Pressure depth problem in English units instead of metric

[Sentience]

Homework Statement

Consider a submarine cruising 32 ft below the free surface of seawater whose density is 64 lbm / (ft^3). What is the increase in the pressure in psi exerted on the submarine when it dives to a depth of 172 ft below the free surface? Assume that the acceleration due to gravity is 32.4 ft/(s^2)

Homework Equations

P = Rho *g * h

The Attempt at a Solution

I am used to metric units and this is in english units.

I muliply 140 ft. (change in depth) by 64 (lb (mass)/ (m^3)) (density) by 32.4 ft/s^2 (gravity)

The answer should be in psi, but I get units of (lbm / ft * s^2)

God I loathe English units.

 

[PhanthomJay]

The English units are very confusing to those familiar with SI units. A 1 lbm weighs 1 pound on Earth. The correct unit of mass is the slug, where 1 slug weighs 32. 4 pounds on Earth (compare to 1 kg weighs 9.8 N).

So in your pressure calculation, you are already given the density of the water as 64 lbs/ft^3. Multiply it by the depth to get the pressure in pound per sq foot, then convert it to pounds per square inch. I have given you a large bit of info here, because I know how confusing it can be, especially when a problem starts fooling around in lbm instead of slugs, or instead of just giving the density as a weight per unit volume, in lbs/ft^3.

 

[PeterO]

The English units are very confusing to those familiar with SI units. A 1 lbm weighs 1 pound on Earth. The correct unit of mass is the slug, where 1 slug weighs 32. 4 pounds on Earth (compare to 1 kg weighs 9.8 N).

So in your pressure calculation, you are already given the density of the water as 64 lbs/ft^3. Multiply it by the depth to get the pressure in pound per sq foot, then convert it to pounds per square inch. I have given you a large bit of info here, because I know how confusing it can be, especially when a problem starts fooling around in lbm instead of slugs, or instead of just giving the density as a weight per unit volume, in lbs/ft^3.

What is this "slug" of which you speak?

SI units are also known as mks - metres , kilograms, seconds

British units are fps - foot, pound, second.

Mass is measured in pounds. Weight [the force, like Newtons] like any other force was the poundal though often given as lb-weight, just as maths books often give weight as kg-weight.

Bathroom scales were calibrated to tell people what mass in pounds would weigh as much as you, just as modern scales tell you what mass in kilograms would weigh as much as you.I spent the first 20 years of my life working in British - or as we knew the, the Imperial system - and have never before heard the term "slug" other than in Western [cowboy] movies where they often had a "slug of whisky" ?

Metric units are also just so much easier to work with!

 

[SteamKing]

The mass in slugs is equal to the weight in lbf divided by g, or slugs = W / 32.2

 

[PeterO]

The mass in slugs is equal to the weight in lbf divided by g, or slugs = W / 32.2

And the definition [obtained from the web] says it all. It is not part of British units at all, but US common system of units.

The slug is the unit of mass in the US common system of units, where the pound is the unit of force.

EDIT: and that slug of Whiskey must have been pretty intoxicating!

 

[PhanthomJay]

What is this "slug" of which you speak?

In the USA, no lay person , including many engineers, know what is a slug, and very few know what a Newton or even a Kilogram is. But physicists must use slugs, or else they'll get very messed up when calculating the acceleration of a mass when subject to a force of so many pounds. When using F=ma, for example, and the force, F, is in pounds, the mass must be in units of slugs to get the acceleration in ft/sec/sec.

SI units are also known as mks - metres , kilograms, seconds

yes, length , mass, and time units

British units are fps - foot, pound, second.

yes, length, force, and time units. I call it the USA system, since it is used exclusively in the US (and Myanmar), although I'm told that the British measure distance along a highway in km, but the speed limit signs are in mph. How bad!

Mass is measured in pounds.

no, it is measured in slugs

Weight [the force, like Newtons] like any other force was the poundal

I used to know what a poundal is, but have long since forgotten. It should be eliminated from all textbooks

though often given as lb-weight, just as maths books often give weight as kg-weight.

Force should be (and is) given in pounds for the technical and lay people, and in N for the SI technical people. One slug weighs about 32 pounds, per W = mg.

Bathroom scales were calibrated to tell people what mass in pounds would weigh as much as you, just as modern scales tell you what mass in kilograms would weigh as much as you.


