Bernoulli's equation book problem

In summary, the conversation involves a student struggling with a physics equation and discussing it with someone who suggests simplifying the equation by removing certain terms and multiplying each term by 2. The student then questions the reasoning behind these steps and the other person clarifies the use of variables and suggests changing one variable to solve the issue. The conversation also mentions the use of Δy to represent the height difference between two points, and a final clarification on the use of √h instead of √(2gh) in the final step of the equation.
  • #1
bobsmith76
336
0

Homework Statement



This book is skipping over too many steps

Screenshot2012-03-20at23208PM.png


where A1 = 1m2
A2 = .5 m2

y1 - y2 = 5m

The Attempt at a Solution



I'm having trouble getting from one step to another.

By my reckoning this equation

Screenshot2012-03-20at23208PM-1.png


can be simplified by removing P0 and ρ since they are the same on both sides of the equation. Then we can multiply each term by 2.

That makes

v12 + 2gy1 = ((A1/A2)v2)2 + 2gy2

Now I subtract 2gy1 from both sides. That makes:

v12 = ((A1/A2)v2)2 + 2gy2 - 2gy1

The book is showing that that is a mistake. I can't figure out why.

Also if I subtract ((A1/A2)v2)2 from both sides that would make (ignoring 2gy)

v12 - ((A1/A2)v2)2

But the book has it as

v12 multiplied by (1- ((A1/A2)v2)2

Why?
 
Last edited:
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  • #2
bobsmith76 said:
can be simplified by removing P0 and ρ since they are the same on both sides of the equation. Then we can multiply each term by 2.
OK.

That makes

v12 + 2gy1 = ((A1/A2)v2)2 + 2gy2
Shouldn't that be v1 on the right hand side, not v2?
 
  • #3
Yea, I guess it should but I'm still stuck with my two questions.
 
  • #4
bobsmith76 said:
Yea, I guess it should but I'm still stuck with my two questions.
First change that v2 to a v1 and your questions may go away.
 
  • #5
Ok, I understand the part about v1 and v2, but would about

2gy2 - 2gy1
 
  • #6
y2-y1 is the height difference between the two points under consideration.
 
  • #7
bobsmith76 said:
Ok, I understand the part about v1 and v2, but would about

2gy2 - 2gy1
What about it? Realize that your book is calling Δy = h.
 
  • #8
In the final step it should be

√h

not

√(2gh)

Because the 2g - 2g = 0
 
  • #9
bobsmith76 said:
In the final step it should be

√h

not

√(2gh)

Because the 2g - 2g = 0
The '2g' factor doesn't cancel!

Example: 5a - 3a = 2a, not 2.
 

1. What is Bernoulli's equation book problem?

Bernoulli's equation book problem is a physics problem that involves calculating the pressure difference between two points in a fluid flow system. It is based on Bernoulli's equation, which relates the velocity, pressure, and height of a fluid at different points in a system.

2. How do you solve the Bernoulli's equation book problem?

To solve the Bernoulli's equation book problem, you first need to identify the two points in the fluid flow system between which you want to calculate the pressure difference. Then, you can use Bernoulli's equation, which states that the sum of the kinetic energy, potential energy, and pressure energy at any point in a system is constant. By setting up and solving equations based on this principle, you can find the pressure difference between the two points.

3. What are the assumptions made in Bernoulli's equation book problem?

The main assumptions made in the Bernoulli's equation book problem are that the fluid is incompressible, the flow is steady, and there is no energy loss due to friction or viscosity. Additionally, the fluid must be moving along a streamline, and the density of the fluid must remain constant throughout the system.

4. What are the units used in Bernoulli's equation book problem?

The units used in Bernoulli's equation book problem depend on the specific variables being calculated. Generally, the units for velocity are meters per second, the units for pressure are pascals, and the units for height are meters. However, it is important to double-check the units of each variable to ensure they are consistent and can be properly manipulated in the equation.

5. What real-world applications use Bernoulli's equation book problem?

Bernoulli's equation book problem has numerous real-world applications, including in industries such as aviation, hydraulics, and aerodynamics. It is used to calculate the pressure difference between two points in a fluid flow system, which is essential for understanding and optimizing the performance of various systems, such as aircraft wings, pipelines, and pumps.

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