Old Lesson 17B*
Due Oct. 9, 2002
*
Pressure Drop in the Bit Nozzles
Pressure Drop in the Annulus
Wellbore Pressure Profiles
*
LOG
(SHEAR
STRESS)
(psi)
for Oil-Well Drilling Fluids
API RP 13D recommends using only FOUR of the six usual viscometer readings:
Use 3, 100, 300, 600 RPM Readings.
The 3 and 100 RPM reading are used for pressure drop calculations in the annulus, where shear rates are, generally, not very high.
*
Example: Pressure Drop Calculations
Example Calculate the pump pressure in the wellbore shown on the next page, using the API method.
The relevant rotational viscometer readings are as follows:
R3 = 3 (at 3 RPM)
R100 = 20 (at 100 RPM)
R300 = 39 (at 300 RPM)
R600 = 65 (at 600 RPM)
*
Fluid Consistency Index (K):
L = 11,400 ft
OD = 4.5 in ID = 3.78 in
L = 11,400 ft
OD = 4.5 in ID = 3.78 in
L = 11,400 ft
OD = 4.5 in ID = 3.78 in
L = 11,400 ft
DPdp = 665 psi
Fluid Consistency Index (K):
OD = 6.5 in ID = 2.5 in
L = 600 ft
OD = 6.5 in ID = 2.5 in
L = 600 ft
*
L = 600 ft
NOTE: NRe > 2,100, so
So,
L = 600 ft
DPdc = 227 psi
Pressure Drop across Nozzles
DN1 = 11 32nds (in) DN2 = 11 32nds (in) DN3 = 12 32nds (in)
DPNozzles = 1,026 psi
DHOLE = 8.5 in
ODDC = 6.5 in
L = 600 ft
DHOLE = 8.5 in
ODDC = 6.5 in
L = 600 ft
DPdc/hole = 31.6 psi
Pressure Drop
Pressure Drop
DPdp/hole = 153.2 psi
+ DPDC/ANN + DPDP/ANN + DPHYD
*
DPHYD = 0
DPANN = DPDC/ANN + DPDP/ANN
= 32 + 153 = 185
2,103 psi
P = 0
Procedures (simplified)
Water Depth
Kick Intensity
0
2,727
At this point the actual (dynamic) BHP is equal to the pore pressure.
New Pore Pressure
Kick Intensity
227
psi
240
psi
13
psi
7,800
psi
1,026
psi
1,108
psi
82
psi
Slow down Rig Pump while increasig MLP Inlet Pressure by
0
psi
Mud Properties
Circulation Rate
32
psi
32
psi
0
psi
153
psi
153
psi
0
psi
23.7
min
5
24.3
min
130
24.3
min
6
230
Density
16
lb/gal
0
psi
11
This exceeds the pore pressure by the AFP (OWM) by
0
psi
8,848
psi
9,536
psi
688
psi
Follow Drillpipe Pressure Reduction Schedule while filling Drillstring with KWM.
Pipe/Hole Annulus - outer dia.
