# Calculation of Pipe Friction Loss

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1 Doc.No F3T071 rev.2 Calculation of Pipe Friction Loss Engineering Management Group Development Planning Department Standard Pump Business Division EBARA corporation October 16th, / 33

2 2 / Work flow of pipe calculation (1) Adding up actual straight length of piping (2) Count number of piping elements (pipe joints, valves and so on) (3) Convert these piping elements to equivalent length of straight pipe (4) Add the equivalent length of straight pipe to the actual straight length (5) Calculate pipe resistance by using calculation method or graphical method.

3 3 / Equivalent Length of Straight Pipe Example A Top View (There is no difference in height.) 90 elbow D: 50 1m 3m 2m gate valve 2m 90 elbow (1) Integrate of actual straight length of piping 2 m + 1 m + 3 m + 2 m = 8m

4 4 / Equivalent Length of Straight Pipe Example A Top View (There is no difference in height.) 90 elbow D: 50mm 1m 3m 2m gate valve 2m 90 elbow (2) Count the number of piping elements (pipe joints, valves and so on) 90 elbow 2 gate valve 1

5 5 / Equivalent Length of Straight Pipe + Piping element loss The table below shows the straight pipe equivalent length that produces the same friction loss caused by piping elements. Pipe dia. Pipe (mm) element 90º elbow unit : m º bend Globe valve Gate valve Check/ foot valve [ Hydraulic Institute ]

6 6 / Equivalent Length of Straight Pipe Example A Top View (There is no difference in height.) 90 elbow D: 50mm 1m 3m 2m gate valve 2m 90 elbow (3) Convert these piping elements to equivalent length of straight pipe 90 elbow 2 gate valve m x 2 = 1.8 m 0.8 m x 1 = 0.8 m 2.6 m

7 2. Equivalent Length of Straight Pipe Example A Top View (There is no difference in height.) 90 elbow D: 50mm 1m 3m 2m gate valve 2m 90 elbow (1) Integrate of actual straight length of piping 8m (3) equivalent length of straight pipe of piping elements 2.6 m Total straight pipe length 10.6 m 10.6m 7 / 33

8 8 / Equivalent Length of Straight Pipe Example B 1m 2m D: 50mm 90 elbow 1m 2m 90 elbow SideView Height 2.5m 2m 90 elbow Total straight pipe length ( ) + ( 0.9 x 4 ) = 11.6 m Height : 2.5m

9 (2) How to obtain the head loss 3. Head Loss for Straight Pipe ( Calculation Method) There are several methods to calculate the pipe friction loss. Among them, the following Darcy-Weisbach equation is commonly used. Hf = V = π 4 λ x L D Q Hf: Head loss (m) x x D 2 x 60 V 2 2 g (Darcy-Weisbach equation) = x L: Pipe length (m) D: Pipe inner diameter (m) V: Flow velocity in pipe (m/s) g: Gravity acceleration (9.8 m/s 2 ) Q: Flow rate (m 3 /min) λ: Loss coefficient (Value variable with fluid viscosity, flow velocity, and diameter/surface roughness of the pipe). The loss coefficient can be obtained using the following equation that assumes water in a new steel pipe. λ = x D Q D 2 9 / 33

10 Flow rate (l/min) 4. Head Loss for Straight Pipe ( Graphical Method) Head Loss for Steel Pipe The head loss for steel pipe are as shown in the graph on the right. This graph however, indicate the head loss per meter for new pipe, and therefore the result obtained must be translated into the length as desired. Taking into consideration an increase of friction loss caused by aging of the inner pipe wall, the obtained value is generally multiplied by 1.5. Head loss (mm/m) 10 / 33

