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We know that pressure inside a container depends on depth. My question is that if this true then if I fill water in a one end closed pipe which has diameter of 2cm and height is 4m and if I fill the same water in a cylinder which has diameter 15cm and height 4m then pressure inside the bottom of the both container is the same? See image enter image description here

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3 Answers 3

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Yes, the pressure at the bottom of the two containers is the same. There is more water in the $15$cm diameter cylinder, but its weight is spread over a greater area.

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  • $\begingroup$ Please elaborate I don't understand . If this is true then if I fill same density water in tube which has a diameter 3mm and same height i.e 4m then also pressure inside the bottom of the container is same ? $\endgroup$
    – Sunu Kodag
    Mar 14, 2019 at 13:42
  • $\begingroup$ @SunuKodag That's how pressure works, yes. The difference is the total force exerted by the fluid (pressure is force per unit area, and the area is different for different diameters). $\endgroup$
    – JMac
    Mar 14, 2019 at 14:05
  • $\begingroup$ @SunuKodag, you can think of it like this: Take a point on the bottom of the cylinder. The only thing pressing down on that point is the thin line of water directly above it. Thus, only by increasing the water directly above each point (increasing the height) can you increase the pressure. $\endgroup$ Mar 14, 2019 at 17:33
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Since Pressure $p$ equals force $F$ per area $A$, your pressure at any given height will be the same in both of your containers. The greater force due to the larger volume is spread over an equally larger area.

$p=\frac{F}{A}$

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Yes, the pressure depends on height only, regardless of the shape of the container...

...as long as the pressure above the vessels is the same in both cases. I suppose you have atmospheric pressure in both cases, so it's the same.

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