7,563
psi
8,156
psi
593
psi
8
HW
0
0
0
in
0
psi
0
psi
0
psi
DC
0
0
0
32nds
TOT. Drillstring
=
If Laminar
0
psi
7,410
psi
7,800
psi
24.3
2,052
24.3
2,237
7,410
psi
Time
Pressure
0
psi
Min
psi
dP/dL
185
psi
8,848
psi
Standpipe
7,563
psi
Time
Pressure
Time
BHP
0
psi
2,103
psi
Min
psi
Min
psi
11,400
ft
8,848
psi
9,011
psi
KWM at top of HW
24.3
0
24.3
0
24.3
0
24.3
0
7,563
psi
29.3
0
29.3
0
Calculations
0.0
0
0.0
0
2,727
psi
Standpipe
Depth
Time
Pressure
0
psi
ok
Difference =
0
psi
ok
0
psi
AFP =
0
psi
Difference =
0
psi
2,103
psi
1,438
psi
=
1,211
psi
153
psi
Time
Pressure
0
psi
Min
psi
=
=
=
2102.9670499035
psi
8847.5969525543
psi
9010.8178961575
psi
7563.1521751633
psi
0
psi
=
=
=
=
=
Shear Rate in Annulus
665.37
psi
31.60
psi
153.15
psi
2102.97
psi
100%
2,237
psi
153
psi
32
psi
1,108
psi
240
psi
2,237
psi
0
2,237
65
1,533
psi
11,400
1,533
1,293
psi
11,999
1,293
153
psi
12,600
153
0
psi
24,000
0
0
psi
0
0
8,003
psi
11,400
8,003
240
psid
8,424
psi
11,999
8,424
9,717
psig
8,003
psi
12,600
8,003
0
psi
24,000
0
9,536
psi
Standpipe
Pressure
8,156
psi
ft
psi
0
psi
2,237
psi
0
2,237
11,400
ft
9,536
psi
11,400
9,536
9,717
psi
11,999
9,717
8,156
psi
12,600
8,156
Calculations
Depth
2236.6841790976
psi
0
2236.6841790976
9535.6068525177
psi
11400
9535.6068525177
9716.9033212696
psi
11999
9716.9033212696
8155.9521751633
psi
12600
8155.9521751633
0
psi
24000
0
=
=
=
=
=
=
=
Shear Rate in Annulus
703.88
psi
31.60
psi
153.15
psi
2236.68
psi
100%
Distance from Standpipe, ft
Distance from Standpipe, ft
Circulating Time, min
Standpipe Pressure, psi
0
0
0
22.1526835574
24.3
22.1526835574
22.6626823648
28
22.6626823648
22.6626823648
22.6626823648
28
28
CONVENTIONAL
Circulating Time, min
Standpipe Pressure, psi
0
0
0
22.1526835574
22.1526835574
24.3
22.6626823648
22.6626823648
28
22.6626823648
22.6626823648
28
28
3519.5516618895
3519.5516618895
4009.0672966894
3087.2241233516
2987.6467847831
3626.8578178815
3113.5613571143
2978.2806676127
3626.8578178815
3207.7920747175
3072.5113852158
3207.7920747175
3072.5113852158
CONVENTIONAL
BHP = PP + AFP
Circulating Time, min
Standpipe Pressure, psi
4009.0672966894
4009.0672966894
3519.5516618895
3576.7397581515
3626.8578178815
2987.6467847831
3603.0769919142
3626.8578178815
2978.2806676127
3697.3077095174
3072.5113852158
3697.3077095174
3072.5113852158
Pressure Drop Calculations
14-Jun-99
Standpipe
8,736
psi
24.3
3,627
Density
14
lb/gal
Density
15
lb/gal
Density
15
lb/gal
22.2
min
22.7
min
22.7
min
Hole Size
3,520
psi
Standpipe
Time
Pressure
10,524
psi
11,233
psi
11,442
psi
8,710
psi
9,303
psi
9,448
psi
17/16 =
1.0625
0
psi
0
psi
0
psi
Constant BHP = New Pore Pressure
3,520
psi
Standpipe
Time
Pressure
Standpipe
Time
Pressure
Min
psi
0.0
4,009
22.2
3,577
22.7
3,603
22.7
3,697
28.0
3,697
3,627
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
CONVENTIONAL
Circulating Time, min
Standpipe Pressure, psi
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
CONVENTIONAL
BHP = PP + AFP
Circulating Time, min
Standpipe Pressure, psi
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7410
7800
7800
7410
0
Equations
Procedures (simplified)
Water Depth
Kick Intensity
0
2,727
At this point the actual (dynamic) BHP is equal to the pore pressure.
New Pore Pressure
Kick Intensity
227
psi
240
psi
13
psi
7,800
psi
1,026
psi
1,108
psi
82
psi
Slow down Rig Pump while increasig MLP Inlet Pressure by
0
psi
Mud Properties
Circulation Rate
32
psi
32
psi
0
psi
153
psi
153
psi
0
psi
23.7
min
5
24.3
min
130
24.3
min
6
230
Density
16
lb/gal
0
psi
11
This exceeds the pore pressure by the AFP (OWM) by
0
psi
8,848
psi
9,536
psi
688
psi
Follow Drillpipe Pressure Reduction Schedule while filling Drillstring with KWM.
Pipe/Hole Annulus - outer dia.
