Exercise 2 Pressure loss in Laminar Flow
a. The velocity of a fluid flowing through a 5" 19.5 lb/ft drillpipe (I. D. = 4.276") at 150 gpm is:
v = Q (gpm) ft/sec.
2.448 x d2
|
3.35 ft/sec. |
150
2.448 x 4.2762
b. If the fluid in the above situation is a Bingham Plastic fluid with a plastic viscosity of 20 cp, a yield point of 15 lb/100 sq. ft and density is 10 ppg the pressure loss in the pipe will be:
|
У |
dP = iy T dL 1,500d2 + 225d
|
15 |
|
dp dl |
20 x 3.35 +
1500 x 4.2762 225 x 4.276
= 0.018 psi/ft = 18 psi per 1000 ft
c. The pressure loss in the above situation if the fluid was a Power Law fluid with an non-Newtonian Index of 0.75 and a consistency index of 70 eq cp would be:
|
kv |
|
dP |
Г 1 Л» 3+Vn
|
0.0416 |
dL 144,000d(1+n)
|
3 + 1/0.75 0.0416 |
dp = 70 x 3.35
dl 144000 x 4.276(175)
= 0.0042 psi/ft
= 4.2 psi per 1000 ft