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Pipe Pressure Loss Calculation Methods

Principal Equaltions

Two principal equations used in computing pressure loss in pipes are:

Darcy-Weisbach Equation

Where l is pipe length, d is pipe diameter, v is average fluid velocity, λ is friction factor and h is amount of pressure loss.

Most pressure loss calculation methods are means to find λ which will then be used in Darcy equation to calculate pressure loss.

Reinolds Number

Where V is average fluid velocity, d is pipe diameter, ν is fluid viscosity.

Reinolds Number indicates amount of fluid turbulency, it is used in many pressure loss calculation methods as input parameter.

Pressure Loss Calculation Methods

Equation for Laminar Flow

Only for laminar flow (Re<2300).

Konakov Equation

Only for smooth pipes and when reinolds number is between 2300 and 10⁶.

Blasius Equation

Only for smooth pipes and when reinolds number is between 2300 and 10⁵.

Hermann Equation

Only for smooth pipes and when reinolds number is between 2x10⁴ and 2x10⁶.

Prandtle Equation

Only for smooth pipes and when reinolds number is between 2300 and 4x10⁶.

Nikoradze Equation

Only for smooth pipes and when reinolds number is between 10⁴ and 10⁸.

Altshul Equation

Where k is absolute roughness (height of bumps on inside pipe surface) and d is pipe diameter.

Colebrook Equation

Karman Equation

Karman Equation 2

Austrian Engineers Society Equation

Where V is average floid velocity, s is pressure loss per pipe length unit (Hydraulic Dip) and n is obtained from table below:

Where k is in meters.

Chezy Equation

Where V is velocity in feet R is hydraulic radius in feet which is d/4 for pipes with circle profile and C equation's coefficient which can be obtained from table below:

Pipe Type	C coefficient
Very Smooth Pipe	140
Smooth and New Cast-Iron Pipe	130
Average Cast-Iron Pipe, New Steel Pipe, Sewerage Pipe	110
Old Cast-Iron Pipe	100
Very Old Cast-Iron Pipe	80

Hazen-Williams Equation

Where V is velocity in feet per second R is hydraulic radius in feet and C equation's coefficient obtained from table below:

Nominal Diameter in Inches	Actual Diameter in Inches	Velocity in feet per second
Nominal Diameter in Inches	Actual Diameter in Inches	1	2	3	4	5	6	8	10	15	20
3/4	0.824	77	81	84	86	87	88	90	92	94	96
1	1.048	79	84	86	88	89	90	92	94	97	99
1 1/4	1.380	81	85	88	90	91	93	94	96	99	101
1 1/2	1.61	82	87	89	90	93	94	96	97	101	103
2	2.0	84	88	90	93	94	95	98	99	103	105
2 1/2	2.5	85	89	92	94	96	97	100	101	104	106
3	3	87	90	94	96	98	99	101	103	106	108
4	4	95	101	104	106	107	108	111	114	116	120
5	5	97	103	106	107	110	111	114	115	118	121
6	6	99	104	107	110	111	114	115	116	121	123
8	8	101	106	110	112	114	115	118	120	123	127
10	10	103	108	112	114	116	118	120	121	125	129
12	12	105	110	114	116	118	120	121	123	127	131
15	15	106	112	115	118	120	121	123	125	129	134
18	18	108	114	116	120	121	123	125	127	131	136
20	20	110	115	118	121	123	125	127	129	134	136
24	24	111	116	120	123	125	127	129	131	136	138
30	30	114	118	121	125	127	129	131	134	138	141
36	36	115	120	123	127	129	131	134	136	141	144
42	42	116	121	125	129	131	134	136	138	141	144
48	48	118	123	127	129	131	134	136	138	144	147
60	60	120	125	129	131	134	136	138	141	147	150
72	72	121	127	131	134	136	138	141	144	147	150
84	84	123	129	134	136	138	141	144	147	150	153
96	96	125	131	136	138	141	144	147	147	153	157

Colebrook's Main Equation

Plotted version of this equation is called Moody diagram which is a very popular method for computing pressure loss.