11 11 / Head Loss Calculation + Example Solution Given information Pipe Size : 100mm Straight pipe Length: 80m Foot Valve : 1pcs 90º Elbow : 4pcs Check Valve : 1pcs Gate Valve : 1pcs Pipe : Steel Flow rate : 1.2m 3 /min To find the friction loss head Straight pipe length : Equivalent straight pipe length on piping elements : Foot Valve : 11.6 x 1 = º Elbow : 1.8 x 4 =7.2 Check Valve : 11.6 x 1 = 11.6 Gate Valve : 0.9 x 1 = m 31.3 m Equivalent total straight length: 111.3m

13 4. Head Loss Calculation + Calculation Method Dia.100 Steel Pipe : external dia. : 114.3mm thickness : 4.5mm -> internal dia. : 105.3mm λ = = x D 2000 x = Q V = x = D x = 2.29 m/sec Total friction head loss : Hf = λ x L D x V 2 2 g = x x x 9.8 = 7.0 m Total head = Ha + Hf = ( ) = 36.0 m Ha : Actual Head Hf : Friction Head Loss *) Velocity Head (V 2 /2g) is Neglected. If include, Total Head = 36.3 m 13 / 33

14 SPAIX Pipe Calculation 14 / 33

15 15 / Case Study (1) [ Calculation ] D: 50mm Height : 2.5m Pipe Size : 50mm Dia.50 Steel Pipe : Straight pipe Length: 11.6m external dia. : 60.5mm Flow rate : 0.3m 3 /min thickness : 3.8mm -> internal dia. : 52.9mm 1 1 λ = = = x D 2000 x Q 0.3 V = x = x = 2.27 m/sec D Total friction head loss : L V Hf = λ x 2 D x 2 g = x x 2 = 1.70 m x 9.8 Total head = Ha + Hf = = 4.20 m Ha : Actual Head Hf : Friction Head Loss *) Velocity Head (V 2 /2g) is Neglected. If include, Total Head = 4.46 m

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18 5. Case Study (1) [ by SPAIX ] 18 / 33

19 5. Case Study (1) [ by SPAIX ] 19 / 33

20 20 / Case Study (2) [ Calculation ] + Example Solution Given information Pipe Size : 100mm Straight pipe Length: 80m Foot Valve : 1pcs 90º Elbow : 4pcs Check Valve : 1pcs Gate Valve : 1pcs Pipe : Steel Flow rate : 1.2m 3 /min To find the friction loss head : Straight pipe length : 80m Equivalent straight pipe length on piping elements : 31.3 m Foot Valve : 11.6 x 1 = º Elbow : 1.8 x 4 =7.2 Check Valve : 11.6 x 1 = 11.6 Gate Valve : 0.9 x 1 = 0.9 Equivalent total straight length: 111.3m

21 6. Case Study (2) [ Calculation ] + Calculation Method Dia.100 Steel Pipe : external dia. : 114.3mm thickness : 4.5mm -> internal dia. : 105.3mm λ = = x D 2000 x = Q V = x = D x = 2.29 m/sec Total friction head loss : Hf = λ x L D x V 2 2 g = x x x 9.8 = 7.00 m Total head = Ha + Hf = ( ) = 36.0 m Ha : Actual Head Hf : Friction Head Loss *) Velocity Head (V 2 /2g) is Neglected. If include, Total Head = m 21 / 33

22 22 / Case Study (2) [ Calculation ] + Example Solution Given information Pipe Size : 100mm Straight pipe Length: 80m Foot Valve : 1pcs 90º Elbow : 4pcs Check Valve : 1pcs Gate Valve : 1pcs Pipe : Steel Flow rate : 1.2m 3 /min

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26 6. Case Study (2) [ by SPAIX ] 26 / 33

27 27 / Case Study (2) [ Calculation ] + Example Solution Given information Pipe Size : 100mm Straight pipe Length: 80m Foot Valve : 1pcs 90º Elbow : 4pcs Check Valve : 1pcs Gate Valve : 1pcs Pipe : Steel Flow rate : 1.2m 3 /min

28 6. Case Study (2) [ by SPAIX ] 28 / 33

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32 32 / Case Study (2) [ by SPAIX ] END

33 END 33 / 33

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