Pipe in Series

Series pipeline – fluid flows in a single flowpath through the

system

When pipes of different diameters are connected end to end to form a pipe line, they are said to be in series.

·        Discharge   :Q = A₁V₁ = A₂V₂ = A₃V₃

·        Head loss    : The difference in liquid surface levels is equal to the sum of

the total head loss in the pipes :

What were the various losses we discussed???

- Friction loss in pipes (major)

Hf = f * (L/D) * v2/2g

- Losses due to bends, fittings, valves, etc – (minor losses)

H_m = K (v2 / 2g)

Example 1 :

Consider the two reservoirs shown in below, connected by a single pipe that changes diameter over its length. The surfaces of the two reservoirs have a difference in level of 9m. The pipe has a diameter of 200mm for the first 15m (from A to C) then a diameter of 250mm for the remaining 45m (from C to B).

For the entrance use k = 0.5 and the exit k = 1.0. The expansion at C is sudden. For both pipes use f = 0.01

H_f1           = head loss for 200mm diameter section of pipe

H_f2           = head loss for 250mm diameter section of pipe

H_m entry      = head loss at entry point

H_m expansion  = head loss at expansion of the pipes, C

H_m exit       = head loss at exit point

Total head loss for the system, H_L = H_f1 + H_f2 + H_m entry + H_m expansion + H_m exit

P₁/g + v₁²/2g + z₁ = P₂/g + v²₂/2g + z₂ + H_L

0 + 0 + 9 = 0 + 0 + 0 + H_L

9 = H_f1 + H_f2 + H_m entry + H_m expansion + H_m exit

All losses are, in terms of Q :

Substitute these into

H_f1 + H_f2 + H_L entry + H_L join (expansion) + H_L exit = 9

and solve for Q, to give Q = 0.158 m³/s

Example 2 :

For the above given diagram, the total head loss is equal to “H”. This total head

loss is contributed by the following components.