Swamee-Jain Equation

This equation actually estimates Colebrook's equation above with 2-5% error.

General Table 1

This table gives friction factor for certain pipe diameter and fluid velocity. Any value obtained from the table should be multiplied by 10^-4.

Nominal Diameter in Inches	Actual Diameter in Inches	Velocity in Feet per Second
Nominal Diameter in Inches	Actual Diameter in Inches	1	2	3	4	5	6	8	10	15	20
3/4	0.824	430	390	365	350	340	330	320	305	290	280
1	1.048	415	370	350	335	325	315	305	295	275	265
1 1/4	1.38	395	355	335	320	310	300	290	280	265	255
1 1/2	1.61	385	345	325	315	300	295	280	275	255	245
2	2	370	334	315	300	290	285	270	265	245	235
2 1/2	2.5	355	325	305	290	280	275	260	255	240	230
3	3	345	315	295	280	270	265	255	245	230	220
4	4	285	255	240	230	225	220	210	200	190	180
5	5	275	245	230	225	215	210	200	195	185	175
6	6	265	240	225	215	210	200	195	190	175	170
8	8	255	230	215	205	200	195	185	180	170	160
10	10	245	220	205	200	190	185	180	175	165	155
12	12	235	215	200	190	185	180	175	170	160	150
14	14	233	210	197	188	183	178	170	165	155	148
16	16	228	205	194	185	180	175	167	162	152	145
18	18	220	200	190	180	175	170	165	160	150	140
20	20	215	195	185	175	170	165	160	155	145	140
24	24	210	190	180	170	165	160	155	150	140	135
30	30	200	185	175	165	160	155	150	145	135	130
36	36	195	180	170	160	155	150	145	140	130	125
42	42	190	175	165	155	150	145	140	135	130	125
48	48	185	170	160	155	150	145	140	135	125	120
60	60	180	165	155	150	145	140	135	130	120	115
72	72	175	160	150	145	140	135	130	125	120	115
84	84	170	155	145	140	135	130	125	120	115	110
96	96	165	150	140	135	130	125	120	120	110	105

General Table 2

This table gives friction factor for a certain pipe type, pipe diameter and fluid velocity. Any value obtained from the table should be multiplied by 10^-4.

Pipe Diameter in Inches	Pipe Type	Velocity in Feet per Second
Pipe Diameter in Inches	Pipe Type	1	2	3	4	5	6	8	10	15	20	30
4	old	435	415	410	405	400	395	395	390	385	375	370
	average	355	320	310	300	290	285	280	270	260	250	250
	new	300	265	250	240	230	225	220	210	200	190	185
	very smooth	240	205	190	180	170	165	155	150	140	130	120
6	old	425	410	405	400	395	395	390	385	380	375	365
	average	335	310	300	285	280	275	265	260	250	240	235
	new	275	250	240	225	220	210	205	200	190	180	175
	very smooth	220	190	175	165	160	150	145	140	130	120	115
8	old	420	405	400	395	390	385	380	375	370	365	360
	average	320	300	285	280	270	265	260	250	240	235	225
	new	265	240	225	220	210	205	200	190	185	175	170
	very smooth	205	180	165	155	150	140	135	130	120	115	110
10	old	415	405	400	395	390	385	380	375	370	365	360
	average	315	295	280	270	265	260	255	245	240	230	225
	new	260	230	220	210	205	200	190	185	180	170	165
	very smooth	200	170	160	150	145	135	130	125	115	110	105
12	old	415	400	395	395	390	385	380	375	365	360	355
	average	310	285	275	265	260	255	250	240	235	225	220
	new	250	225	210	205	200	195	190	180	175	165	160
	very smooth	190	165	150	140	140	135	125	120	115	110	105
16	old	405	395	390	385	380	375	370	365	360	350	350
	average	300	280	265	260	255	250	240	235	225	215	210
	new	240	220	205	200	195	190	180	175	170	160	155
	very smooth	180	155	140	135	130	125	120	115	110	105	100
20	old	400	395	390	385	380	375	370	365	360	350	350
	average	290	275	265	255	250	245	235	230	220	215	205
	new	230	210	200	195	190	180	175	170	165	160	150
	very smooth	170	150	135	130	125	120	115	110	105	100	95
24	old	400	395	385	380	375	370	365	360	355	350	345
	average	285	265	255	250	245	240	230	225	220	210	200
	new	225	200	195	190	185	180	175	170	165	155	150
	very smooth	165	140	135	125	120	120	115	110	105	100	95
30	old	400	385	380	375	370	365	360	355	350	350	345
	average	280	255	250	245	240	230	225	220	210	205	200
	new	220	195	190	185	180	175	170	165	160	155	150
	very smooth	160	135	130	120	115	115	110	110	105	100	95
36	old	395	385	375	370	365	360	355	355	350	345	340
	average	275	255	245	240	235	230	225	220	210	200	195
	new	215	195	185	180	175	170	165	160	155	150	145
	very smooth	150	135	125	120	115	110	110	105	100	95	90
48	old	395	385	370	365	360	355	350	350	345	340	335
	average	265	250	240	230	225	220	215	210	200	195	190
	new	205	190	180	175	170	165	160	155	150	145	140
	very smooth	140	125	120	115	110	110	105	100	95	90	90

