Flow in sloped drain line 1

[LDAggarwal]

Would appreciate some assistance: I've had a look at Art's Fluid Flow spreadsheet and using Hill's flow in a sloped line equation.
I keep getting a negative velocity (and hence a negative flow) as the log part of the equation is always less than one. This is mainly driven by the roughness and viscosity being particularly low numbers.
Perhaps I've got my units wrong, but Hill does state "consistent units" in his article.
Any help would be great appreciated.
Thanks,
David.

 

[ione]

LDAggarwal,

Could you expand a bit your post? Which kind of fluid? Which equation (I do mean the one with the "log part of the equation is always less than one")?

 

[katmar]

I have also been confused by Hill's units and resolving it is on my "must do someday" list.

Try

http://www.cispi.org/handbook/chapter8.pdf

for a simple explanation with lots of tables of worked examples.

Katmar Software
Engineering & Risk Analysis Software

http://katmarsoftware.com

 

[LDAggarwal]

Thanks for your help Katmar, much appreciated. At least I can make progress to an acceptable solution.
Ione: actually I was just testing the equation for water first before I applied it to my application, so if you refer to Hills article: Designing Piping for Gravity Flow, Chemical Engineering Magazine, Sept 05 1983. I think the excel interpretation of the formula is:
velocity of liquid in sloped pipe is
=sqrt(32*gravity*hydraulic radius*incline)*log(roughness/14.8/hydraulic radius+0.22*kinematic viscosity/hydraulic radius/sqrt(gravity*hydraulic radius*incline),10)
And the log brackets part of the equation invariably ends up being between 0 and 1, which results in a negative velocity.
So if anyone feels like checking it out and finding out where I'm going wrong, that would be greatly appreciated. For arguments sake, I used the following values:
8" circular pipe which is 50% full, assume ID is 200mm, hydraulic radius is therefore 0.05 (pi()*power(200/2000,2)/2/pi()/0.2*2)
incline is 1:200 or 0.005
roughness is 0.006m (I know this is a VERY rough pipe, if you don't like my number use 0.25mm or 0.046mm instead)
kinematic viscosity is 0.000001 m2/s
gravity is 9.81 m/s2
Good luck!
Regards,
David.

 

[ione]

LDAggarwal,

It seems you are right: there must be a bug in the formula.

[sqrt(32*g*hydraulic radius*incline)] in the second member is, in terms of units, [m/s].

So the argument of the second term (the log argument) must be a pure number as we are calculating a velocity.

Now the argument of the logarithm is in effect a pure number, but being in the range (0,1) the logarithm always gives a negative result.

If the argument were:

[roughness/14.8/hydraulic radius+0.22*kinematic viscosity/hydraulic radius/sqrt(gravity*hydraulic radius*incline)]^(-1)

then the logarithm would always give a positive result.

I think Mr. Art Montemayor or Mr. Hill could dispel our doubts.

 

[chemsac2]

In original paper of Hill, velocity is indicated as VL-bar indicating usage of absolute value of velocity.

I have used absolute velocity for slope determination and have also calculated it using another method. Results match except that Hill formula gives negative value. Taking absolute value seems to be the way out.

Regards,

Sachin

 

[katmar]

Hills' 1983 paper references this formula to the publication "Tables for the hydraulic design of storm drains, sewers and pipelines" by P Ackers and published by Her Majesty's Stationery Office, 1969. I do not have this publication, but a bit of Googling showed me that it has been superceded by the similarly named "Tables for the hydraulic design of pipes, sewers and channels" authored by HR Wallingford and DIH Barr. The latest edition seems to be 8th Ed, Jan 2006.

Thanks to the preview facility in Google Books I was able to see that in the Wallingford and Barr version of the same formula there is very clearly a minus sign in front of the formula. I have tried the formula against some other tables I have and I get very similar answers, so I agree with Sachin that the Hills version of the formula is correct and that we should simply take the absolute value of the calculated answer.

Katmar Software
Engineering & Risk Analysis Software

http://katmarsoftware.com

 

[HamishMcTavish]

Just a note for future reference - HR Wallingford is / was an organisation called Hydraulic Research based in Wallingford, England UK.

Regards, HM

No more things should be presumed to exist than are absolutely necessary - William of Occam

 

[ione]

A minus sign in the formula is just the same thing as applying the logarithm to the inverse of the argument. Thanks both to Sachin and Katmar for having confirmed my intuition.