7,563
psi
8,156
psi
593
psi
8
HW
0
0
0
in
0
psi
0
psi
0
psi
DC
0
0
0
32nds
TOT. Drillstring
=
If Laminar
0
psi
7,410
psi
7,800
psi
24.3
2,052
24.3
2,237
7,410
psi
Time
Pressure
0
psi
Min
psi
dP/dL
185
psi
8,848
psi
Standpipe
7,563
psi
Time
Pressure
Time
BHP
0
psi
2,103
psi
Min
psi
Min
psi
11,400
ft
8,848
psi
9,011
psi
KWM at top of HW
24.3
0
24.3
0
24.3
0
24.3
0
7,563
psi
29.3
0
29.3
0
Calculations
0.0
0
0.0
0
2,727
psi
Standpipe
Depth
Time
Pressure
0
psi
ok
Difference =
0
psi
ok
0
psi
AFP =
0
psi
Difference =
0
psi
2,103
psi
1,438
psi
=
1,211
psi
153
psi
Time
Pressure
0
psi
Min
psi
=
=
=
2102.9670499035
psi
8847.5969525543
psi
9010.8178961575
psi
7563.1521751633
psi
0
psi
=
=
=
=
=
Shear Rate in Annulus
665.37
psi
31.60
psi
153.15
psi
2102.97
psi
100%
2,237
psi
153
psi
32
psi
1,108
psi
240
psi
2,237
psi
0
2,237
65
1,533
psi
11,400
1,533
1,293
psi
11,999
1,293
153
psi
12,600
153
0
psi
24,000
0
0
psi
0
0
8,003
psi
11,400
8,003
240
psid
8,424
psi
11,999
8,424
9,717
psig
8,003
psi
12,600
8,003
0
psi
24,000
0
9,536
psi
Standpipe
Pressure
8,156
psi
ft
psi
0
psi
2,237
psi
0
2,237
11,400
ft
9,536
psi
11,400
9,536
9,717
psi
11,999
9,717
8,156
psi
12,600
8,156
Calculations
Depth
2236.6841790976
psi
0
2236.6841790976
9535.6068525177
psi
11400
9535.6068525177
9716.9033212696
psi
11999
9716.9033212696
8155.9521751633
psi
12600
8155.9521751633
0
psi
24000
0
=
=
=
=
=
=
=
Shear Rate in Annulus
703.88
psi
31.60
psi
153.15
psi
2236.68
psi
100%
Distance from Standpipe, ft
Distance from Standpipe, ft
Circulating Time, min
Standpipe Pressure, psi
0
0
0
22.1526835574
24.3
22.1526835574
22.6626823648
28
22.6626823648
22.6626823648
22.6626823648
28
28
CONVENTIONAL
Circulating Time, min
Standpipe Pressure, psi
0
0
0
22.1526835574
22.1526835574
24.3
22.6626823648
22.6626823648
28
22.6626823648
22.6626823648
28
28
3519.5516618895
3519.5516618895
4009.0672966894
3087.2241233516
2987.6467847831
3626.8578178815
3113.5613571143
2978.2806676127
3626.8578178815
3207.7920747175
3072.5113852158
3207.7920747175
3072.5113852158
CONVENTIONAL
BHP = PP + AFP
Circulating Time, min
Standpipe Pressure, psi
4009.0672966894
4009.0672966894
3519.5516618895
3576.7397581515
3626.8578178815
2987.6467847831
3603.0769919142
3626.8578178815
2978.2806676127
3697.3077095174
3072.5113852158
3697.3077095174
3072.5113852158
Pressure Drop Calculations
14-Jun-99
Standpipe
8,736
psi
24.3
3,627
Density
14
lb/gal
Density
15
lb/gal
Density
15
lb/gal
22.2
min
22.7
min
22.7
min
Hole Size
3,520
psi
Standpipe
Time
Pressure
10,524
psi
11,233
psi
11,442
psi
8,710
psi
9,303
psi
9,448
psi
17/16 =
1.0625
0
psi
0
psi
0
psi
Constant BHP = New Pore Pressure
3,520
psi
Standpipe
Time
Pressure
Standpipe
Time
Pressure
Min
psi
0.0
4,009
22.2
3,577
22.7
3,603
22.7
3,697
28.0
3,697
3,627
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
CONVENTIONAL
Circulating Time, min
Standpipe Pressure, psi
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
CONVENTIONAL
BHP = PP + AFP
Circulating Time, min
Standpipe Pressure, psi
0
0
0
0
0
0
0
0
0
0
0
0
0
Procedures (simplified)
Water Depth
Kick Intensity
0
2,727
At this point the actual (dynamic) BHP is equal to the pore pressure.
