turbulence, can lead to inaccuracies in the predicted results. In real-world scenarios, these assumptions may not hold true, and therefore the predicted values may not reflect the actual fluid behavior.

Are there any limitations to Bernoulli's equation?

Yes, there are limitations to Bernoulli's equation. It is only applicable to steady, incompressible, and inviscid flows. It also assumes that the flow is one-dimensional and along a streamline. Furthermore, the equation is only valid for fluids with a constant density.

How can the limitations of Bernoulli's equation be overcome?

The limitations of Bernoulli's equation can be overcome by using more advanced equations, such as the Navier-Stokes equations, which take into account the effects of viscosity and turbulence. Additionally, experimental data and numerical simulations can be used to validate the results obtained from Bernoulli's equation and account for any discrepancies.

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