Yep, the column has less volume, but I was interested in what effect it would have on pressure.

Pressure is only dependent on height, so it would decrease the pressure by not being there. If removing the column made the height of the water above the points C and D only half as deep, then the pressure would be half. It would have the same effect if it were 1" in diameter or 12" in diameter.

 

Another 'challenge'.

Is point E in the top-sealed tube above or below atmospheric pressure?

 

I'm not sure, but I would say below. Reason being, I think there would need to be a vacuum in the tube, otherwise the level would drop to the level in the other tube

 

Kindly, go through my attachment.
The attached material says that the points A and B will have equal pressure. The points A and B lie on different depths and they dont lie on same plane too. But how the pressure is same? Also, there is mention of effect of gravity. I dont understand what role gravity plays here? Pls, help members.

 

Kindly, go through my attachment.
The attached material says that the points A and B will have equal pressure. The points A and B lie on different depths and they dont lie on same plane too. But how the pressure is same? Also, there is mention of effect of gravity. I dont understand what role gravity plays here? Pls, help members.

The image in your document shows the cylinder floating in space and says "in the absence of gravity...". Notice it says nothing of depth; imagine a fishtank floating in outspace; which way is down? there is no down, there is no up, there is no weight because there is no gravity, so there is no "depth". The reason the pressure in a tank of water gets higher the deeper you go, is because the molecules are effected by gravity, giving them weight. Imagine on a football field, you are tackled and you wind up at the bottom of a dog pile; the pressure will get higher because gravity is bringing the weight of more and more players on top of you. same with water molecules; they all dogpile on top of eachother and get heavier and heavier. if you were dogpiled in outer space, in the absence of gravity, you wouldn't feel any pressure. same with water.

 

You are effectively returning to the question you asked in post #1. The effect of gravity is the key to your problem of understanding. I notice the pressure in a liquid column is the topic at the top of the page. Do you understand how gravity gives rise to the differential pressure in a vertical liquid column? Imagine a sealed column of liquid without any gravity (say in free space) - will there be any pressure differential inside the column?

 

Thanks for the replies, Strantor and t_n_k.
In the first place, is there a situation without gravity, when the cylinder floats in the water, as given in my attachment?
t_n_k, i think there wont be differential pressure in a sealed column of liquid, in the absence of gravity

 

In the first place, is there a situation without gravity, when the cylinder floats in the water, as given in my attachment?

Your book may be a little confusing the way they drew that picture. notice the 2nd paragraph of section 5.3.2 starts talking about "if the effect of gravity can be neglected...", then they talk about the picture in fig 5.11, then they go on to address the effects of gravity at the bottom of the page. figure 5.11 is representing a column in space, not floating in water; the effects of gravity are not taken into account in that picture. (it even says at the bottom of the paragraph "This is the proof of Pascal's Law when the effect of gravity is not taken into account"

 

Now consider my attachment,
Imagine the cylinder is surrounded by water on all sides.
Now let me derive the equation,
The vertical forces acting are,
1)Force PaA acting vertically downward on the top surface
2) Weight mg of the liquid column acting vertically downwards
3) Force PbA at the bottom surface acting vertically upwards
where Pa and Pb are the pressures at the top and bottom faces of the cylinder inside the liquid, A is the area of cross section of the circular face and m is the mass of the cylindrical liquid column.
at equilibrium PaA+mg-PbA = 0 or PaA+mg = PbA
Pb = Pa+mg/A, but m = Ahρ
so Pb = Pa+Ahρg/A which gives Pb = Pa + hρg
Can i construe Pb = Pa + hpg as the equation for the statement " Change in pressure at any point in an enclosed fluid at rest is transmitted undiminished to all points in the fluid and act in all directions"

 

Another 'challenge'.

Is point E in the top-sealed tube above or below atmospheric pressure?

I think it is below the atmospheric pressure, since it lies above the point A of the adjacent cylinder. Am i right?

 

You are effectively returning to the question you asked in post #1. The effect of gravity is the key to your problem of understanding. I notice the pressure in a liquid column is the topic at the top of the page. Do you understand how gravity gives rise to the differential pressure in a vertical liquid column?

Imagine a sealed column of liquid without any gravity (say in free space) - will there be any pressure differential inside the column?

I think there won't be any pressure differential inside the column