# pressure=densityxgravityxheight

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Goodmorning/Goodevening everyone

I have this assignment:

A weatherman carried an aneroid barometer from the ground floor to his office atop of sears tower in Chicago. On the ground level, the barometer read 30.15in Hg absolute; on top it reads 28.607in Hg absolute. Assume that the average atmospheric air density was 0.075lb/ft^3, estimate the height of the building.

First I solve for the change in pressure

30.15-28.607 = 1.543inHg

Then converted it to lb/ft^2 =109.165

Pressure= density x gravity x height

109.165lb/ft^2 = 0.075h

109.165/0.075 =h

H= 1455ft

Why is that I need to neglect or disregard gravity in this problem?

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Is 0.075 lb/ft^3 a density?

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Is 0.075 lb/ft^3 a density?

Yes

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Yes

Are you sure? Density is mass/volume. Is "lb" a unit of mass?

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• 2 months later...

it must be specific weight. but as you can see in the formula,

specific gravitysubstance= specific weightsubstance/specific weightwater

specific weight is also equal to: mass*gravity/Volume thus, density*mass

substitute the terms then you can cancel the gravity. then you can conclude that density is directly equal to specific weight.

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Are you sure? Density is mass/volume. Is "lb" a unit of mass?

Yes, it is, swansont.

You apparently are thinking of the pound-force, swansont. The pound is a unit of mass.

Why is that I need to neglect or disregard gravity in this problem?

You don't. What you need to do is to be careful with units, particularly when working with English units. The lb in your 0.075 lb/ft^3 is the pound Avoirdupois, a unit of mass. The lb in your 109.165 lb/ft^2 is incorrect. That should be 109.165 pounds-force per square foot, or 109.165 lbf/ft^2. The pound (lb or lbm) is a unit of mass, the pound-force (lbf) is a unit of force.

In the metric system, one uses F=ma. That doesn't work with force expressed in pounds-force, mass in pounds, and acceleration in feet per second squared. One must instead use the more generic form of Newton's second law: Force is proportional to (rather than equal to) mass times acceleration. Mathematically, F=kma. A force of one pound-force accelerates a one pound mass 32.174 ft/s^2, so k=1/32.174 with this choice of units.

This means your expression "pressure = density x gravity x height" needs a bit of modification to work with English units. With pressure in lbf/ft^2 and density in lbm/ft^3, the correct expression is [imath]P=\frac 1{32.174} \rho g h[/imath]. Since g=32.174 ft/s^2, your expression simplifies to [imath]P=\rho h[/imath] if you express pressure in lbf/ft^2 and density in lbm/ft^3.

Edited by D H
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the actual formula for this is ΔP = wh or simply pressure differential is equal to specific weight x height, where specific weight is density times gravity. actually lb/ft3 is not standard and should be converted to slugs/ft3 to get actual density by dividing it by gravitational constant, 32.174, and getting 0.002378 which is the standard density at sea level.

Note if you use the equation without converting it units will not cancel out, such that h = delta P/rho x g which g has a unit of time, second, which cannot cancel out unless you convert the 0.075 lb/ft3 into slugs/ft3.

Doing so h = ΔPg/ρg, both g or gravity will cancel out thus you get h as ΔP/ρ.

Edited by gabdecena
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actually lb/ft3 is not standard and should be converted to slugs/ft3 to get actual density by dividing it by gravitational constant, 32.174, and getting 0.002378 which is the standard density at sea level.

Nonsense. I do understand where this nonsense comes from, but that doesn't stop it from being nonsense. A lot of schools now teach that the slug is the US customary unit of mass, and that pounds are a unit of force. This is nonsense. The slug is a non-standard unit used by some (but not all) engineers in the US. Other engineers are quite happy using the pound as a unit of mass and the pounds-force as a unit of force. The pound (Avoirdupois pound) is defined as 0.45359237 kilograms, exactly. The pound-force is defined as 4.4482216152605 newtons, exactly.

Weight is legally and colloquially a synonym for mass in the US. Better said, mass is a synonym for weight. Weight is a much, much older word than is mass. English has two words for the same concept for the same reason that the animals that provides pork are called swine. The Norman invaders spoke French, and their French words eventually became English words. It took a few more centuries after 1066 for the descendants of those Norman aristocrats to invade the merchant class. Mass didn't become an English word until the 15th century.

We in the technical community don't like it when the lay community pervert our own words. For example, "Evolution is just a theory." To avoid being hypocrites, we in the technical community should avoid doing the same to perfectly good English words such as weigh and weight. The supposed confusion between mass and weight is an invented controversy. As noted above, there is no confusion in everyday English. When your friend says he weighs 155 pounds (or 70 kilograms), fight back the urge to correct him. His usage is correct.

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Nonsense. I do understand where this nonsense comes from, but that doesn't stop it from being nonsense. A lot of schools now teach that the slug is the US customary unit of mass, and that pounds are a unit of force. This is nonsense. The slug is a non-standard unit used by some (but not all) engineers in the US. Other engineers are quite happy using the pound as a unit of mass and the pounds-force as a unit of force. The pound (Avoirdupois pound) is defined as 0.45359237 kilograms, exactly. The pound-force is defined as 4.4482216152605 newtons, exactly.

Weight is legally and colloquially a synonym for mass in the US. Better said, mass is a synonym for weight. Weight is a much, much older word than is mass. English has two words for the same concept for the same reason that the animals that provides pork are called swine. The Norman invaders spoke French, and their French words eventually became English words. It took a few more centuries after 1066 for the descendants of those Norman aristocrats to invade the merchant class. Mass didn't become an English word until the 15th century.

We in the technical community don't like it when the lay community pervert our own words. For example, "Evolution is just a theory." To avoid being hypocrites, we in the technical community should avoid doing the same to perfectly good English words such as weigh and weight. The supposed confusion between mass and weight is an invented controversy. As noted above, there is no confusion in everyday English. When your friend says he weighs 155 pounds (or 70 kilograms), fight back the urge to correct him. His usage is correct.

I understand that not all uses it but we have follow unit consistency on most problems to get the answers correct since some old textbooks have their answers in slugs or some other units. Organizations were formed to make a standard unit for this units such as SI units. I am sorry we have different views but answer is just the same but of different units on most cases. But we in aeronautics community use slugs or either kg in the density and not lbs.

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I understand that not all uses it but we have follow unit consistency on most problems to get the answers correct since some old textbooks have their answers in slugs or some other units. Organizations were formed to make a standard unit for this units such as SI units. I am sorry we have different views but answer is just the same but of different units on most cases. But we in aeronautics community use slugs or either kg in the density and not lbs.

To add also it is important te get correct units and to be consistent to prevent miscalculations which is very critical for engineers specially on structural designs which even a minute error can cause catastrophic failure which we are responsible of. So if the given is in this unit we should answer the question on the same unit also which is the case on most textbooks.

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Gravity is independent of height. Hence it cancels out.

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