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1. Faculty of Engineering Department of Civil Engineering Water Supply Engineering Dr. Abdullah Azzam (Ph.D.) Assistant Professor & Head of the Departments (MSDS & MCEM) Email: [email protected] Contact No. [phone] April 6, 2025

2. 23 rd March 2025 Lecture No. 5 Basic Principles of Pipe Flow II

3. Form Resistance The form-resistance losses are due to bends, elbows, valves, enlargers, reducers, and so forth. Unevenness of inside pipe surface on account of imperfect workmanship also causes form loss. Thus, the name “minor loss” for form loss is a misnomer when applied to a pipe network. In a water supply network, form losses play a significant role. However, form losses are unimportant in water transmission lines like gravity mains or pumping mains that are long pipelines having no off-takes.

4. Pipe Bend In the case of pipe bend, kf depends on bend angle and bend radius R (Fig. 2.3). Expressing a in radians, Swamee (1990) gave the following equation for the form-loss coefficient: It should be noticed that Eq. (2.8) does not hold good for near zero bend radius. In such a case, Eq. (2.9) should be used for loss coefficient for elbows.

5. 2. Elbows Elbows are used for providing sharp turns in pipelines (Fig. 2.4). The loss coefficient for an elbow is given by Where, α = elbow angle in radians.

6. 3. Valves Valves are used for regulating the discharge by varying the head loss accrued by it. For a 20% open sluice valve, loss coefficient is as high as 31. Even for a fully open valve, there is a substantial head loss. Table 2.2 gives kf for fully open valves. The most commonly used valves in the water supply systems are the sluice valve and the rotary valve as shown in Fig. 2.5 and Fig. 2.6, respectively.

7. 3. Valves (Sluice Valve) For partly closed valves, Swamee (1990) gave the following loss coefficients:

8. 3. Valves (Rotary Valve) A partly closed rotary valve is shown in Fig. 2.6. The loss coefficients can be estimated using the following equation ( Swamee , 1990): where α = valve closure angle in radians. Partly or fully closed valves are not considered at the design stage, as these situations develop during the operation and maintenance of the water supply systems.

9. 4. Transitions

10. Gradual Contraction A gradual pipe contraction is shown in Fig. 2.7. The loss coefficient can be obtained using the following equation:

11. Gradual Expansion A gradual expansion is depicted in Fig. 2.8. The following relationship can be used for the estimation of loss coefficient:

12. Optimal Expansions Transition Based on minimizing the energy loss, Swamee et al. (2005) gave the following equation for optimal expansion transition in pipes and power tunnels as shown in Fig. 2.9: where x = distance from the transition inlet.

13. Abrupt Expansion & Abrupt Contraction The loss coefficient for abrupt expansion as shown in Fig. 2.10 is kf = 1 Swamee (1990) developed the following expression for the loss coefficient of an abrupt pipe contraction as shown in Fig. 2.11:

14. Pipe Junction Little information is available regarding the form loss at a pipe junction where many pipelines meet. The form loss at a pipe junction may be taken as where Vmax = maximum velocity in a pipe branch meeting at the junction. In the absence of any information, kf may be assumed as 0.5.

15. Pipe Entrance There is a form loss at the pipe entrance (Fig. 2.12). Swamee (1990) obtained the following equation for the form-loss coefficient at the pipe entrance: where R = radius of entrance transition. It should be noticed that for a sharp entrance, kf = 0.5

16. Pipe Outlet A form loss also generates at an outlet. For a confusor outlet (Fig. 2.13), Swamee (1990) found the following equation for the head-loss coefficient: where d = outlet diameter. Putting D/d = 1 in Eq. (2.17), for a pipe outlet, kf = 1.

17. Overall Form Loss

18. Example No. 2.2A A pumping system with different pipe fittings is shown in Fig. 2.15. Calculate residual pressure head at the end of the pipe outlet if the pump is generating an input head of 50 m at 0.1 m3/s discharge. The GI pipe diameter D is 0.4 m. The contraction size at point 3 is 0.2 m; pipe size between points 6 and 7 is 0.2 m; and Confusor outlet size d =0.2 m. The rotary valve at point 5 is fully open. Consider the following pipe lengths between points: Points 1 and 2 =150 m, points 2 and 3 =0.8 m; and points 3 and 4 =0.8 m Points 4 and 6 =300 m, points 6 and 7 =35 m; and points 7 and 8 =120 m

19. Example No. 2.2A

20. Example No. 2.2A

21. Home Work A pumping system with different pipe fittings is shown in Fig. Calculate residual pressure head at the end of the pipe outlet if the pump is generating an input head of 80 m at 0.2 m3/s discharge. The CI pipe diameter is shown in figure.

22. Thank You!