Formulae Related to Ponding

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Equivalent Feet of Pipe (Pipe Fittings)

• A fitting or valve generates more friction than straight pipe. This friction is often expressed as the length of straight pipe which will generate the equivalent friction loss. Thus all the friction losses in a pipe system can be added to determine the total friction loss for the system.
  
  
• One can calculate the effect of a fitting by means of the following formula:
  Length = 2.75 * CF * D
  where
  Length = equivalent length of pipe for the fitting or valve
  CF = coefficient of friction for the pipe fitting
  D = inside diameter of the fitting in inches
  
  
  Assumptions:
  The pipe system is full of water.
  The inner surface of the pipe is clean.
  The water is as clear as tap water.
  
  
• The following table lists the equivalent feet of pipe for PVC fittings of a certain diameter:
  

  PVC Fitting	0.50 " Pipe	1.00 " Pipe	1.50 " Pipe	2.00 " Pipe	2.50 " Pipe	3.00 " Pipe	4.00 " Pipe	6.00 " Pipe	8.00 " Pipe
  90-deg Long Radius Elbow	1.0	1.7	2.7	4.3	5.1	6.3	8.3	12.5	16.5
  90-deg Standard Elbow	1.6	2.6	4.0	5.5	6.2	7.7	10.1	15.2	20.0
  90-deg Street Elbow	2.6	4.4	6.7	8.6	10.3	12.8	16.8	25.3	33.3
  Square Corner Elbow	3.0	5.0	7.6	9.8	11.7	14.6	19.1	28.8	37.9
  45-deg Standard Elbow	0.8	1.4	2.1	2.8	3.3	4.1	5.4	8.1	10.6
  45-deg Street Elbow	1.3	2.3	3.5	4.5	5.4	6.6	8.7	13.1	17.3
  Stnd T Flow Through Run	1.0	1.7	2.7	4.3	5.1	6.3	8.3	12.5	16.5
  Stnd T Flow Through Branch	4.0	6.0	8.1	12.0	14.3	16.3	22.1	32.2	39.9
  Insert Coupling (CF = 0.3636)	0.5	1.0	1.5	2.0	2.5	3.0	4.0	6.0	8.0
  Male-Female Adapter (CF = 0.8181)	1.1	2.2	3.4	4.5	5.6	6.7	9.0	13.5	18.0

  
  
• The following table lists the equivalent feet of pipe for PVC valves of a certain diameter:
  

  PVC Valve	0.50 " Pipe	1.00 " Pipe	1.50 " Pipe	2.00 " Pipe	2.50 " Pipe	3.00 " Pipe	4.00 " Pipe	6.00 " Pipe	8.00 " Pipe
  Angle Valve, Fully Open	7.8	13.1	20.1	25.8	30.9	38.4	50.3	75.8	99.8
  Butterfly Valve, Fully Open				7.8	9.3	11.5	15.1	22.7	29.9
  Check Valve, (Swing) Fully Open	5.2	8.7	13.4	17.2	20.6	25.5	33.6	50.5	66.6
  Gate Valve, Fully Open (FO)	0.4	0.7	1.1	1.4	1.6	2.0	2.7	4.0	5.3
  Gate Valve, 3/4ths Open (2.7 * FO)	1.1	1.9	2.9	3.7	4.4	5.5	7.2	10.9	14.4
  Gate Valve, Half Open (12.3 * FO)	5.0	8.6	13.2	17.0	20.3	25.1	33.0	49.7	65.4
  Gate Valve, 1/4th Open (69.2 * FO)	28.4	48.4	74.0	95.5	114.2	141.2	185.4	279.6	368.1
  Globe Valve, Fully Open	17.6	29.7	45.6	58.6	70.0	86.9	114.0	172.0	226.0

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Friction Head Loss (Feet)

• Source of data: engineering specs
  
  
• Note: It is best to keep your friction loss (per 100 feet of pipe) to less than 5 feet.
  
  
• Friction head loss (in feet) for water flowing through 100 feet of Schedule 40 PVC pipe of various diameters:

  US GPH	US GPM	0.50" Pipe	1.00" Pipe	1.50" Pipe	2.00" Pipe	2.50" Pipe	3.00" Pipe	4.00" Pipe	6.00" Pipe
  60	1	1.16
  300	5	22.88	1.69	0.22
  600	10	82.59	6.08	0.73	0.21	0.09	0.03
  900	15	175.01	12.89	1.55	0.45	0.19	0.07
  1200	20	-	21.96	2.64	0.77	0.33	0.11	0.03
  1500	25	-	33.20	4.00	1.17	0.49	0.17	0.04
  1800	30	-	46.54	5.60	1.64	0.69	0.24	0.06
  2100	35	-	61.91	7.45	2.18	0.92	0.32	0.08
  2400	40	-	79.28	9.54	2.79	1.18	0.41	0.11
  2700	45	-	-	11.87	3.47	1.46	0.51	0.13
  3000	50	-	-	14.43	4.22	1.78	0.61	0.16
  3600	60	-	-	20.22	5.92	2.49	0.86	0.23
  4200	70	-	-	26.90	7.87	3.32	1.15	0.30
  4500	75	-	-	30.57	8.94	3.77	1.30	0.34
  4800	80	-	-	34.45	10.08	4.25	1.47	0.39
  5400	90	-	-	42.85	12.53	5.28	1.82	0.48	0.07
  6000	100	-	-	52.08	15.23	6.42	2.22	0.59	0.08
  7500	125	-	-	-	23.03	9.70	3.35	0.89	0.12
  US GPH	US GPM	0.50" Pipe	1.00" Pipe	1.50" Pipe	2.00" Pipe	2.50" Pipe	3.00" Pipe	4.00" Pipe	6.00" Pipe

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Straight Pipe Flow

• Source of the formula: mort@mauimail.com
  
  
• Characteristics of water in pipe
  • Flow resistance is due to the surface roughtness of the pipe and turbulance
  • Turbulance is related to the pipe diameter and the velocity of flow
  • Water flow can be APPROXIMATED by Chezy's formula
  • If the formula calculates a flow of 1000 GPH, the real-world flow will probably be between 900 and 1100 GPH.
  
