Weight verses pressure

[250]

 

 

 

 

Hello, I don’t have a clear picture of this, can you help me grasp it?

 

 

There are two pipes, filled with water, twenty feet high, vertical, and opened at the top. Pipe (1) is twenty feet diameter, and pipe (2) is two feet diameter. The pressures at the bottom of both pipes are the same. Please explain how 196 tons of water and less than 1 ton of water have the same pressure at the bottom? Exclude piping

 

One cubic foot of water weighs 62.42796 lbs.

 

Pipe one: = 6283 cu.ft. of water,and weighs 392184 lbs.

 

Pipe two: = 20 cu.ft. of water, and weighs 1248 lbs.

 

 

250

 

 

[Cap'n Refsmmat]

The weight is the force the water exerts on the bottom. The pressure is the force per unit of area. So you have to consider the area of the bottom of the pipe, which is related to its diameter.

 

If you had two pipes with an equal weight of water in them, but one was much narrower, the pressure at the bottom would be higher because all that force would be on a small area.

 

So,

 

[math]\mbox{Pressure} = \frac{\mbox{Force}}{\mbox{Area}}[/math]

 

Use that formula when trying to figure out the problem.

[250]

Thank you CAP,

 

Is it because the weight is being supported by more area?

 

So the bigger the hole at the bottom of the tank means more pressure is required to stop it from leaking?

 

So then the size of the hole in a pressure gauge is very critical for its accuracy?

 

I think I am getting this, thx

 

 

 

250

 

 

 

 

[Cap'n Refsmmat]

Bigger hole at bottom = less pressure. Consider: the force at the bottom is the weight of the water. So:

 

[math]\mbox{Pressure} = \frac{\mbox{Weight}}{\mbox{Area}}[/math]

 

If the area at the bottom increases, the total pressure decreases.

[250]

Hi cap,

 

I just want to make sure; we are on the same track, so I must give all fact that I am thinking, because I am confused.

 

Pipe one: = 6283 cu.ft. of water,and weighs 392184 lbs.

 

The water height always stays the same; let's say it has a water refill valve at 20'.

 

At the bottom I drilled a Hole that is one square inch gives you 8.66 pounds per square inch. And so if i drilled a larger hole to one square foot, 8.66 x 144=1247 pounds per square foot. a increase in pressure

 

So what is it that I am doing wrong?

 

So the bigger the hole at the bottom of the tank means more pressure is required on the cork, to stop it from leaking?

 

Your formula, Pressure= weight/area, if the area is increased then so is the weight, keeping the pressure the same?

 

I think i understand this, or i am really sc-wed up. please explain if this is wrong.

 

250

[Cap'n Refsmmat]

Your formula, Pressure= weight/area, if the area is increased then so is the weight, keeping the pressure the same?

 

No. The weight of the water can't change unless you remove or add water. If the area is increased, the pressure must go down.

 

Suppose I have one pound of water on a one-square-foot hole in the bottom. A cork plugging that hole has a pressure of [math]\frac{1 \mbox{ pound}}{1 \mbox{ foot}^2} = 1 \mbox{ lb/ft}^2[/math] on it.

 

Suppose I now have the same water on a two-square-foot hole in the bottom. A cork plugging that hole has a pressure of [math]\frac{1 \mbox{ pound}}{2 \mbox{ foot}^2} = \frac{1}{2} \mbox{ lb/ft}^2[/math] on it.

 

See?

[250]

Hi cap,

 

Please be patient

 

Does not every square foot of surface support the weight of the water, if so then one square foot holds Xlbs of water, so then two square feet holds 2Xlbs of water or twice as much weight?

 

CAP- said:

 

Suppose I have one pound of water on a one-square-foot hole in the bottom. A cork plugging that hole has a pressure of on it.

 

Suppose I now have the same water on a two-square-foot hole in the bottom. A cork plugging that hole has a pressure of on it.

 

See?

 

One pound of water on one foot area is not the same as one pound of water on two square feet. The 1lbs/2'squared has half as much water? You do not have the same water.

 

Would you be so kind and show me how, what I wrote before is wrong?

 

At the bottom I drilled a Hole that is one square inch gives you 8.66 pounds per square inch. And so if i drilled a larger hole to one square foot, 8.66 x 144=1247 pounds per square foot. a increase in pressure

 

 

250

[Cap'n Refsmmat]

Hi cap,

 

Please be patient

 

Does not every square foot of surface support the weight of the water, if so then one square foot holds Xlbs of water, so then two square feet holds 2Xlbs of water or twice as much weight?

 

The same amount of water is in each pipe. One pound of water is in each pipe. If the area increases at the bottom, that cannot increase the amount of water in the pipe, so the total force stays constant.

 

If you drill a larger hole but keep the amount of water constant, the pressure will decrease, because the force will remain constant while the area it is applied to increases.

[250]

Ok I think I hear you, the bigger the hole in the bottom of the tank the less pressure their is at the bottom of the tank, even though the height of the water stays the same. Are you saying this is correct?

 

 

250

 

 

[Cap'n Refsmmat]

If there is the same volume of water in the pipe, a larger-diameter base will mean lower pressure on the base. Yes.

[Ophiolite]

Guys the only thing that matters is the density of the water, the depth of the water and the local value of g. That determines the pressure.

 

p = ρgh

 

where p is pressure, ρ is density, g is the gravitional constant and h is the height of the water column, all in appropriate units. We can neglect variations in g for water columns that are not of siginificant thickness.

[Cap'n Refsmmat]

Right, so if I had a larger-diameter pipe with an equal volume of water in it, the height of the water column would be smaller, resulting in less pressure at the base of the water column.

 

But yes, that would have been a much faster way to solve the problem in the OP, though it doesn't explain the "why?"...

[250]

ok, thx

 

250

Edited November 15, 2010 by 250