Pressure and Weight in Water Tank

[user100]

Hi all,

Can someone clarify whether the following is right?

Assume a Cylindrical tank with a base area of 2000 sq.cm, is filled with water upto 15 metres ( tank starts from ground level)

1) The pressure at the bottom of tank will be 2.5 bar ( approx) i.e 1 bar pressure for every 10 metres + 1 bar atmospheric pressure.

2) Now if i want to find weight at specific part of base area, say 100 sq.cm, then (conversion 1 bar = 1 kgf/cm2). Hence weight on 100 sq.cm will be 2.5 kilogram * 100 sq.cm = 250 kilogram

Whether the above working is right?? If so is it right to say " A water tank of 15 metres will exert 250 kilogram weight for every 100 sq.cm"

Please clarify. Thank you.

 

[Simon Bridge]

Welcome to PF;
I'm guessing this is an upright cylinder - so the base is a circle?

You should state your reasoning ... are you just following rules?

1. the bottom of the tank has to support the entire weight of the water above it, and the air pressure on the top.
pressure is force over area. If you know the density of the water you can work out the weight.

2. you have to decide if "weight" includes the atmospheric pressure too.

 

[user100]

Welcome to PF;
I'm guessing this is an upright cylinder - so the base is a circle?

You should state your reasoning ... are you just following rules?

1. the bottom of the tank has to support the entire weight of the water above it, and the air pressure on the top.
pressure is force over area. If you know the density of the water you can work out the weight.

2. you have to decide if "weight" includes the atmospheric pressure too.

Yes. Sorry if i wasn't clear. it's my first post.

1. Yes, the base is circle.
2. Let me explain how i arrived at the working. From wiki and other sites, i learned that Pressure increases 1 bar or 100 kpa for every 10 metres depth. So the depth is 15 m, so 1.5 bar. I also understood that pressure is fixed 1 bar for few kilometres from ground level. So the pressure at the bottom of tank will be 1.5+1 = 2.5 bar.

​http://www.unit-conversion.info/pressure.html From this site, i converted 2.5 bar to 2.5 kilogram force per sq.cm

So i came to rash conclusion that weight ON THE BASE AREA of tank on specific part say 100 sq.cm will be 2.5*100 = 250 Kilogram. Is it wrong?

 

[Simon Bridge]

The reasoning is fine - apart from maybe at the end.
The reason you are uncertain is that you basically relied on other people's tools to get your answer, so you cannot be sure that they are giving you the correct results.

You can check if you have the correct numbers by reworking the problem using the physics instead.

Do some algebra first:
If the base area is A and the height of the water is h, then the equation for the volume of water is:
V=...

If the density of water is p, and the force of gravity is g, then the total weight of water is:
W=Mg=...

Since pressure is force over area, what pressure does the water exert due to it's weight?

How does P(atmos) factor into this?

Write out the equation. Plug in the numbers - you can use SI units now.
Note 1bar=100kPa, 1atmos=1.011bar=101.1kPa.

The pressure exerted by the water weight is the amount of weight over 1sq.m
how many times does 100sq.cm fit into 1sq.m? hint 100sq.cm = 10cm x 10cm square.

You should find a calculation like that gives you more confidence.

 

[SteamKing]

I also understood that pressure is fixed 1 bar for few kilometres from ground level.

In general, the standard atmospheric pressure of 1013.25 millibars is defined as the average pressure at sea level:

http://en.wikipedia.org/wiki/Atmospheric_pressure

Because air is a fluid, the atmospheric pressure also depends on the altitude at which measurements are taken, but for various reasons, the variation in atmospheric pressure with altitude is not linear, in general. Most of the atmospheric mass is located between mean sea level and an altitude of approximately 17 km, which is also called the troposphere.

 

[user100]

The reasoning is fine - apart from maybe at the end.
The reason you are uncertain is that you basically relied on other people's tools to get your answer, so you cannot be sure that they are giving you the correct results.

You can check if you have the correct numbers by reworking the problem using the physics instead.

Do some algebra first:
If the base area is A and the height of the water is h, then the equation for the volume of water is:
V=...

If the density of water is p, and the force of gravity is g, then the total weight of water is:
W=Mg=...

Since pressure is force over area, what pressure does the water exert due to it's weight?

How does P(atmos) factor into this?

Write out the equation. Plug in the numbers - you can use SI units now.
Note 1bar=100kPa, 1atmos=1.011bar=101.1kPa.

The pressure exerted by the water weight is the amount of weight over 1sq.m
how many times does 100sq.cm fit into 1sq.m? hint 100sq.cm = 10cm x 10cm square.

You should find a calculation like that gives you more confidence.

Ok sir, understood.

If i want area of circle as 2000 sq.cm, using formula ∏r2, we can get radius as .2524 m

Then the volume for 15 m height will be ∏r2h, so volume is 3000 litres.

Since density of 1 litre water is almost equal to 1 kilogram
Weight(mg) will be 3000 * 9.8 = 29400 / 2000 sq.cm = 14.7 Newtons per sq.cm or 1.5 kg/ sq.cm

Adding atm of 1 bar, which is 1 kg / sq.cm. Total of 2.5 kg /sq.cm

So this is how they arrived in Online conversion sites that 2.5 bar equals 2.5 kg / sq.cm. Right??

(p.s I didn't even have, basic formal education in physics. out of own interest I'm learning through internet. So if there are any silly mistakes, kindly bear and guide me through.)

Now my question is, everywhere, everyone are saying that pressure will be same for a given height. How is it possible? when volume changes doesn't pressure change in above calculation?

I.e let's take base area as 2000 sq.cm and height of 15m as constant in Two scenarios:-
In scenario 1 the tube becomes narrow from base area resulting in volume of 2000 litres.

In Scenario 2 the tube becomes wide from base area, resulting in volume of 4000 litres

Question:-

So When they say pressure remains same at same height, does it mean that weight will be 2.5kg / sq.cm in all 3 scenarios, where volume is 2000,3000,4000 litres (base area 2000 sq.cm, height 15 m constant)?? How is it possible? where am i wrong??

 

[IPNightly]

In scenario 1 the tube becomes narrow from base area resulting in volume of 2000 litres.

In Scenario 2 the tube becomes wide from base area, resulting in volume of 4000 litres

Question:-

So When they say pressure remains same at same height, does it mean that weight will be 2.5kg / sq.cm in all 3 scenarios, where volume is 2000,3000,4000 litres (base area 2000 sq.cm, height 15 m constant)?? How is it possible? where am i wrong??

You're not wrong... here's a way to think about it. Imagine you had an empty 1 m cube tank with an immensely strong 1 mm thick dividing wall in it that you can slide to make two tanks of various sizes.

Now slide the divider to 1 cm away from one wall and fill the tiny 1 cm section.

The pressure on the walls and floor inside that 1 cm slice is exactly the same whether you fill up the rest of the tank or not. That should be easy to see - imagine you fill up the rest of the tank now to exactly the same level ... do you expect there to be a pressure difference between the 99 cm wide section and the 1 cm wide section?

If you dyed the water in the large tank red and punched a small hole at the base of the dividing wall would you expect red water to gush through the hole to equalise the pressure? Of course not - the pressure is identical on either side of the dividing wall.

Even if the thin side of the tank is 0.1 mm wide (capillary effects not withstanding), the pressure at the bottom is still exactly the same as the pressure in a tank of exactly the same depth that is 1 km wide.