  
• Chezy formula for velocity of water flowing through a straight pipe:
  Vel = C * ( ( R * S ) ^ 1/2 )
  where
  Vel = velocity of the water in feet per second
  C = constant of roughness = 140 (or 150) for 2-6 inch PVC pipe
  R = hydraulic radius = cross sectional area / wetted perimeter
  S = hydraulic slope = head of water / length of pipe
  
  
• Chezy's C coefficient of roughness
  • Is only good to two digits
  • Depends on the diameter and type of pipe
  • Also depends on the velocity of flow
  
  
• Calculation of hydraulic radius for round pipe
  A = cross sectional area of pipe in feet
  P = wetted perimeter of pipe in feet
  D = diameter of pipe in feet A = 1/4 * PI * ( D ^ 2 )
  P = PI * D
  R = ( 1/4 * PI * ( D ^ 2 ) ) / ( PI * D )
  R = D / 4 = diameter / 4
  
  
• Therefore, the velocity of water in feet per second is as follows:
  Vel = C * ( ( ( D / 4 ) * ( H / L ) ) ^ 1/2 )
  
  
• The actual discharge volume is calculated by multiplying the speed of the flowing water by the area of the pipe. Again, the area of the round pipe is ( PI / 4 ) * ( D^2 ). The formula for volume in cubic feet per second is as follows:
  Vol = Vel * ( ( PI / 4 ) * ( D ^ 2 ) )
  Vol = C * ( ( PI / 4 ) * ( D ^ 2 ) ) * ( ( ( D / 4 ) * ( H / L ) ) ^ 1/2 )
  
  
• To determine the volume in other units, perform the desired operation listed below:
  • Convert CFS into GPM:
    Vol in GPM = [ Vol in CFS ] * 448.831
    
    
  • Convert CFS into GPH:
    Vol in GPH = [ Vol is CFS ] * 26929.86
  
  
• Sample Calculation
  • The system uses 3-inch inside diameter pipe. The total length of pipe is 20 feet, and the head is 5 feet. There are no fittings.
    
    
  • Calculation of water velocity
    Vel in FPS = C * ( ( ( D / 4 ) * ( H / L ) ) ^ 1/2 )
    Vel in FPS = 140 * ( ( ( 0.25 / 4 ) * ( 5.0 / 20 ) ) ^ 1/2 )
    Vel in FPS = 140 * ( ( ( 0.25 / 4 ) * ( 0.25 ) ) ^ 1/2 )
    Vel in FPS = 140 * ( ( ( 0.25 * 0.25 ) / ( 2 * 2 ) ) ^ 1/2 )
    Vel in FPS = 140 * ( 0.25 / 2 )
    Vel in FPS = 17.5 feet per second
    
    
  • Calculation of water volume
    Vol in CFS = Vel * ( ( PI / 4 ) * ( D ^ 2 ) )
    Vol in CFS = 17.5 * ( 3.14159 / 4 ) * ( 0.25 ^ 2 ) )
    Vol in CFS = 17.5 * 0.7854 * 0.0625
    Vol in CFS = 0.8590 CFS
    Vol in GPM = 0.8590 * 448.831 = 385.6 GPM
    Vol in GPH = 0.8590 * 26929.86 = 23,133 GPH
  
  
• You now have the information for straight pipe ONLY -- connections, valves, and tees have NOT been considered at this point.

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Velocity of Water in a Pipe (Feet per Second)

• Source of data: engineering specs
  
  
• Here are some sample velocities for water flowing through Schedule 40 PVC pipe of various diameters:

  US GPH	US GPM	0.50" Pipe	1.00" Pipe	1.50" Pipe	2.00" Pipe	2.50" Pipe	3.00" Pipe	4.00" Pipe	6.00" Pipe
  60	1	1.13
  300	5	5.64	1.93
  600	10	11.27	3.86	1.62
  900	15	16.91	5.79	2.42	1.46	1.02	0.66	0.38
  1200	20	-	7.72	3.32	1.95	1.37	0.88	0.51
  1500	25	-	9.64	4.04	2.44	1.71	1.10	0.64
  1800	30	-	11.57	4.85	2.92	2.05	1.32	0.76
  2100	35	-	13.50	5.65	3.41	2.39	1.54	0.90
  2400	40	-	15.43	6.46	3.90	2.73	1.77	1.02
  2700	45	-	-	7.27	4.39	3.07	1.99	1.15
  3000	50	-	-	8.08	4.87	3.42	2.21	1.28
  3600	60	-	-	9.69	5.85	4.10	2.65	1.53
  4200	70	-	-	11.31	6.82	4.78	3.09	1.79
  4500	75	-	-	12.12	7.31	5.12	3.31	1.92
  4800	80	-	-	12.93	7.80	5.47	3.53	2.04
  5400	90	-	-	14.54	8.77	6.15	3.97	2.30	1.01
  6000	100	-	-	16.16	9.75	6.83	4.41	2.56	1.12
  US GPH	US GPM	0.50" Pipe	1.00" Pipe	1.50" Pipe	2.00" Pipe	2.50" Pipe	3.00" Pipe	4.00" Pipe	6.00" Pipe

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