Q. 3 At a sudden enlargement of water main from 240mm to 480mm diameter, the hydraulic gradient rises by 10mm. Estimate the rate of flow. (July 2014, july 2015) Ans: Rise of hydraulic gradient line = 10mm From Continuity equation      Q  V1 V2 4 0.482 0.242 4 V1 = 4× V2 Loss of head in sudden expansion V1      H V2   2 2    g exp ansion Applying Bernoulli’s equation between upstream and downstream of sudden expansion p V p V 2 2       Z Z H Eq.1 1 1 2 2 exp 2 2 ansion  g   1 2 g    p p Given rise of hydraulic gradient line = 10mm = 0.01m = 2 1  w The elevation is same for horizontal enlargement Z1 = Z2 and also V1 = 4× V2 Substituting in eq.1    p2 Z V2  V1  p1 Z 4V     V2    2 2 2 2   2 g   g 1  2  g  2 1   p  p 15 9 V V 2 2 0.01    2 1 2 2 g  s w  0.181m / V2 2  2  g 0.482 0.181 0.03275m3 /      Q s 4 The rate of flow Q = 0.03275 m3/s
Q. 3 At a sudden enlargement of water main from 240mm to 480mm diameter, the hydraulic gradient rises by 10mm. Estimate the rate of flow. (July 2014, july 2015) Ans: Rise of hydraulic gradient line = 10mm From Continuity equation Q   4  0.242 V1    0.482 4 V2 V1 = 4× V2 Loss of head in sudden expansion H   V1  V2   exp ansion  2   2  g  Applying Bernoulli’s equation between upstream and downstream of sudden expansion p V 2 p V 2 1  Z  1  2  Z  2  H Eq.1 1 2  g  2 2  g exp ansion  p  p  Given rise of hydraulic gradient line = 10mm = 0.01m = 2 1  w The elevation is same for horizontal enlargement Z1 = Z2 and also V1 = 4× V2 Substituting in eq.1 p1  Z 4V   2  p2  Z  V2   V1  V2   2 1 2  g  2  1 2  g  2  2  g   p  p  15 V 2 9 V 2 2 1  0.01  2  2  w V2  0.181m / s 2  g 2  g Q    0.482  0.181  0.03275m3 / s 4 The rate of flow Q = 0.03275 m3/s
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