777gne
Mechanical
- Jun 2, 2004
- 47
After quite a bit of help from Latexman last year (this thread: I have been calculating frictional losses for power law fluids rather successfully. Most of the calculations I have double checked by a fluids lab that I work with and my calculated pressure drop is typically 10% higher than theirs. I don't know the exact method they're using but have to assume the approach is different otherwise I've been getting lucky!
I've been using the following formula:
delta P = [(3 * n + 1 / n)^n * (Q / pi * r^3)^n * (2 * L * K / r)] / 144
where:
n = flow index (unitless) - obtained from rheology test
Q = flow rate ft^3/s
r = radius of pipe ft
L = length of pipe ft
K = proportionality coefficient (unitless) - obtained from rheology test
delta P = frictional loss psi
As I mentioned before it's been smooth sailing the handful of times I've used this forumula, however I ran into a bump in the road recently. The rheology data usually gives the apparent viscosity in a format such as: v = 100,000*y^-.0500 (just an example) which is common to express v in terms of the expected shear rate (probably not news to anyone reading this).
As Latexman pointed out, by definition the exponent above reflects n-1, so in the example above n = .95. The problem I recently encountered involves a negative value of n. From the rheology test v = 394,623*y^-1.0062. So I'm dealing with a Dilitant fluid now and not sure how to approach frictional loss calcs.
Any insight/advice is most appreciated.
I do have reason to believe that the lab may have possibly made an error on the analysis, but I'm going to assume for now that they have it right.
I've been using the following formula:
delta P = [(3 * n + 1 / n)^n * (Q / pi * r^3)^n * (2 * L * K / r)] / 144
where:
n = flow index (unitless) - obtained from rheology test
Q = flow rate ft^3/s
r = radius of pipe ft
L = length of pipe ft
K = proportionality coefficient (unitless) - obtained from rheology test
delta P = frictional loss psi
As I mentioned before it's been smooth sailing the handful of times I've used this forumula, however I ran into a bump in the road recently. The rheology data usually gives the apparent viscosity in a format such as: v = 100,000*y^-.0500 (just an example) which is common to express v in terms of the expected shear rate (probably not news to anyone reading this).
As Latexman pointed out, by definition the exponent above reflects n-1, so in the example above n = .95. The problem I recently encountered involves a negative value of n. From the rheology test v = 394,623*y^-1.0062. So I'm dealing with a Dilitant fluid now and not sure how to approach frictional loss calcs.
Any insight/advice is most appreciated.
I do have reason to believe that the lab may have possibly made an error on the analysis, but I'm going to assume for now that they have it right.