# Gravitational constant in english units

Gold Member

## Main Question or Discussion Point

Hello,

I am taking a fluid mechanics class right now, so I deal a lot with water flowing through a pipe, and equations involving the density of the fluid.

The problem is, that since I'm an engineering major, we use way too many english units. There is something inherent about non-SI units I believe that makes my calculations hard to follow, especially when dealing with the density of a fluid.

The book will randomly divide the density by the gravitational constant, and I am having trouble understanding why the gravitational constant is omitted sometimes and not omitted other times when doing calculations, and how I can keep it straight when to include or not include it.

For example, the equation p = ρgh. You end up dividing out the constant g.

Also, a kg m/s^2 is one Newton. Is a lb_m ft/s^2 a lb_f??

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Chestermiller
Mentor
Hello,

I am taking a fluid mechanics class right now, so I deal a lot with water flowing through a pipe, and equations involving the density of the fluid.

The problem is, that since I'm an engineering major, we use way too many english units. There is something inherent about non-SI units I believe that makes my calculations hard to follow, especially when dealing with the density of a fluid.

The book will randomly divide the density by the gravitational constant, and I am having trouble understanding why the gravitational constant is omitted sometimes and not omitted other times when doing calculations, and how I can keep it straight when to include or not include it.

For example, the equation p = ρgh. You end up dividing out the constant g.

Also, a kg m/s^2 is one Newton. Is a lb_m ft/s^2 a lb_f??
No. The conversion factor is $\frac{1}{32.2}\frac{lb_fsec^2}{lb_mft}$.

Gold Member
why is it then that the conversion in SI units is not 1 N s^2/9.8 kg m??

AlephZero
Homework Helper
In "English units" (which are no longer used in England in science and engineering, so they really ought to be called "stupid American units" IMHO) the weight of 1 pound mass, on the surface of the earth, is 1 pound force.

In SI units, the weight of one kilogram is 9.8 Newtons.

Of course the weight of one kilogram would be 1 kilogram-force, except that nobody uses "kilogram-force" as a scientific unit.

(A force of 1 Newton is approximately the weight of one apple, which is a nice coincidence.)

• 1 person
Gold Member
Then what the heck is the difference between a slug and a pound mass?? Two english units for the measurement of mass

Chestermiller
Mentor
Then what the heck is the difference between a slug and a pound mass?? Two english units for the measurement of mass
A slug is 32.2 lbm. Slug is really the mass unit you want to use if you want F = ma to give you the force in lbf. One lbf is the force you need to exert on a mass of 1slug to give it an acceleration of 1 ft/sec2. If you exert a force of 1 lbf on a 1 lbm, its acceleration will be 32.2 ft/sec^2.

D H
Staff Emeritus
Of course the weight of one kilogram would be 1 kilogram-force, except that nobody uses "kilogram-force" as a scientific unit.
The same influences that drive various American engineers to use the pound mass as the unit for mass and the pound force as the unit of force drive their metric counterparts to use the kilogram-force. For example, space agencies in metric countries ofttimes expresses rocket thrust in units of kilogram-force (aka kilopond) rather than in newtons.

You wouldn't find "stupid American units" to be quite so stupid if all you had was a simple two-pan balance for dividing things...

AlephZero
Homework Helper
You wouldn't find "stupid American units" to be quite so stupid if all you had was a simple two-pan balance for dividing things...
Are you claiming that a simple two-pan balance works differently depending on the unit system you use to model it?

O well, I guess idea that the same laws of physics apply everywhere in the universe was wrong - they are different in the USA.

No, I'm saying one can divide a pound of, for instance water, into 16 separate ounces of water with primitive technology. There is no easy way to divide a litre of water into 10 decilitres of water using a two-pan balance.
The point is, such things as "stupid units" had a reason for existing.

jhae2.718
Gold Member
No, I'm saying one can divide a pound of, for instance water, into 16 separate ounces of water with primitive technology. There is no easy way to divide a litre of water into 10 decilitres of water using a two-pan balance.
The point is, such things as "stupid units" had a reason for existing.
Regardless, historical reasons are no justification for continuing on with the usage of inferior units when we have much better options available.

Sure, there's going to be a big hurdle at the beginning, but it's worth it long term.

AlephZero
Homework Helper
The same influences that drive various American engineers to use the pound mass as the unit for mass and the pound force as the unit of force drive their metric counterparts to use the kilogram-force. For example, space agencies in metric countries ofttimes expresses rocket thrust in units of kilogram-force (aka kilopond) rather than in newtons.
I have never seen a mathematical or computer model from a European company that used anything other than the newton as a force unit. What they put in their press releases (and/or sales presentations when selling to the USA) is a different matter, or course.

The thing that really ****** me off about US units is not so much the conversion factor, as the fact that US engineers seem incapable of deciding what value to actually use. Getting three different versions of the same model of the same object, from the same US company, with three different conversion factors, is "normal" - even after the formal contract has specified what units systems are to be used, including the agreed value.

AlephZero
Homework Helper
No, I'm saying one can divide a pound of, for instance water, into 16 separate ounces of water with primitive technology. There is no easy way to divide a litre of water into 10 decilitres of water using a two-pan balance.
Yeah. I suppose that explains why there were 14 pounds in a stone, and 20 hundredweight in a ton sophiecentaur
Gold Member
I guess it's just by chance that a well informed USA treasury decided to use 100 Cents in a dollar and not 12 $hillings or something. The justification for using 16oz in a pound sounds more like numerology than Maths, Engineering of Science. I guess it's just by chance that a well informed USA treasury decided to use 100 Cents in a dollar and not 12$hillings or something. The justification for using 16oz in a pound sounds more like numerology than Maths, Engineering of Science.
I doubt the people who invented and used such measures a few thousand years ago would agree with you.

I'm not claiming the funny old units are better or anything, but they were perfectly practical and useful in the entirely different ancient world. This is how we get folks thinking that space aliens built the Egyptian pyramids... because they can't possibly believe anyone who used something so ridiculous as numbers based on twelves or sixties could have achieved anything.

sophiecentaur
Gold Member
Using a number base that has many factors is brilliant for doing mental arithmetic. Also, there are good reasons for using units that relate to body dimensions. Technology changes things.

Borek
Mentor
they were perfectly practical and useful in the entirely different ancient world.
That's what we probably all agree with.

And it is exactly a reason why continuing to use them today is so nonsensical.

sophiecentaur
Gold Member
It's still nice to know that eggs, at 31/2d each, are 3/6 a dozen. (Look it up.)

... If you exert a force of 1 lbf on a 1 lbm, its acceleration will be 32.2 ft/sec^2.
To the OP (and anyone else confused by g and gc, where the factors of 32 go) in fluid mechanics, read the above sentence over & over again until it sinks in.

As far as changing from inch to metric/SI goes, I think it would have happened a long time ago if the Earth's circumference had worked out to 2.56 cm per inch rather than the 2.54 factor we have. At 2.56, you could cut "metric" threads on an inch screw lathe using the normal set of change gears; with the 2.54 factor you need a 127 tooth gear - harder to make and if you do make one, it is too big in diameter to fit in the lathe gearbox. Thousands of factories and shops with probably millions of expensive lathes and mills = lots of resistance to changing standards. With modern CNC stuff it doesn't matter anymore, but for essentially all of the 20th century it did.

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