Units in Drag Force Equation - (Gravitational Constant)

[MR_9331106]

Hi All,

I'm just starting out using Mathcad Prime 6.0, and I'm trying to solve a very simple equation for the drag force on our machine when submerged in a flowing river. I am using the USCS Unit system, and I believe my confusion centers around English units of mass (slug) and how to keep units consistent. 

Example 1: I use 1.94 slug/ft^3 for the density of water. This gives me output units of lbf, which are correct, but they are off by a factor of gravity - 30.046 lbf should be a little over 961 lbf.

Example 2: I use 62.4 lbf/ft^3 for the specific weight of water. Now numerically I'm correct but the units have the extra factor of "ft/s^2".

I'm hoping someone might be able to help me obtain the both the correct numeric value of 966.42, with units of lbf.

Thank You for Your Consideration,

Mitch

[ValeryOchkov]

The extra factor is g! Density is density but specific weight is specific weight. Mass/volume and Force/volume/

[MR_9331106]

Hi Valery,

Thank You for the response, I understand the factor is g, but using this this would numerically change my second example.

I wish I could use SI units, as you used in your response, but in our industry it would be very uncommon to do so.

I'm afraid I'm still stuck.

-Mitch

[ChrisKaswer]

As you know, a "slug" is a different unit from a "lbf", so you can't use the same equation for both and expect consistent units for a result. You will need to standardize on a "density" unit and account for gravity, or not, in your equation.

Alternatively, if you use Mathcad 15, you could create a drop-down unit choice and use an "If" statement to set the equation up to handle the units based on user selection. Rumor has it Prime 7 will have some controls...maybe a simple drop-down like we have in v15. I've used this approach many times with great success.

Update - the equation you used for the drag force requires a mass density, not weight density...the Mathcad Prime result supports this. If you simply change the gamma unit tag in example #2 from "lbf" to "lb", you will get the correct result. The mass density of water is 62.4 pounds mass/ft^2. Recall the numeric value of 1 pound of mass weighs (has a force of) 1 pound and is only valid in earth's gravity. The correct drag force should be about 30 lbf.

Yes - I wish the US would just drop this terrible unit system once and for all!

I hope this helps!

[Werner_E]

The OP already got the result 30 lbf (which I also think is correct) - just see his first calculation.
The 1.94 slug in his calculation are equivalent to the 62.4 lb which you suggested!

The problem is that for some reason he thinks that the result should be about 960 lbf.

I already asked and hopefully he will tell us why he is thinking that the force should be that high.

[terryhendicott]

Hi,

"I wish I could use SI units, as you used in your response, but in our industry it would be very uncommon to do so."

It is time the USA joins the remainder of the world with the metric system.

Cheers

[Werner_E]

I am out of my comfort zone but the equation and the result (30 lbf) look good to me.

Why do you think that the drag force should be as high as 966 lbf ?

[Fred_Kohlhepp]

See the attached file, (it was created in Prime 4).

You're getting wrapped up between density and "specific weight."  Welcome to English units!

[Werner_E · Accepted solution]

I don't think that @MR_9331106  confused density and specific weight.
He knew that in his formula density is required and used it correctly. But for some reason he thought that the result would not be correct, because he expected a different and much higher result. He still has not answered my question as to why he expects that (in my opinion much too large) result.

That he used lbf instead of mass in his second approach was only done to get a result which he thinks is numerical correct, but of course you won't get force that way. He thought that the difference could be caused by a factor similar to the value of g.

Another explanation while we wait for his answer could be this

The calculation

could also be set up that way

maybe someone confused slug and lb and had defined the water density the wrong way and so got the wrong result, which @MR_9331106  now thinks is the correct one!?

This also would explain the factor 32.174.

We will be wiser when @MR_9331106  decides to answer.

[MR_9331106]

@Werner_E , Thank You very much for your input, and sorry for the delay -  I'm just super busy, trying to get this report completed for a project submittal.

You are exactly correct, in that I was looking at a hand calc example from my predecessor, and I was taking it as gospel, when in fact he was confusing specific weight and density. This was for a larger machine in a slightly faster flow, but I thought my values had to be in this ball park. Please see below:

Reading both of your posts made me question everything, so then I dug deeper into previous calculations done for our machines, and found this calculation, done by a structural engineering consultant. (It also helps that it looks like these calculations were performed in Mathcad.) This was for a huge system in a fast river, so the values are quite high, but they handled specific weight and density correctly:

So now my calculation looks like this, where I have added the extra steps just to make it clear I'm playing fair with my units:

Thanks Again to @Werner_E  and all for your help! I'm better now as a result.

Take Care,

Mitch