New Pore Pressure
Kick Intensity
227
psi
240
psi
13
psi
7,800
psi
1,026
psi
1,108
psi
82
psi
Slow down Rig Pump while increasig MLP Inlet Pressure by
0
psi
Mud Properties
Circulation Rate
32
psi
32
psi
0
psi
153
psi
153
psi
0
psi
23.7
min
5
24.3
min
130
24.3
min
6
230
Density
16
lb/gal
0
psi
11
This exceeds the pore pressure by the AFP (OWM) by
0
psi
8,848
psi
9,536
psi
688
psi
Follow Drillpipe Pressure Reduction Schedule while filling Drillstring with KWM.
Pipe/Hole Annulus - outer dia.
7,563
psi
8,156
psi
593
psi
8
HW
0
0
0
in
0
psi
0
psi
0
psi
DC
0
0
0
32nds
TOT. Drillstring
=
If Laminar
0
psi
7,410
psi
7,800
psi
24.3
2,052
24.3
2,237
7,410
psi
Time
Pressure
0
psi
Min
psi
dP/dL
185
psi
8,848
psi
Standpipe
7,563
psi
Time
Pressure
Time
BHP
0
psi
2,103
psi
Min
psi
Min
psi
11,400
ft
8,848
psi
9,011
psi
KWM at top of HW
24.3
0
24.3
0
24.3
0
24.3
0
7,563
psi
29.3
0
29.3
0
Calculations
0.0
0
0.0
0
2,727
psi
Standpipe
Depth
Time
Pressure
0
psi
ok
Difference =
0
psi
ok
0
psi
AFP =
0
psi
Difference =
0
psi
2,103
psi
1,438
psi
=
1,211
psi
153
psi
Time
Pressure
0
psi
Min
psi
=
=
=
2102.9670499035
psi
8847.5969525543
psi
9010.8178961575
psi
7563.1521751633
psi
0
psi
=
=
=
=
=
Shear Rate in Annulus
665.37
psi
31.60
psi
153.15
psi
2102.97
psi
100%
2,237
psi
153
psi
32
psi
1,108
psi
240
psi
2,237
psi
0
2,237
65
1,533
psi
11,400
1,533
1,293
psi
11,999
1,293
153
psi
12,600
153
0
psi
24,000
0
0
psi
0
0
8,003
psi
11,400
8,003
240
psid
8,424
psi
11,999
8,424
9,717
psig
8,003
psi
12,600
8,003
0
psi
24,000
0
9,536
psi
Standpipe
Pressure
8,156
psi
ft
psi
0
psi
2,237
psi
0
2,237
11,400
ft
9,536
psi
11,400
9,536
9,717
psi
11,999
9,717
8,156
psi
12,600
8,156
Calculations
Depth
2236.6841790976
psi
0
2236.6841790976
9535.6068525177
psi
11400
9535.6068525177
9716.9033212696
psi
11999
9716.9033212696
8155.9521751633
psi
12600
8155.9521751633
0
psi
24000
0
=
=
=
=
=
=
=
Shear Rate in Annulus
703.88
psi
31.60
psi
153.15
psi
2236.68
psi
100%
Distance from Standpipe, ft
Distance from Standpipe, ft
Circulating Time, min
Standpipe Pressure, psi
0
0
0
22.1526835574
24.3
22.1526835574
22.6626823648
28
22.6626823648
22.6626823648
22.6626823648
28
28
CONVENTIONAL
Circulating Time, min
Standpipe Pressure, psi
0
0
0
22.1526835574
22.1526835574
24.3
22.6626823648
22.6626823648
28
22.6626823648
22.6626823648
28
28
3519.5516618895
3519.5516618895
4009.0672966894
3087.2241233516
2987.6467847831
3626.8578178815
3113.5613571143
2978.2806676127
3626.8578178815
3207.7920747175
3072.5113852158
3207.7920747175
3072.5113852158
CONVENTIONAL
BHP = PP + AFP
Circulating Time, min
Standpipe Pressure, psi
4009.0672966894
4009.0672966894
3519.5516618895
3576.7397581515
3626.8578178815
2987.6467847831
3603.0769919142
3626.8578178815
2978.2806676127
3697.3077095174
3072.5113852158
3697.3077095174
3072.5113852158
Pressure Drop Calculations
14-Jun-99
