4 fL V 2   H 4 fL1Q 1 1 2gD  32 fL1Q     gD 2 5 1 2 1 2gD1    D1 4   0.3 32 0.04    1500 H Q (0.2)5    g 2  0.0343 / sec Q m3 Case-2: When Pipeline is branched midway for connecting two reservoirs H = 20m, f = 0.015, L1 = 800m, D1 = 0.2m L2 = D2 = 0.2m L3 = 1200m, D3= 0.2m Q1 = Q2 + Q3 = 2Q2   Q Q2 =   1 2   4 4 fL V fL V 2 2   H 1 1 2 2 2gD1 2gD2 0.5Q 2 32  0.04  750  32 32 32  0.04  750  fL Q fL Q Q 2 2 2 20     1 1 2 2 1 1 0.65 0.65   gD gD       g g 2 5 2 5 2 2 0.04338 / sec  Q m 3 Increase in Discharge = (Q1 Q) = (0.04338-0.0343) = 0.00908m3/sec – The velocity of water in a 60cm diameter and 15mm thick cast iron pipe (E=1.04x1011 Pa) is changed from 3 m/s to zero in 1.25 s by closure of a valve i) if the pipe length is 800m what will be the water hammer pressure at the valve? What will be the corresponding pressure rise if the closure takes place in; ii) 2s and iii) 0.8s respectively? Bulk module of elasticity of water is 2.11 x 109 N/m2. (July2013, July 2015) D = 60cm = 0.6m, L = 800m, t = 15mm = 0.015m Ans:Given: E = 1.04 × 1011 Pa, K = 2.11 × 109 N/m2 , V = 3m/s Case-1 Time of Closure Tc = 1.25 sec
4 fL V 2 H  1 1  2gD 4 fL1Q    32 fL1Q   2 gD 5 1 2 1 2gD1   D1  4   H  0.3  32  0.04 1500 Q  2  g  (0.2)5 Q  0.0343 m3 / sec Case-2: When Pipeline is branched midway for connecting two reservoirs H = 20m, f = 0.015, L1 = 800m, D1 = 0.2m L2 = D2 = 0.2m L3 = 1200m, D3= 0.2m Q1 = Q2 + Q3 = 2Q2  Q  Q2 =  1   2  4 fL V 2 4 fL V 2 H  1 1  2 2 2gD1 32 fL Q 2 2gD2 32 fL Q 2 32  0.04  750  Q 2 32  0.04  750  0.5Q 2 20  1 1  2 2  1  1  2 gD 5  2 gD 5  2  g  0.65  2  g  0.65 Q  0.04338 m 3 / sec Increase in Discharge = (Q1 – Q) = (0.04338-0.0343) = 0.00908m3/sec The velocity of water in a 60cm diameter and 15mm thick cast iron pipe (E=1.04x1011 Pa) is changed from 3 m/s to zero in 1.25 s by closure of a valve i) if the pipe length is 800m what will be the water hammer pressure at the valve? What will be the corresponding pressure rise if the closure takes place in; ii) 2s and iii) 0.8s respectively? Bulk module of elasticity of water is 2.11 x 109 N/m2. (July2013, July 2015) Ans:Given: D = 60cm = 0.6m, L = 800m, t = 15mm = 0.015m E = 1.04 × 1011 Pa, K = 2.11 × 109 N/m2 , V = 3m/s Case-1 Time of Closure Tc = 1.25 sec
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