Work and Fluid Force: Calculus II

[think4432]

You're welcome. I'm off to dinner now. Will check back in later to see if you have the depth formula figured out.

Thank you!

You are definitely my hero!

 

[LCKurtz]

Would the depth be to the top of the liquid?

If that's the case, then when y = -2 then the depth would be 7...and that's not in the picture.

y = -3 then 8

But that's obviously not right...right?

Here's a picture with the y values shown. You should be able to fill in the depth table by looking at it.

 

[think4432]

Here's a picture with the y values shown. You should be able to fill in the depth table by looking at it.

The depth from the top of the fluid to the end of the triangle is 5 feet
At -1: 4 feet
At -2: 3 feet
At -3: 2 feet
At -4: 1 feet
At -5: 0 feet

-5-y = formula?

-5 - 4 = -1
-5 - 3 = -2
-5 - 2 = -3
-5 - 1 = -4
-5 - 0 = -5

Very nice picture, by the way! Thank you!

 

[think4432]

Thank you!

You are definitely my hero!

I integrated this out and got 2(y^2) - (y^3)/9

And plugged in the limits from 0 to 4 with the pi and 62.4 out in front and came up with an answer of

224/9 pi (62.4)

And when I multiplied the 62.4 out it came out to be 1553.066 pi

Would this be correct? Just seems bit of a weird number?

Please check it out for me?

 

[LCKurtz]

The depth from the top of the fluid to the end of the triangle is 5 feet
At -1: 4 feet
At -2: 3 feet
At -3: 2 feet
At -4: 1 feet
At -5: 0 feet

-5-y = formula?

-5 - 4 = -1
-5 - 3 = -2
-5 - 2 = -3
-5 - 1 = -4
-5 - 0 = -5

Very nice picture, by the way! Thank you!

Now I see what you are thinking incorrectly. The term depth means how far underwater is that y value. The values in the table should be how far under water is it -- the length of the column of water above it, not below it. Try again.

 

[think4432]

Now I see what you are thinking incorrectly. The term depth means how far underwater is that y value. The values in the table should be how far under water is it -- the length of the column of water above it, not below it. Try again.

So

At -1: 1 feet
At -2: 2 feet
At -3 : 3 feet
At -4: 4 feet
At -5: 5 feet

?

 

[LCKurtz]

So

At -1: 1 feet
At -2: 2 feet
At -3 : 3 feet
At -4: 4 feet
At -5: 5 feet

?

Finally! Yes. So what is the formula; it isn't 5 - y. If I recall correctly, that is the only thing that was wrong with your setup.

 

[think4432]

Finally! Yes. So what is the formula; it isn't 5 - y. If I recall correctly, that is the only thing that was wrong with your setup.

I understand that it is the depth in the y direction and all...but I got to admit that I still do not know how to figure out the formula.

I know this is probably really bad...but I just don't know!

I also replied to the other question after I integrated it...could you please check that for me? The answer...

Because it seems really odd to me!

 

[think4432]

Finally! Yes. So what is the formula; it isn't 5 - y. If I recall correctly, that is the only thing that was wrong with your setup.

Wait, After staring at this for a while...

Would -y work?

-(-1) = 1 feet

-(-2) = 2 feet

-(-3) = 3 feet

-(-4) = 4 feet

-(-5) = 5 feet

?!?

 

[LCKurtz]

Wait, After staring at this for a while...

Would -y work?

-(-1) = 1 feet

-(-2) = 2 feet

-(-3) = 3 feet

-(-4) = 4 feet

-(-5) = 5 feet

?!?

Yes. And if you look at the picture is should be "obvious" that the depth is -y.

 

[think4432]

Yes. And if you look at the picture is should be "obvious" that the depth is -y.

I see that it could be -y by looking at the picture and where the coordinate system is set...

But I posted this question earlier [again] on the forums...because I actually have to turn this in before 5pm today and I didn't know if you would be online before then or not.

And someone else told me something different.

Heres the thread:

https://www.physicsforums.com/showthread.php?t=411314

So now I have 2 different answers...and I am even more confused. :[

 

[LCKurtz]

I integrated this out and got 2(y^2) - (y^3)/9

And plugged in the limits from 0 to 4 with the pi and 62.4 out in front and came up with an answer of

224/9 pi (62.4)

And when I multiplied the 62.4 out it came out to be 1553.066 pi

Would this be correct? Just seems bit of a weird number?

What's weird about it? Might as well mulitply it on out to get 4879.1. And don't forget to put proper units on it.

 

[think4432]

What's weird about it? Might as well mulitply it on out to get 4879.1. And don't forget to put proper units on it.

Hah.

I don't know..

Maybe the decimal? Or something.

I was hoping for like a nice perfect rounded answer [because we did a couple in class and they were pretty nice numbers...so I just figured that this one would be nice and perfect too]

Haha.