Standpipe
8,736
psi
24.3
3,627
Density
14
lb/gal
Density
15
lb/gal
Density
15
lb/gal
22.2
min
22.7
min
22.7
min
Hole Size
3,520
psi
Standpipe
Time
Pressure
10,524
psi
11,233
psi
11,442
psi
8,710
psi
9,303
psi
9,448
psi
17/16 =
1.0625
0
psi
0
psi
0
psi
Constant BHP = New Pore Pressure
3,520
psi
Standpipe
Time
Pressure
Standpipe
Time
Pressure
Min
psi
0.0
4,009
22.2
3,577
22.7
3,603
22.7
3,697
28.0
3,697
3,627
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
CONVENTIONAL
Circulating Time, min
Standpipe Pressure, psi
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
CONVENTIONAL
BHP = PP + AFP
Circulating Time, min
Standpipe Pressure, psi
0
0
0
0
0
0
0
0
0
0
0
0
0
Procedures (simplified)
Water Depth
Kick Intensity
0
2,727
At this point the actual (dynamic) BHP is equal to the pore pressure.
New Pore Pressure
Kick Intensity
227
psi
240
psi
13
psi
7,800
psi
1,026
psi
1,108
psi
82
psi
Slow down Rig Pump while increasig MLP Inlet Pressure by
0
psi
Mud Properties
Circulation Rate
32
psi
32
psi
0
psi
153
psi
153
psi
0
psi
23.7
min
5
24.3
min
130
24.3
min
6
230
Density
16
lb/gal
0
psi
11
This exceeds the pore pressure by the AFP (OWM) by
0
psi
8,848
psi
9,536
psi
688
psi
Follow Drillpipe Pressure Reduction Schedule while filling Drillstring with KWM.
Pipe/Hole Annulus - outer dia.
7,563
psi
8,156
psi
593
psi
8
HW
0
0
0
in
0
psi
0
psi
0
psi
DC
0
0
0
32nds
TOT. Drillstring
=
If Laminar
0
psi
7,410
psi
7,800
psi
24.3
2,052
24.3
2,237
7,410
psi
Time
Pressure
0
psi
Min
psi
dP/dL
185
psi
8,848
psi
Standpipe
7,563
psi
Time
Pressure
Time
BHP
0
psi
2,103
psi
Min
psi
Min
psi
11,400
ft
8,848
psi
9,011
psi
KWM at top of HW
24.3
0
24.3
0
24.3
0
24.3
0
7,563
psi
29.3
0
29.3
0
Calculations
0.0
0
0.0
0
2,727
psi
Standpipe
Depth
Time
Pressure
0
psi
ok
Difference =
0
psi
ok
0
psi
AFP =
0
psi
Difference =
0
psi
2,103
psi
1,438
psi
=
1,211
psi
153
psi
Time
Pressure
0
psi
Min
psi
=
=
=
2102.9670499035
psi
8847.5969525543
psi
9010.8178961575
psi
7563.1521751633
psi
0
psi
=
=
=
=
=
Shear Rate in Annulus
665.37
psi
31.60
psi
153.15
psi
2102.97
psi
100%
2,237
psi
153
psi
32
psi
1,108
psi
240
psi
2,237
psi
0
2,237
65
1,533
psi
11,400
1,533
1,293
psi
11,999
1,293
153
psi
12,600
153
0
psi
24,000
0
0
psi
0
0
8,003
psi
11,400
8,003
240
psid
8,424
psi
11,999
8,424
9,717
psig
8,003
psi
12,600
8,003
0
psi
24,000
0
9,536
psi
Standpipe
Pressure
8,156
psi
ft
psi
0
psi
2,237
psi
0
2,237
11,400
ft
9,536
psi
11,400
9,536
9,717
psi
11,999
9,717
8,156
psi
12,600
8,156
Calculations
Depth
2236.6841790976
psi
0
2236.6841790976
9535.6068525177
psi
11400
9535.6068525177
9716.9033212696
psi
11999
9716.9033212696
8155.9521751633
psi
12600
8155.9521751633
0
psi
24000
0
=
=
=
=
=
=
=
Shear Rate in Annulus
703.88
psi
31.60
psi
153.15
psi
2236.68
psi
100%
Distance from Standpipe, ft
Distance from Standpipe, ft
Circulating Time, min
Standpipe Pressure, psi
