(I didn't even have a basic formal education in physics. I'm learning through the internet out of my own interest, so if there are any silly mistakes, kindly bear with and guide me through.)
Everywhere, everyone is saying that pressure will same be for a given height. How is it possible? When volume changes, doesn't pressure change in calculations?
[Pressure will be 2.5 bars approximately (including atmospheric pressure) for a height of 15 metres from ground level. I checked on many sites that 2.5 bars equals 2.5 kg/cm².]
Now let's take base area as 2000 cm² and height of 15 m as constant in three scenarios:
EACH SCENARIO IS INDEPENDENT AND TUBES ARE SEPARATE, I.E NOT CONNECTED WITH EACH OTHER
In scenario 1 a straight vertical tube from ground level will have capacity of 3000 litres with a weight of 2.5 kg per cm² [3000 litres / 2000 cm² = 1.5 kg/cm² + 1 kg/cm² atmospheric pressure].
In scenario 2 the tube becomes narrow from the base area, resulting in a volume of 2000 litres.
In scenario 3 the tube becomes wide from the base area, resulting in a volume of 4000 litres
Question:
When they say pressure remains the same at a given height, does it mean that weight will be 2.5 kg/cm² in all 3 scenarios, where volume is 3000, 2000, or 4000 litres (base area 2000 cm², height 15 m constant)? How is it possible? Where am I wrong?
Best Answer
Consider this diagram showing the three columns you describe all connected to the same body of water:
Your question asks whether the three pressures $P_1$, $P_2$ and $P_3$ will be the same. The answer is obviously yes, because the columns are all connected to the same body of water. For example if $P_1 > P_2$ then water would flow from the base of column 1 to the base of column 2 until the pressures became equal.
OK, but the next question is whether the heights of all the columns are the same. Again the answer is yes because if they weren't we could connect the tops of the columns, let water flow between them and we would have a perpetual motion machine.
So we conclude that the pressure is only related to the height $h$ and does not depend on the shape of the column. Specifically, the relationship between pressure and height is:
$$ P = \rho g h $$
where $\rho$ is the density of the fluid and $g$ is the gravitational acceleration (9.81 m/sec$^2$).