1. Water Resources Engineering
WEM401
Water Resources Engineering
Lecture – 2.4
Pipe Network Analysis;
Hydraulic Transients
Vishnu Prasad Pandey, PhD
Asian Institute of Technology (AIT)

2. Hardy Cross Method for pipe network analysis Hydraulic transients
Contents
Outline
Remarks
II. Water Distribution Systems
Water distribution systems and its components
Pipe flow equation
Hydraulics of simple networks
Pump system analysis
Network simulation
Hydraulic transients
Duration: 7.5 hrs
Assignment: 1
Responsibility: Dr. Vishnu Pd. Pandey
Introduction
Hardy Cross Method for pipe network analysis
Hydraulic transients

3. Q & h must satisfy the continuity & energy Eqns
Introduction
In municipal water supply system, there are several branches, junctions and circuits, such that the system is complex.
Pipe network analysis involves determining pipe “flow rates (Q)” & “pressure heads (h)” at the outflow points of the networks.
Q & h must satisfy the continuity & energy Eqns
Hardy-Cross (in 1936); Professor of Structural University of Illions Urbana-Champaign, USA)

4. Hardy-Cross Method
Hardy-Cross method is one of the widely used method for analyzing a complex system of pipes forming closed loops
This is a method of successive approximation that applies head balance approach
Outflows from the system are generally assumed to occur at the nodes/junctions
For a given pipe system with known outflows, the Hardy-Cross method is an iterative procedure based on initially iterated flows in the pipe
At each junction these flows must satisfy the continuity criteria & energy criteria

5. Hardy-Cross Method Basic requirements for Hardy-Cross method:
Continuity equation: Qin = Qout (for each junction)
Energy equation: Algebraic sum of HL around any closed circuit = zero.
For each loop or circuit the HL is +ve in clockwise dirn & –ve in anticlockwise dirn
Dary-Weisbach Eqn satisfy in each pipe

6. Hardy-Cross Method: Steps
With given inflow & outflow, assume suitable Q & its direction in each pipe that satisfy continuity Eqn at each junction
Divide pipe network into a number of loops
Include each pipe in at least one of the loops
For each loop, compute HL in each pipe & sum them up:
Also compute for each circuit; w/o considering sign (i.e., absolute value is taken)
Compute the correction:

7. Hardy-Cross Method: Steps
Compute the corrected flow as Qi+1 + ΔQ, where Qi+1 = previous value of flows
If ΔQ is +Ve  Add it to Q in clockwise dirN & subtract it from Q in anti-clockwise dirN & vice- versa.
For a common pipe of two loops, apply correction from both loops considering appropriate sign for each
Use corrected Q for the next trial & repeat steps 3-5 until the correction becomes negligible.
Computer solutions:
EPANET; KYpipes; WaterCAD; CyberNET

8. Hydraulic Transients Hydraulic transient developed due to Wave
Sudden closure of the valve & corresponding rise in velocity
Wave
Temporal variation of water surface, which is propagated in the fluid media
Celerity (C)
The relative velocity of wave w.r.t. velocity of fluid
If C is celerity, V is fluid velocity, & VW is wave velocity;
C = VW + V; if both move in opposite direction
C = VW + V; if both move in the same direction

9. Hydraulic Transients Celerity (C)
Total pressure: as discussed in Hydropower lecture

10. Hydraulic Transients: Water Hammer
When water flowing in a long pipe is suddenly brought into rest by closing the valve
Momentum of flowing water will be destroyed
Wave of high pressure will be setup
KE of flowing fluid will be converted into the internal pressure energy with rise of pressure
The wave of high pressure will be transmitted along the pipe with velocity equal to that of sound (C)
May create noise called “knocking”
The phenomenon of sudden rise in pressure in the pipe  Water Hammer (of Water Blow)
Water hammer is an example of fast hydraulic transient

11. Hydraulic Transients: Water Hammer
Water Hammer is caused by changes in velocity, which are caused by:
Valve operation (i.e. closure & opening)
Power failures
Starting or shutdown of pumps (hydro-turbines)
Fluctuation in power demand in turbines
Rupture of the line, etc.
Mechanical failure of the control devices like valves
Effects of water hammer
High-pressure fluctuations in pipelines
Rupture of pipe or valve if fluctuations beyond safety limit
Higher pressure requirements for the design of pipeline & penstocks, etc.

12. Hydraulic Transients: Water Hammer
Magnitude of pressure rise depends on:
Time taken to close the valve
Velocity of flow
Length of pipe
Elastic properties of the pipe materials as well as that of the flowing fluid (i.e., water in this case)
Critical time of closure = 2L/C; 2L = distance travelled from valve to tank and back; C = velocity of the wave pressure
Gradual closure: if T > 2L/C; T = time required to close
Sudden closure: if T < 2L/C

13. Hydraulic Transients: Water Hammer
Steady-state condition prior to valve movement
Transient conditions at t<L/C
Transient conditions at t =L/C
Transient conditions at L/C < t < 2L/C
Transient conditions at t =2L/C
Transient conditions at 2L/C < t < 3L/C
Transient conditions at t =3L/C
Transient conditions at 3L/C < t < 4L/C.
Transient conditions at t = 4L/C.
After t =4L/C, the cycle repeats & continues indefinitely if the friction in the pipe is zero.
Clockwise & anticlockwise arrows denotes the direction of reflection of the wave front.
Fig.: Propagation of Water Hammer Pressure Waves (Neglecting pipe friction)

14. Hydraulic Transients: Water Hammer
Pressure different points
@ B (Valve)

15. Hydraulic Transients: Water Hammer
@ M (Mid-point)
Time (t)
Surge tanks are provided to protect the pipes from Water Hammer.
@ A (End-point)
Time (t)