# pascal's law and variation of pressure with depth

#### logearav

Joined Aug 19, 2011
243
Pascal's law states that " Pressure in a fluid at rest is same at all points if they are at the same height.
Also I read, Pressure increases with depth or height.
I am confused. Though both the versions are correct, i can't find a correlation between these two statements and i can't understand. Revered members, Pls help in clarifying.

#### BillO

Joined Nov 24, 2008
999
The two statements are consistent with each other, so I do not see your problem. Can you be more specific?

#### logearav

Joined Aug 19, 2011
243
Mr. Billo, Pressure is same at all points when they are at same height. Now consider the scenario of swimming pool, where the same swimming pool has 2 feet depth for kids, 5 feet depth for grown up, and 10 feet depth for adults. Whether pressure is same for all the depth?

#### Papabravo

Joined Feb 24, 2006
20,386
Mr. Billo, Pressure is same at all points when they are at same height. Now consider the scenario of swimming pool, where the same swimming pool has 2 feet depth for kids, 5 feet depth for grown up, and 10 feet depth for adults. Whether pressure is same for all the depth?
No. If you go to the deep end and go down 2 feet the pressure will be the same as if you go to the shallow end and go down 2 feet. At the shallow end you can't go any deeper because you run into concrete. At the deep end you can go dwon to ten feet and that is the limit.

#### BillO

Joined Nov 24, 2008
999
Papa is correct.

The height is measured either down (-) from the surface (locally), or up (+) from the center of gravity of the planet (globally).

Another way to look at it would be that the pressure is the same where the depth of the water is the same for a given body of water. Pressure will increase as the depth increases.

Is this what you need to know?

#### logearav

Joined Aug 19, 2011
243
Suppose a take a beaker of 4 feet height and fill it with water full to the brim. I mark three points A, B,C at the top, middle and bottom of the beaker. As pascal's law states, that the pressure is same everywhere, if the fluid is at rest, i presume that the points A, B, C will have the same pressure.
Now, we have another statement, " Pressure increases with height". This is where my confusion arises, i.e, how the point A,B, C will have same pressure when they are located at different heights from the top of the beaker.

#### AlexR

Joined Jan 16, 2008
732
Consider the following diagram of a closed tank with a filling pipe that is open to the atmosphere.

The law states that Pressure increases with depth or height so that as you go down from point A to B to C the pressure will increase.

The law also states that pressure in a fluid at rest is same at all points if they are at the same height. This means that as long as points C and D are at the same height above the base of the tank they will both be at the same pressure, obviously point B will be at a lower pressure and point A will be at a still lower pressure.

#### t_n_k

Joined Mar 6, 2009
5,455
I thought Pascal's Law states that if the pressure at any point in an incompressible confined fluid increases by a certain value then the pressure at every other point in the fluid increases by that same value. It doesn't state that the pressure is everywhere the same. Only the pressure change has to be the same due (say) to an external force or an increase in hydrostatic head. One therefore may have different hydrostatic pressures at different levels in an enclosed fluid without violating Pascal's Law.

#### Wendy

Joined Mar 24, 2008
23,276
Hmmm, if you have an aquarium with the same basic depth of water (but no water column), will C and D have the same pressure?

#### BillO

Joined Nov 24, 2008
999
Hmmm, if you have an aquarium with the same basic depth of water (but no water column), will C and D have the same pressure?
Yes. They will still be at the same depth so will have the same pressure.

#### logearav

Joined Aug 19, 2011
243

#### steveb

Joined Jul 3, 2008
2,436
It seems to me he is right about the definition of Pascal's Law. You can Google the defintion and see very similar statements.

The two principles you stated are correct. Still it's important to get the terminology correct for accuracy when communicating. The nomenclature is not as critical if you are just trying to understand the principles, but when a person sees an error like this, he would be remiss if he didn't mention it. Who knows, you may be about to make a public presentation on the subject, and you wouldn't want to be embarrassed by making a public mistatement.

#### logearav

Joined Aug 19, 2011
243
Thanks Mr. steveb for your suggestion.

#### logearav

Joined Aug 19, 2011
243
Mr. AlexR, i got your point. In case, if the beaker is fitted with a piston and when i compress the liquid, what about the pressure at the points A and B in the cylindrical tube and points C and D in the fish tank? I think, due to compression the pressure at point A will change( say increase of 2 Pascal) and similarly the point B will also experience a change of 2 pascal from its previous value. Points C and D will have same pressure as before.
Am i right? Correct me if i am wrong. Thanks again Mr. Alex.

#### t_n_k

Joined Mar 6, 2009
5,455
Hmmm, if you have an aquarium with the same basic depth of water (but no water column), will C and D have the same pressure?
Were you rather asking whether the (equal) pressures at the same depths C & D in the tank would be the same irrespective of whether the water column portrayed in AlexR's diagram was there or not?

#### t_n_k

Joined Mar 6, 2009
5,455
How do you know whether I'm male or female?

As to the correctness of my post I would refer you to Wikipedia

http://en.wikipedia.org/wiki/Pascal's_law

Quote: "Note that the variation with height does not depend on any additional pressures. Therefore Pascal's law can be interpreted as saying that any change in pressure applied at any given point of the fluid is transmitted undiminished throughout the fluid. Equation: (P1)(V1) = (P2)(V2)"

Mind you not everybody implicitly trusts Wikipedia - which is a reasonable position to adopt.

#### strantor

Joined Oct 3, 2010
6,690
logearav,
I think I see where your misunderstanding lies.
Suppose a take a beaker of 4 feet height and fill it with water full to the brim. I mark three points A, B,C at the top, middle and bottom of the beaker. As pascal's law states, that the pressure is same everywhere, if the fluid is at rest, i presume that the points A, B, C will have the same pressure.
No! lets say point B is 2 feet down, and let's say you have a magical sensor which can detect the pressure right through the glass. you take your magical sensor and put it right on the letter "B" (exactly 2ft down) and it measures 2psi. now, turn your beaker around so the "B" is facing away from you and measure exactly 2 ft down, you will read 2psi as well. to help you understand, I will expound on the great mr. Pascal's law: "the pressure is same everywhere within a given plane, if the fluid is at rest"
if you go down and measure the pressure at point "C", you might read 3psi. points A,B, and C are not equal because they are not in the same plane.
Now, we have another statement, " Pressure increases with height". This is where my confusion arises, i.e, how the point A,B, C will have same pressure when they are located at different heights from the top of the beaker.
If you were put a piston in the top of the beaker and apply 5psi to the water, all your points would increase by 5 psi. so point A would read 6psi, point B would read 7psi, and point C would read 8psi.

#### logearav

Joined Aug 19, 2011
243
Thanks Strantor. So, even if there is compression, the pressure change is reflected suitably at every point on the fluid. Am I correct?
I am indebted to all the members who contributed to this thread taking pains in explaining the concept. I sincerely thank everyone.

#### Wendy

Joined Mar 24, 2008
23,276
Were you rather asking whether the (equal) pressures at the same depths C & D in the tank would be the same irrespective of whether the water column portrayed in AlexR's diagram was there or not?
Yep, the column has less volume, but I was interested in what effect it would have on pressure.