Monroe L. Weber-Shirk S chool of Civil and Environmental Engineering Pipe Networks 

Closed Conduit Flow: Review ä Energy equation ä Head loss ä major losses ä minor losses ä EGL and HGL ä Non circular conduits ä Pipeline systems ä pipe networks ä measurements ä manifolds and diffusers ä Pumps ä Energy equation ä Head loss ä major losses ä minor losses ä EGL and HGL ä Non circular conduits ä Pipeline systems ä pipe networks ä measurements ä manifolds and diffusers ä Pumps

Pipeline systems: Pipe networks ä Water distribution systems for municipalities ä Multiple sources and multiple sinks connected with an interconnected network of pipes. ä Computer solutions! ä KYpipes ä WaterCAD ä CyberNET ä Water distribution systems for municipalities ä Multiple sources and multiple sinks connected with an interconnected network of pipes. ä Computer solutions! ä KYpipes ä WaterCAD ä CyberNET

Water Distribution System Assumption ä Each point in the system can only have one _______ ä The pressure change from 1 to 2 by path a must equal the pressure change from 1 to 2 by path b ä Each point in the system can only have one _______ ä The pressure change from 1 to 2 by path a must equal the pressure change from 1 to 2 by path b a b 1 2 pressure

a b 1 2 Pressure change by path a Water Distribution System Assumption ä Pipe diameters are constant ä Model withdrawals as occurring at nodes so V is constant ä Pipe diameters are constant ä Model withdrawals as occurring at nodes so V is constant Or sum of head loss around loop is _____. zero (Need a sign convention)

Pipes in Parallel A A B B Q1Q1 Q1Q1 Q total energy proportion ä Find discharge given pressure at A and B ä ______& ____ equation ä add flows ä Find head loss given the total flow ä assume a discharge Q 1 ’ through pipe 1 ä solve for head loss using the assumed discharge ä using the calculated head loss to find Q 2 ’ ä assume that the actual flow is divided in the same _________ as the assumed flow ä Find discharge given pressure at A and B ä ______& ____ equation ä add flows ä Find head loss given the total flow ä assume a discharge Q 1 ’ through pipe 1 ä solve for head loss using the assumed discharge ä using the calculated head loss to find Q 2 ’ ä assume that the actual flow is divided in the same _________ as the assumed flow Q2Q2 Q2Q2 S-J

Networks of Pipes ä ____ __________ at all nodes ä The proper relationship between head loss and discharge must be maintained for each pipe ä Darcy-Weisbach equation ä _____________ ä Exponential friction formula ä _____________ ä ____ __________ at all nodes ä The proper relationship between head loss and discharge must be maintained for each pipe ä Darcy-Weisbach equation ä _____________ ä Exponential friction formula ä _____________ A 0.32 m 3 /s0.28 m 3 /s ? b a 1 2 Mass conservation Swamee-Jain Hazen-Williams

Network Analysis Find the flows in the loop given the inflows and outflows. The pipes are all 25 cm cast iron (  =0.26 mm). Find the flows in the loop given the inflows and outflows. The pipes are all 25 cm cast iron (  =0.26 mm). A B CD 0.10 m 3 /s 0.32 m 3 /s 0.28 m 3 /s 0.14 m 3 /s 200 m 100 m

Network Analysis ä Assign a flow to each pipe link ä Flow into each junction must equal flow out of the junction ä Assign a flow to each pipe link ä Flow into each junction must equal flow out of the junction A B CD 0.10 m 3 /s 0.32 m 3 /s 0.28 m 3 /s 0.14 m 3 /s arbitrary

Network Analysis ä Calculate the head loss in each pipe f=0.02 for Re> k 1,k 3 =339 k 2,k 4 =169 k 1,k 3 =339 k 2,k 4 =169 A B CD 0.10 m 3 /s 0.32 m 3 /s 0.28 m 3 /s 0.14 m 3 /s Sign convention +CW