German Engineers Society Tables

This table directly gives pressure loss in meters of H20 for a certain pipe type, pipe diameter and flow.

Flow in litres per second	Diameter in millimeters
Flow in litres per second	40	50	70	80	100	125	150	200	250	300
1	33.5	10.8	1.78	0.93	0.32
1.5	75	22.4	3.8	1.96	0.66	0.22	0.09
2	130	38.5	6.5	3.3	1.12	0.37	0.15
3	282	83.5	14	7.05	2.35	0.77	0.31	0.074
4		145	24.1	12.1	3.98	1.31	0.52	0.123	0.042
5		221	37	18.5	6.05	1.96	0.78	0.185	0.062
6		312	52.5	26	8.58	2.74	1.09	0.255	0.087	0.033
7			70.1	34.9	11.5	3.6	1.45	0.339	0.114	0.044
8			91.5	45.2	14.7	4.65	1.84	0.43	0.145	0.056
9			114	56.5	18.3	5.75	2.29	0.53	0.178	0.07
10			140	69.5	22.3	7	2.79	0.65	0.218	0.085
15				151	49	15.3	5.95	1.36	0.45	0.178
20					84	26.3	10.3	2.32	0.76	0.302
30						57	22	5	1.6	0.64
40						98	37.5	8.65	2.75	1.09
50							57	13.3	4.21	1.65
60							80	18.8	5.95	2.34
70								25.3	8.05	3.12

Flow in litres per second	Diameter in millimeters
Flow in litres per second	400	500	600	700	800	900	1000	1100	1200
10	0.021
15	0.044
20	0.075	0.025
30	0.157	0.052	0.02
40	0.265	0.088	0.035	0.017
50	0.405	0.132	0.052	0.026	0.014
60	0.565	0.184	0.074	0.036	0.018	0.011
70	0.755	0.245	0.098	0.047	0.025	0.014

Flow in litres per second	Diameter in millimeters
Flow in litres per second	40	50	70	80	100	125	150	200	250	300
80								32.9	10.3	4.05
90								41.2	13	5.05
100								50.5	15.9	6.2
150									34.1	13.65
200										23.5
300