4879.1 lb/ft^3

Thank you! Once again!

 

[LCKurtz]

I see that it could be -y by looking at the picture and where the coordinate system is set...

But I posted this question earlier [again] on the forums...because I actually have to turn this in before 5pm today and I didn't know if you would be online before then or not.

And someone else told me something different.

Heres the thread:

https://www.physicsforums.com/showthread.php?t=411314

So now I have 2 different answers...and I am even more confused. :[

Halls is setting it up using a different coordinate system. So everything looks different including the equation of the slanted side. It should eventually give the same answer.

[Edit] He also has a typo on the second line, 5 - x should be 5 - y

 

[LCKurtz]

4879.1 lb/ft^3

Thank you! Once again!

What are the units for work? And do you get them in this problem?

 

[think4432]

Halls is setting it up using a different coordinate system. So everything looks different including the equation of the slanted side. It should eventually give the same answer.

[Edit] He also has a typo on the second line, 5 - x should be 5 - y

I see!

Ok. But with my coordinate system.

The integral is (-y)(-7/4y - 7/4) dy from the limits [0,4]

So integrating 7/4(y^2) + (7/4)y

And get 7/24(y^2) (2y + 3)

154/3 as the final answer?

 

[think4432]

What are the units for work? And do you get them in this problem?

They gave us the units for the water density as lb/ft^3

Ohh.

But the units for work would be (ft)(lb)

Correct?

 

[LCKurtz]

I see!

Ok. But with my coordinate system.

The integral is (-y)(-7/4y - 7/4) dy from the limits [0,4]

So integrating 7/4(y^2) + (7/4)y

And get 7/24(y^2) (2y + 3)

154/3 as the final answer?

The only thing you had wrong in your original post was the depth of 5-y instead of -y. Why are you now suddenly saying y goes from 0 to 4? Don't you remember your choice of coordinates?

 

[LCKurtz]

They gave us the units for the water density as lb/ft^3

Ohh.

But the units for work would be (ft)(lb)

Correct?

Yes, and you should be able to explain how you get those units as the result of the units on the variables in your calculations.

 

[think4432]

Yes, and you should be able to explain how you get those units as the result of the units on the variables in your calculations.

Yes. Thats where I got the units from.

 

[think4432]

The only thing you had wrong in your original post was the depth of 5-y instead of -y. Why are you now suddenly saying y goes from 0 to 4? Don't you remember your choice of coordinates?

Oh! Oh! Oh!

Sorry! Sorry! I was looking at the other thread and got mixed up!

The limits are -5 to -1!

-154/3?

I did something wrong?

 

[LCKurtz]

Oh! Oh! Oh!

Sorry! Sorry! I was looking at the other thread and got mixed up!

The limits are -5 to -1!

-154/3?

I did something wrong?

Do you have -5 as the lower limit and -1 as the upper like you should? It should come out positive and don't forget the water density.

 

[think4432]

Do you have -5 as the lower limit and -1 as the upper like you should? It should come out positive and don't forget the water density.

Theres no pi in this problem, correct?

So the problem is just the limits a = -1 and b = -5 and integrating (7/24)(y^2) + (2y+3)

With the water density of 62.4 lb/ft^3 outside of the integral as a constant? Correct?

 

[think4432]

I still get 154/3(62.4)

And then when I multiply that out I get 3203.2 ft(lb)

 

[LCKurtz]

Do you have -5 as the lower limit and -1 as the upper like you should? It should come out positive and don't forget the water density.

Theres no pi in this problem, correct?

So the problem is just the limits a = -1 and b = -5...

Did you read my question: Do you have -5 as the lower limit and -1 as the upper like you should?

 

[think4432]

Did you read my question: Do you have -5 as the lower limit and -1 as the upper like you should?

Yes. Sorry I just had a typo A = -5 and B = -1

When you evaluate -5 [lower limit] you get -1225/24
And when you evaluate the -1 [upper limit] you get 7/24

So 7/24 - (-1225/24)

You get 154/3 times the weight density.

Which is 154/3 * 62.4

= 3203.2

?

 

[LCKurtz]

I still get 154/3(62.4)

And then when I multiply that out I get 3203.2 ft(lb)

The numbers look OK now. But you need to quit guessing at the units. What was this problem asking for? What would the correct units for the answer be? Do you actually get those units?

I'm going offline now for the rest of the day. People arriving for big Father's Day party. Hopefully you can finish it up.

 

[think4432]

The numbers look OK now. But you need to quit guessing at the units. What was this problem asking for? What would the correct units for the answer be? Do you actually get those units?

I'm going offline now for the rest of the day. People arriving for big Father's Day party. Hopefully you can finish it up.

Ok! Thank you very much.

Happy Fathers Day to you! Hope you enjoy the rest of your day!

Thanks so much for your help though.

You are great.