Will the pressures at the bottom of two similar water tanks with same level of water be different? See below.?

Question

One tank is at sea level and the other tank is at 1000m above sea level.

Answer 1

The pressure at the bottom of the tank is the sum of the pressure due to the water level and the atmospheric pressure at that place.

As the water level in both the tanks are equal the pressure due to water in both the tanks are same.

But the atmospheric pressure at a height of 1000 m is less than the atmospheric pressure at sea level.

Approximately the pressure at 1000 km is less by an amount 11450 Pa from the sea level.

Answer 2

No. Due to different Alitude.

Consider the following Bernoulli's equation

P + (Density x Gravity x Height) + (0.5 x density x speed^2)
Initial pressure Static Pressure Dynamic Pressure

If in 2 tanks but different alitude of 1000m above the sea level,

1. Initial Pressure changes as the Pont A and point B different in 1000m. Therefore, the Pressure Change shall be Density of air x Gravity x 1000 meter which is about 1.1772 bar different if given density of air is 1.2 for dry air

2. Static Pressure no change as the amount of water and height of the water from the bottom is the same.

3. No dynamic pressure.

Answer 3

Take it to the extreme. The pressure anywhere in a water tank outside the influence of a gravitational field will be only whatever pressure is applied to the water, such as by forcing air into the tank. If your tank is open to the atmosphere, the pressure reduces as the elevation increases.

Water is not compressible, so air displaced doesn't change with altitude.

To be sure of the answer, you'd need to compute atmospheric pressure as a function of altitude, and also the weight of a column of water of varying height as a function of altitude. Use these computations to see whether there can be any combination of water height and altitude where increasing the altitude increased the net pressure.

Answer 4

The pressure at the bottom of the tank located at sea level is higher that the one located 1000 m above the sea level.

1. Atmospheric pressure at 1000m above sea level is lower so the absolute pressure (Pabs= Patm+ Pg) is definitely lower than that located at sea level.

2. The pull of gravity 1000m above sea level is less than the pull of gravity at sea level.

Pg= (height)(density)(acceleration due to gravity)

Therefore the specific weight of water at higher elevation is lower so the gage Pressure is also lower.

Answer 5

The tank with the least gravity acting on it will have the lesser bottom pressure, since the weight of the water and the air above it are the main sources of that pressure.

Therefore the tank closest to sea level should have the highest pressure at the bottom.


Here's my reasoning:

Water density is 1000 kg per cubic meter, but this fact isn't really important for the analytical purpose here. The density of water at 1000 meters above sea level is not significantly different than at sea level, so that's not an important consideration in this case, so it can be treated as constant here.

pressure = (density of water) × (gravity) × (depth) + (air pressure)

Pressure is defined as the force or weight per unit area.


Let:
G = gravity at sea level
g = gravity at 1000 meters above sea level
P = Air pressure at sea level
p = Air pressure at 1000 meters above sea level

Remember that (G > g) and (P > p)

The gravity (G) at sea level is greater than the gravity (g) at 1000 meters above sea level and air pressure (P) is greater at sea level than the air pressure (p) at 1000 meters above sea level.

So according to the pressure equation above, if the same tank was moved to sea level, the pressure at the bottom would be greater than at 1000 meters above sea level due to the larger gravity and air pressure values acting on it, from which the water pressure primarily originates.

The absolute or total pressure at a given depth is the sum of the contribution from the weight of the water plus the air pressure at the top surface coming from the atmosphere above it.

or in mathematical terms:

pressure = (density of water) × (gravity) × (depth) + (air pressure)

Where the water pressure acts equally in all directions.

In this analytical case, we don't need to consider the area of the bottom, just the relative relationships.

Since both the air pressure and the acting gravity are less at 1000 meters than at sea level, the equation indicates that the tank with the greatest gravity and air pressure acting on it will have the highest bottom pressure.

In other words, the tank at sea level will have the highest bottom pressure due to the reasons given above.

Or is my understanding of the physics involved in error in some way?

NOTE:
If I am wrong, I hope somebody here will contact me with the relevant equations and demonstrate the error and show me where I went wrong. I'm deadly serious about that. I take science seriously and will yield to any proven error. When it comes to foolish errors, I've had my moments of glory that would make the 3-Stooges blush with envy. I just hope this is not one of them. Even if it is, I still need to know so I can modify my future reasoning accordingly.

Above all else, the integrity of science must be maintained.

 

Answer 6

Actually, the pressure at the bottom of the tank at altitude will be higher. The reason is that the weight of water column is reduced by the bouyancy effect, equal to the weight of air displaced by the water. Since air is denser at sea level, the weight of the displaced air is greater and there is a greater bouyant effect on the column of water.

EDIT (8/28/06): Congratulations to Jay T; he has the right answer! Apparently the gravity variation trumps the air density effect. To all others, air pressure has no effect, since it acts on all parts of the water column equally and cancels out. I have made calcuations to determine the amount of water pressure difference and you can find these in two pages here

Page 1: http://img179.imageshack.us/img179/2023/waterpressvsaltp1st5.png
Page 2: http://img61.imageshack.us/img61/4903/waterpressvsaltp2ek8.png

The difference for a tank 2m high is about 4 kg/m*sec^2 or 5.5*10^-4 psi. The calculations were done in MathCad, which thankfully takes care of all the units nicely,

Answer 7

Relative to the local atmosphere pressure the pressure at the bottom of both tanks will be the same for all practical purposes.

Answer 8

in case you communicate approximately the unit tension on the backside of each and every tank that is going to be comparable through comparable point of water in the two the tanks. needless to say, the commulative tension on the backside of the tank with a much wider base is going to be extra desirable than that on the backside of the thinner tank.

Answer 9

The pressures will be slightly different, as the force of gravity at the higher elevation will be slightly less. Without precision instruments, the difference would not be visible.

Answer 10

Yes