# Homework Help: Bernoulli's equation book problem

1. Mar 20, 2012

### bobsmith76

1. The problem statement, all variables and given/known data

This book is skipping over too many steps

where A1 = 1m2
A2 = .5 m2

y1 - y2 = 5m

3. The attempt at a solution

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

By my reckoning this equation

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: Mar 20, 2012
2. Mar 20, 2012

### Staff: Mentor

OK.

Shouldn't that be v1 on the right hand side, not v2?

3. Mar 20, 2012

### bobsmith76

Yea, I guess it should but I'm still stuck with my two questions.

4. Mar 20, 2012

### Staff: Mentor

First change that v2 to a v1 and your questions may go away.

5. Mar 20, 2012

### bobsmith76

Ok, I understand the part about v1 and v2, but would about

2gy2 - 2gy1

6. Mar 20, 2012

### emailanmol

y2-y1 is the height difference between the two points under consideration.

7. Mar 20, 2012

### Staff: Mentor

What about it? Realize that your book is calling Δy = h.

8. Mar 20, 2012

### bobsmith76

In the final step it should be

√h

not

√(2gh)

Because the 2g - 2g = 0

9. Mar 20, 2012

### Staff: Mentor

The '2g' factor doesn't cancel!

Example: 5a - 3a = 2a, not 2.