Network Analysis ä The head loss around the loop isn’t zero ä Need to change the flow around the loop ä the ___________ flow is too great (head loss is positive) ä reduce the clockwise flow to reduce the head loss ä Solution techniques ä Hardy Cross loop-balancing (___________ _________) ä Use a numeric solver (Solver in Excel) to find a change in flow that will give zero head loss around the loop ä Use Network Analysis software ä The head loss around the loop isn’t zero ä Need to change the flow around the loop ä the ___________ flow is too great (head loss is positive) ä reduce the clockwise flow to reduce the head loss ä Solution techniques ä Hardy Cross loop-balancing (___________ _________) ä Use a numeric solver (Solver in Excel) to find a change in flow that will give zero head loss around the loop ä Use Network Analysis software clockwise optimizes correction

Numeric Solver ä Set up a spreadsheet as shown below. ä the numbers in bold were entered, the other cells are calculations ä initially  Q is 0 ä use “solver” to set the sum of the head loss to 0 by changing  Q ä the column Q 0 +  Q contains the correct flows ä Set up a spreadsheet as shown below. ä the numbers in bold were entered, the other cells are calculations ä initially  Q is 0 ä use “solver” to set the sum of the head loss to 0 by changing  Q ä the column Q 0 +  Q contains the correct flows

Solution to Loop Problem A B CD 0.10 m 3 /s 0.32 m 3 /s 0.28 m 3 /s 0.14 m 3 /s Q 0 +  Q     Better solution is software with a GUI showing the pipe network.

Pressure Network Analysis Software: WaterCAD™ A B CD 0.10 m 3 /s 0.32 m 3 /s 0.28 m 3 /s 0.14 m 3 /s junction pipe reservoir

Network Elements ä Controls ä Check valve (CV) ä Pressure relief valve ä Pressure reducing valve (PRV) ä Pressure sustaining valve (PSV) ä Flow control valve (FCV) ä Pumps ä Reservoirs ä Tanks ä Controls ä Check valve (CV) ä Pressure relief valve ä Pressure reducing valve (PRV) ä Pressure sustaining valve (PSV) ä Flow control valve (FCV) ä Pumps ä Reservoirs ä Tanks

Check Valve ä Valve only allows flow in one direction ä The valve automatically closes when flow begins to reverse ä Valve only allows flow in one direction ä The valve automatically closes when flow begins to reverse closed open

Pressure Relief Valve Valve will begin to open when pressure in the pipeline ________ a set pressure (determined by force on the spring). pipeline closed relief flow open exceeds Low pipeline pressure High pipeline pressure

Pressure Regulating Valve Valve will begin to open when the pressure ___________ is _________ than the setpoint pressure (determined by the force of the spring). sets maximum pressure downstream closed open less downstream High downstream pressure Low downstream pressure

Pressure Sustaining Valve Valve will begin to open when the pressure ________ is _________ than the setpoint pressure (determined by the force of the spring). sets minimum pressure upstream closedopen upstream greater Low upstream pressure High upstream pressure

Flow control valve (FCV) ä Limits the ____ ___ through the valve to a specified value, in a specified direction ä Commonly used to limit the maximum flow to a value that will not adversely affect the provider’s system ä Limits the ____ ___ through the valve to a specified value, in a specified direction ä Commonly used to limit the maximum flow to a value that will not adversely affect the provider’s system flow rate

Reservoirs ä Are modeled as ________ water level sources ä Can supply any demand! ä Are modeled as ________ water level sources ä Can supply any demand! constant

Tanks ä Obey conservation of mass ä Have a finite size ä Water level moves up and down and thus _______ in system change! ä Need to define tank geometry ä Obey conservation of mass ä Have a finite size ä Water level moves up and down and thus _______ in system change! ä Need to define tank geometry pressures

Pumps ä Require a Pump Curve (discharge vs. head) ä Initial setting ä Controls for extended time analysis ä Require a Pump Curve (discharge vs. head) ä Initial setting ä Controls for extended time analysis

Water Distribution System ä Reservoir - used to model a clear well ä Pump to lift water to elevated storage tank ä turns on and off based on water level in tank ä Tank feeds distribution grid ä Demands applied at junctions ä Reservoir - used to model a clear well ä Pump to lift water to elevated storage tank ä turns on and off based on water level in tank ä Tank feeds distribution grid ä Demands applied at junctions