Understanding Pressure and Flow Dynamics in a Water Pipe

[JenniferBlanco]

Hi,I have a problem here and would appreciate it if someone could help me out. I seem to know just one Question out of the 5 q's and seem to have difficulty in trying to figure out the answer. I feel so dumb right now.

Here it is.http://img62.imageshack.us/img62/4361/physicsdn2.jpg

A cylindrical shaped pipe can carry water from a very large elevated container on the left to a lower container on the right. The area of the wider portion of the pipe containing the point b has a cross sectional area of 7.80 X 10^-3 m^2 and the narrower section containing points c and d has a cross sectional area of 3.14 x 106-4 m^2.
Point C is at a height of y2=2m above point d. A water valve closes the elevated container at point a and thus there is initially only water in the upper container and none in the pipe. The rectangular block has dimensions 10cm x 3cms x 3cms and mass of 0.075KG and it rests on the bottom of the lower container before any water enters the lower container

Q1.If the pressure at the surface is 1atm,what is the absolute pressure at point a which is at a depth of y1=2 meters below the surface of the water in the tank?

Ans. I have no clue.

Now the valve at point A is opened.

Q2. Consider the pressure at points b and c. At which of these points is the pressure least?

Ans. I am sure it is B

Q3. If the speed of the water at point b is 6m/sec,whats the speed at point c?Q4. Determine the speed at point D where the water initially enters the lower container.

Q5. As the water level rises in the lower container,the block eventually begins to float. What is the height h of the water level at the instant the block is lifted off the bottom of the container,ie. the block begins to float?



Jennifer

 

[JenniferBlanco]

Can any anyone help me? :(

 

[Hootenanny]

Lets start with Q(2). Do you know an expression for static fluid pressure (it should be in your notes/text)?

 

[JenniferBlanco]

The Pressure due to the weight of liquid is

P=F/A or P=pgh where p=density

 

[Hootenanny]

My apologies, I meant question (1); your answer to question (2) is quite correct. Now, for question one all that seems left to do is plug in the numbers and obtain the result.

 

[JenniferBlanco]

Its ok. Anyways, I got 19.6 atm for the 1st Question. is that ok?

 

[Hootenanny]

Its ok. Anyways, I got 19.6 atm for the 1st Question. is that ok?

I'm not checking your math for you Now for question three, tell me what you know about Fluid kinetic Energy.

P.S. I am remiss, forgive me, I have neglected to welcome you to the forums.

 

[JenniferBlanco]

Thanks for the welcome :)

I actually don't know anything about Fluid Kinetic Energy All I know is Kinetic energy decreases in pipes which will lead to reduction in the speed of the fluid.

BTW are Q1,2 right?

 

[Hootenanny]

If you have plugged the correct numbers into the formula correctly and done the math right, Q.1 will be correct. Q.2 is correct. Now, for Q.3 there is an have you every heard of Bernoulli's Equation?

 

[JenniferBlanco]

yes

The equation is for any 2 points is -

P +1/2pv1^2 +pgy = constant

For Q1. I did
1 x 9.8 x 2 = 19.6atm

 

[Hootenanny]

Correct, now how do you think we can apply this to Q.3?

 

[JenniferBlanco]

we could set the equations up by making them equal.

Then

P1 +1/2pv1^2 +pgy1 = P2 +1/2pv2^2 +pgy2

 

[Hootenanny]

Indeed, this would be correct. The same method can be applied to answer Q.4; and Q.5 is a simple Buoyancy question.

 

[JenniferBlanco]

Would we take Pressure to be equal to 1atm?

 

[JenniferBlanco]

I got all the answers except for the last one. Is there some equation I can use?

 

[Hootenanny]

I got all the answers except for the last one. Is there some equation I can use?

You need to use Archimedes Principle which states that the Buoyant force on any object is equal to the weight of water it displaces. Therefore, you need to find the point at which the weight of displaced water is equal to the weight of the block.

Does that makes sense?

 

[JenniferBlanco]

Thanks Hootenany! I figured out how to do the questions ;)

 

[Hootenanny]

Thanks Hootenany! I figured out how to do the questions ;)

Good stuff! Twas a pleasure