0
0
0
22.1526835574
24.3
22.1526835574
22.6626823648
28
22.6626823648
22.6626823648
22.6626823648
28
28
CONVENTIONAL
Circulating Time, min
Standpipe Pressure, psi
0
0
0
22.1526835574
22.1526835574
24.3
22.6626823648
22.6626823648
28
22.6626823648
22.6626823648
28
28
3519.5516618895
3519.5516618895
4009.0672966894
3087.2241233516
2987.6467847831
3626.8578178815
3113.5613571143
2978.2806676127
3626.8578178815
3207.7920747175
3072.5113852158
3207.7920747175
3072.5113852158
CONVENTIONAL
BHP = PP + AFP
Circulating Time, min
Standpipe Pressure, psi
4009.0672966894
4009.0672966894
3519.5516618895
3576.7397581515
3626.8578178815
2987.6467847831
3603.0769919142
3626.8578178815
2978.2806676127
3697.3077095174
3072.5113852158
3697.3077095174
3072.5113852158
Pressure Drop Calculations
14-Jun-99
Standpipe
8,736
psi
24.3
3,627
Density
14
lb/gal
Density
15
lb/gal
Density
15
lb/gal
22.2
min
22.7
min
22.7
min
Hole Size
3,520
psi
Standpipe
Time
Pressure
10,524
psi
11,233
psi
11,442
psi
8,710
psi
9,303
psi
9,448
psi
17/16 =
1.0625
0
psi
0
psi
0
psi
Constant BHP = New Pore Pressure
3,520
psi
Standpipe
Time
Pressure
Standpipe
Time
Pressure
Min
psi
0.0
4,009
22.2
3,577
22.7
3,603
22.7
3,697
28.0
3,697
3,627
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
CONVENTIONAL
Circulating Time, min
Standpipe Pressure, psi
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
CONVENTIONAL
BHP = PP + AFP
Circulating Time, min
Standpipe Pressure, psi
0
0
0
0
0
0
0
0
0
0
0
0
0
Pipe Flow - Laminar
In the above example the flow down the drillpipe was turbulent.
Under conditions of very high viscosity, the flow may very well be laminar.
NOTE: if NRe < 2,100, then
Friction Factor in Pipe (fp):
Then
and
Annular Flow - Turbulent
In the above example the flow up the annulus was laminar.
Under conditions of low viscosity and/or high flow rate, the flow may very well be turbulent.
NOTE: if NRe > 2,100, then Friction Factor in the Annulus:
Then
and
Example
The above fluid is flowing in the annulus between a 4.5” OD string of drill pipe and an 8.5 in hole.
The fluid density is 12.5 lb/gal.
What is the minimum circulation rate that will ensure turbulent flow?
(why is this of interest?)
*
280 2.197 1,044
300 2.354 1,154
350 2.746 1,446
400 3.138 1,756
450 3.531 2,086
452 3.546 2,099
452.1 3.547 2,100
Optimum Bit Hydraulics
Under what conditions do we get the best hydraulic cleaning at the bit?
maximum hydraulic horsepower?
maximum impact force?
Both these items increase when the circulation rate increases.
*
or,
*Note that a small change in the pipe diameter results in large change in the pressure drop! (q = const.)
Eq. 4.66e
Decreasing the pipe ID 10% from 5.0” to 4.5” would result in an
increase of frictional pressure drop by about 65% !!
*
737
0
1,000
2,000
3,000
4,000
5,000
6,000
7,000
8,000
9,000
05,00010,00015,00020,00025,000