Consider RHS of eq(1) Mass x acceleration = × Vol × change in velocity /time V1  (iii)   Q   V2    =volume/time × change in velocity     a2 p1  p2  pQV1 V2 Substitution (ii) & (iii) in eq(i)   V1    V2 V2 p1 p2 Both by (Specific weight ‘’)    p p V  V V (iv)       1 2 2 1 2    g Applying Bernoulli’s equation between (1) and (2) with the centre line of the pipe as    V p p V 2 2   1 2 2g  hL 1 2 V  V  2V V V 2 2  hL 2g and Considering head loss due to sudden expansion hLonly. 2 2 2 2 2 2 2isV1Vh2 Z1  Z 2V1V2 2 h   orViz1 ontVa2l  V2  hL 2V2 V1 2g V  Z p1 2g 2 p V   2  1  1 2g  2 2 Z2  2g
Consider RHS of eq(1) Mass x acceleration = × Vol × change in velocity /time   Q  V1  V2     (iii)  =volume/time × change in velocity a2  p1  p2   pQV1 V2  Substitution (ii) & (iii) in eq(i)  p1  p2   V2 V1 V2  Both by (Specific weight ‘’)  p  p  V V V   1 2   2 1 2    (iv)    g Applying Bernoulli’s equation between (1) and (2) with the centre line of the pipe as  p  p  V 2 V 2 1 2   1 2 2g  hL 2V V V  V 2 V 2  and hL  2g Considering head loss due to sudden expansion hLonly. 2 2 2 2 2 2 Z1  Z 2 2isV1Vh2 orViz1 ontVa2l hL  h  2V1V2  2V2  V1 V2 Z  p1 1  V 2  1  2g 2g Z2  2g p V 2 2  2  2g
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