1 Topic I. 9. Water Supply Networks Dimensioning Determination of Design Water Flowrates (Water Quantities) Design Flows Division §Take off (distributed) flow §Crossover flow §Fire flow

2 Determination of Design Water Flowrates (Water Quantities) Take off (Distributed) Flow §Specific water quantity - q 0, l/s.m q 0 = (Q max,h -  Q c ) /  l r, l/s.m Q max,h - total hourly maximal consumption of the settlement, l/s Q c - concentrated (big) consumption, l/s l r - reduced length of the pipe, m l r = .l, m l - real pipe length, m  - reducing coefficient;  = 1 at the pipes with bilateral take off along its length;  = 0,5 at the pipes with unilateral take off along its length

3 Determination of Design Water Flowrates (Water Quantities) §Design water flowrate - Q d, l/s Q d = .q 0.l r + Q cr, l/s Q cr - crossover flowrate, l/s  - coefficient of equivalent distribution flowrate;  = 0,5 - 0,6 §Crossover flowrate - Q cr, l/s Q cr = q 0.  l r +  Q c + Q f, l/s Q f - fire flwrate, l/s

4 Design Flows Division  Q п.р - sum of the take off flows of all the pipes, fed by the one under consideration Q п.р - the current pipe take off (distributed) flow Q k - concentrated (big) take off flows, fed by the pipe under consideration Q пп - fire flow Q tp - the current pipe crossover flow Q op - design flowrate (water quantity)

5 Hydraulic Calculations Pressure Pipe Flow Parameters §Flowrate - Q §Velocity - v §Pipe diameter - D §Hydraulic gradient - I §Head losses - h §Coefficient of head losses -

6 Hydraulics Relationships (1) Continuity equation (2) Chezy equation (3) Collebrook - White equation (4) Darcy - Weisbah equation

7 Pressure Pipe Dimensioning §Number of flow parameters - 6 §Necessary number of hydraulics equations - 6 §Available number of hydraulics equations - 4 §Number of flow parameters to be accepted - 2

8 Branched Distribution Network Dimensioning Without (a) and with (b) fixed service reservoir position a)

9 Branched Distribution Network Dimensioning Accepted (Known) Flow Parameters I. Without fixed service reservoir position §Flowrate - known, calculated in advance according to the definite method §Velocity - accepted in a range, as follows: mean economical velocities - v = 0,6 - 0,9 m/s for D < 300 mm; v = 0,9 - 1,5 m/s for D > 350 mm low limit for the velocity - v > 0,3 m/s upper limits for the velocity - v < 2 m/s, normally; v < 3 m/s, with fire

10 Branched Distribution Network Dimensioning Accepted (Known) Flow Parameters I. With fixed service reservoir position §Flowrate - known, calculated in advance according to the definite method §Mean hydraulic gradient - known, calculated through the service reservoir elevation and dynamic head at the critical point - M:

11 Branched Distribution Network Dimensioning Auxiliary Dimension Tools §Tables §Graphs §Equations - hydraulic, empirical

12 Looped Distribution Network Dimensioning Main Approaches: I. Virtual transfer of the looped network into branched one §Definition of the flows directions (according to the branches lay out) §Calculation of the design flowrates for every pipe §Dimensioning of the pipes and calculation of the head losses §Determination of the dynamic hydraulic head spatial distribution and the service reservoir elevation (position) II.Considering the hydraulic connections in the real looped network §Preliminary definition (acceptation) of the flows directions in the network §Considering of the mass conservation low (continuity equation) at every node of the network §Considering of the energy conservation low (head losses balance) at every arbitrary chosen loop (ring) of the network

13 Looped Distribution Network Dimensioning Continuity equation  Q = 0  Q - algebraic sum +Q - flows entering the node -Q - flows leaving the node Head losses balance  h = 0 or  s.Q  = 0 s - head losses lump coefficient (Darcy - Weisbah coefficient, where is a non-linear function of Q): If neglecting dependence of Q, the following relationship is valid:  s.Q 2 = 0

14 Looped Distribution Network Dimensioning Head losses balance §For the head losses balance keeping, a correction flowrate - q is introduced, according to the design method of Lobachev - Kross (Lobachov,1932; Hardy Cross, 1936): q =  h / 2.  s.Q, l/s  h - head losses misbalance value at the relevant network loop (ring)  s.Q - head losses at the relevant network loop (ring) §The correction flowrate values - q for every pipe in the network are calculated applying the iterative calculation procedure over entire the network. Since both the mass and head losses balances have to be considered simultaneously at every node and loop of the network, respectively, calculations include simultaneous solution of system of N-number equations (N = number of nodes - 1, plus number of relevant loops) at every step of iteration. The number of unknown (searched for) water flowrates - Q is equal to the number of the pipes in the loop network and therefore is equal to N. The calculations are performed by means of computer and relevant software.

15 Looped Distribution Network Dimensioning Head losses balance (scheme)