I spent the first 20 years of my life working in British - or as we knew the, the Imperial system - and have never before heard the term "slug" other than in Western [cowboy] movies where they often had a "slug of whisky" ?

Or in my garden where there a host of nasty looking wormlike slugs, yuk.

Metric units are also just so much easier to work with!

Not if your from the USA as an engineer! I seriously doubt the US will convert to SI in my lifetime, in spite of efforts by the government to do so over the past 40 years. For example, I know that Grade 60 steel has a yield stress of 60,000 psi. I have no idea what that equates to in Pascals unless I get my calculator out, and there are so many darn zeroes in SI that the best of us will be overwhelmed by the decimal point or exponents, causing costly mistakes by both engineers and the construction folks, and not have a good 'feel' for the numbers . Sometimes a construction person will ask me how much an assembly weighs so he/she can lease the correct lifting crane. If I tell him it weighs 10,000 pounds, he'll probably use a 40 ton crane for a good safety factor. If I told him it weighs 45,000 N, he'd likely throw a hammer at me.

 

[PeterO]

In the USA, no lay person , including many engineers, know what is a slug, and very few know what a Newton or even a Kilogram is. But physicists must use slugs, or else they'll get very messed up when calculating the acceleration of a mass when subject to a force of so many pounds. When using F=ma, for example, and the force, F, is in pounds, the mass must be in units of slugs to get the acceleration in ft/sec/sec. yes, length , mass, and time units yes, length, force, and time units. I call it the USA system, since it is used exclusively in the US (and Myanmar), although I'm told that the British measure distance along a highway in km, but the speed limit signs are in mph. How bad! no, it is measured in slugs I used to know what a poundal is, but have long since forgotten. It should be eliminated from all textbooks Force should be (and is) given in pounds for the technical and lay people, and in N for the SI technical people. One slug weighs about 32 pounds, per W = mg. Or in my garden where there a host of nasty looking wormlike slugs, yuk. Not if your from the USA as an engineer! I seriously doubt the US will convert to SI in my lifetime, in spite of efforts by the government to do so over the past 40 years. For example, I know that Grade 60 steel has a yield stress of 60,000 psi. I have no idea what that equates to in Pascals unless I get my calculator out, and there are so many darn zeroes in SI that the best of us will be overwhelmed by the decimal point or exponents, causing costly mistakes by both engineers and the construction folks, and not have a good 'feel' for the numbers . Sometimes a construction person will ask me how much an assembly weighs so he/she can lease the correct lifting crane. If I tell him it weighs 10,000 pounds, he'll probably use a 40 ton crane for a good safety factor. If I told him it weighs 45,000 N, he'd likely throw a hammer at me.

Interesting background, but I have since found that the slug is an American unit not a British unit.

the FPS system - foot pound second is also a length - mass - time system outside of America, with poundal being the unit of force - not that it was used outside the lab, just like Newtons are not used outside the lab. We order 2 kg of potatoes, and the grocer uses a spring balance that tells him 2 kg - even though we know the weight was actually 19.6 N

Just as you tell the the contractor the assembly weighs 10,000 pounds, we tell him it weighs 4500 kg, or 4.5 tonnes - making it very easy to work out what crane to get.

 

[Sentience]

Ok, now I'm really confused. According to wikipedia a psi is a pound FORCE per square inch. Am I doing this right?

140 ft. * (64 pounds MASS/ cubic feet) * (32.4 ft / seconds ^2) * (1 lb force / 1 pound mass * 32.4 ft/s^2) * ( 1 square foot / 144 square inches)

=

62.2 pounds per square inch

Which sounds way too low to me, considering the amount of water involved. Please help :(

 

[SteamKing]

As a shortcut, seawater also weighs 64 lbf/cu. ft. (fresh water is 62.4 lbf/cu.ft.)
If you were to take a column of seawater which had a square base 1 foot on each side and which was 140 feet tall, the total weight of seawater in this column would be:
64 lbf/ft^3 * 140 ft^3 = 8960 lbf

Now, the pressure at the base of the column is equal to the weight of the seawater divided by the area, or P = W / A, which is:

P = 8960 lbf / 1 ft^2 = 8960 lbf/ft^2

Since there are 144 square inches in each square foot, the pressure above can be also expressed as:

P = (8960 lbf/ft^2 ) / (144 in^2/ft^2) = 62.2 lbf / in^2 = 62.2 psi

 

[Sentience]

Thank you very much! This forum rocks!