Flow in litres per second	Diameter in millimeters
Flow in litres per second	400	500	600	700	800	900	1000	1100	1200
80	0.97	0.314	0.125	0.06	0.031	0.018	0.011
90	1.32	0.39	0.156	0.074	0.039	0.022	0.013
100	1.49	0.48	0.19	0.09	0.047	0.027	0.016	0.01
150	3.22	1.02	0.405	0.192	0.099	0.056	0.034	0.021	0.014
200	5.55	1.75	0.695	0.325	0.17	0.094	0.056	0.035	0.023
300	12.1	3.8	1.5	0.7	0.363	0.199	0.12	0.073	0.048
400	20.9	6.6	2.6	1.2	0.62	0.339	0.202	0.124	0.082
500		10.2	3.95	1.85	0.94	0.515	0.31	0.19	0.123
600		14.4	5.6	2.6	1.32	0.725	0.437	0.265	0.174
700		19	7.55	3.5	1.77	0.975	0.582	0.355	0.231
800			9.7	4.49	2.29	1.25	0.75	0.452	0.295
900			12.2	5.6	2.85	1.58	0.94	0.57	0.37
1000			14.8	8.85	3.52	1.94	1.15	0.695	0.455
1500				14.8	7.7	4.23	2.5	1.51	0.99
2000						7.4	4.3	2.6	1.71
3000							9.4	5.7	3.7
4000									6.35

Flow in litres per second	Diameter in millimeters
Flow in litres per second	40	50	70	80	100	125	150	200	250	300
1	33	10	1.8	0.9	0.3	0.94
1.5	74	22	3.8	1.9	0.63	0.205	0.78
2	125	39	6.5	3.25	1.08	0.36	0.138
3	275	83	14.5	7.3	2.32	0.75	0.295	0.076
4	475	150	25	12.8	4	1.3	0.51	0.128	0.039
5		230	39	19.8	6.2	2	0.79	0.192	0.06
6		320	56	28.3	9	2.8	1.12	0.271	0.086	0.034
7			76	38.5	12	3.8	1.5	0.365	0.115	0.046
8			100	49.5	15.5	4.95	1.95	0.46	0.147	0.059
9			125	62	19.6	6.2	2.45	0.58	0.183	0.074
10				77	24.5	7.7	2.95	0.7	0.224	0.091
15				175	54	16.8	6.45	1.52	0.48	0.196
20					95	29.6	11.2	2.6	0.845	0.34
30						65	25	5.8	1.85	0.73
40							44	10.2	3.2	1.28
50							68	16	4.95	1.95
60								22.7	7	2.78
70								30.3	9.4	3.7

Flow in litres per second	Diameter in millimeters
Flow in litres per second	400	500	600	700	800	900	1000	1100	1200
10	0.021
15	0.045
20	0.078	0.025
30	0.168	0.055	0.022
40	0.285	0.098	0.037	0.018
50	0.435	0.145	0.057	0.027	0.014	0.027	0.014
60	0.61	0.205	0.081	0.038	0.0195	0.011
70	0.83	0.275	0.108	0.051	0.026	0.0145

Flow in litres per second	Diameter in millimeters
Flow in litres per second	40	50	70	80	100	125	150	200	250	300
80								39	12.2	4.8
90									15.3	6
100									19	7.4
150									42.5	16.5
200										29
300										65

Flow in litres per second	Diameter in millimeters
Flow in litres per second	400	500	600	700	800	900	1000	1100	1200
80	1.07	0.36	0.14	0.064	0.033	0.0185	0.0108
90	1.35	0.45	0.17	0.08	0.041	0.023	0.0135
100	1.65	0.55	0.21	0.097	0.05	0.028	0.0165	0.012
150	3.7	1.2	0.46	0.215	0.108	0.06	0.036	0.022	0.0145
200	6.5	2.6	0.8	0.37	0.185	0.103	0.061	0.038	0.025
300	14.5	4.55	1.76	0.81	0.41	0.23	0.132	0.083	0.054
400	25	8	3.1	1.42	0.72	0.4	0.23	0.145	0.094
500		12.5	4.8	2.2	1.1	0.61	0.355	0.22	0.145
600		18	6.8	3.2	1.55	0.87	0.51	0.31	0.205
700		24.5	9.2	4.25	2.1	1.17	0.69	0.42	0.275
800			12	5.5	2.68	1.5	0.9	0.55	0.355
900			15.4	8	3.4	1.9	1.12	0.7	0.45
1000			19	8.6	4.2	2.31	1.37	0.85	0.55
1500				18.5	9.5	5.1	3	1.85	1.2
2000						9	5.4	3.2	2.08
3000								7	4.55
4000									7.9