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- 1. Collector pipes in siphonic roof drainage systems: to incline or not? Marc Buitenhuis Hydraulic research engineer Akatherm International BV, Panningen, The Netherlands 10-09-2008AbstractSome install horizontal collector pipes of siphonic roof drainage systems under a fall angle orinclination. This is however causing a delay in the priming of the system and thus is not onlyunnecessary but even disadvantageous. The hydraulic jump that has to form to close the innerperiphery of the pipe and make it work syphonic is less pronounced when the collector pipehas an inclination. 1. Introduction of the hydraulic jump depends on 2 parameters:Some install collector pipes of syphonic 1. the velocity of the flow streamingroof drainage systems under inclination into the horizontal pipethinking that the water will then be 2. the resistance of the pipe beyondtransported easier through the pipe system. the entrance of the collector pipe.This however is not the case in syphonicroof drainage systems as will be explainedin this article. It will even delay thepriming of the system and thus workdisadvantageous. 2. Principle of syphonic roof drainage Figure 1. Forming of the hydraulic jump at start up of siphonic roof drainage systemThe working principle of syphonic roofdrainage is the full bore flow of the system. The principle can be compared to theAt full bore flow the water column closing stream of vehicles on highways or raceoff the pipe diameter will generate a tracks. Vehicles can accelerate optimallysuction pressure dragging the water from on roads that are straight and keep onthe roof in its wake. One thus has to obtain being straight for miles. As soon as there isand maintain a full bore flow for optimal a curve in the road the vehicles have tofunctioning of the system. slow down. When the first vehicleThe full bore flow is initiated by the decelerates the one behind him has tohydraulic jump (see figure 1) at the decelerate also and the distance betweenentrance of the horizontal part of tail pipe the vehicles decreases. This is very oftenor collector pipe of the system. The shape
- 2. the moment for accidents to happen: thereis an increasing chance for collision. For incompressible inviscid flow theyExactly this is the case for fluid particles in become: a stream. When particles are redirected DV ρ = ρg − ∇pfrom the vertical downfall to horizontal Dtflow the fluid is decelerated. As fluid and are known in this form as Euler’sparticles have no brakes they will collide equations.and the only way they can go is up, pcreating height and thus a hydraulic jump. The headloss ΔH is defined as ΔH = ρ . gThe above explains 2 things: first of all Substituting this in the above Euler’swhy an increasing length of vertical tail equations and dividing by ρ gives:pipe leads to earlier priming, secondly why DV an increasing resistance in the collector = g − g∇H Dtpipe leads to this same result. In streamline coordinates along the x-axisAn increasing length of tail pipe gives and taking the z-direction the direction ofmore time for acceleration of the water gravity:coming from the roof, thus to higher DV ∂Vx ∂Vxvelocities at the bend to the horizontal = +Vx = −g∇ − g∇ = z H Dt ∂t ∂xpipe. This will lead to a higher hydraulic ∂Hjump when the flow is decelerated in the − g ⋅ sin β − ghorizontal pipe. ∂xAlso the more the flow is decelerated in With a constant diameter of the pipe andthe horizontal pipe, thus the higher the thus constant cross section, A, this can beresistance downstream of the bend, the further rewritten to: higher the hydraulic jump will be. DQ ∂Q Q ∂Q = + = −A ⋅ g∇z − A ⋅ g∇H =The higher the hydraulic jump will be the Dt ∂t A ∂xearlier the full pipe diameter will be closed ∂H − A ⋅ g ⋅ sin β − A ⋅ goff by water and priming will start. ∂xWhen the horizontal pipe is (slightly)inclined the water will run off easier and with β the angle between the horizontalthus the hydraulic jump will be less streamline x and the directionpronounced, delaying the onset to priming perpendicular to the gravity (β positiveof the system. when the streamline ascends). 3. Theoretical backgroundIn this section the theoretical backgroundfor the phenomenon described above willbe derived. QIn fluid dynamics the Navier-Stokes xequations are the general form of themomentum equations that account for fluid -βmotion and are written as: g D ( ρV ) = ρg − ∇p + µ∇2V Dt For a descending collector pipe the angle βwhere ρ is the density, thus is negative, the term with this V is the velocity parameter thus positive, driving the speedp is the pressure, in the collector pipe up and thus making itμ is the viscosity decelerate less, producing a less
- 3. pronounced hydraulic jump and thusdelaying priming (full bore flow) in the 4. Conclusionssystem. In this article it has been illustrated thatIn a steady incompressible, inviscid, full other then for conventional roof drainagebore flow integration of Euler’s equations systems an inclination of the collector pipeover a streamline gives the well known in a siphonic roof drainage system is notBernoulli equation: advantageous and will delay the priming ofp V2 the system. Thus it is advised to install the + gz + = constρ 2 collector pipes horizontally for properThis equation is often referred to to easily siphonic functioning.explain the principle of siphonic roofdrainage. 5. References 1. Fox, Robert W., McDonald, Alan T. Introduction to fluid mechanics, third edition, 1985, School of Mechanical Engineering Purdue University, John Wiley & Sons 2. Scott Arthur, John A. Swaffield, Siphonic roof drainage: current understanding, 2001, Water research group, Department of civil and offshore engineering, Heriot-Watt University, Edinburg, Scotland (UK) 3. G.B. Wright, S. Arthur, J.A. Swaffield, Numerical simulation of the dynamic operation of multi-outlet siphonic roof drainage systems, 2005, Drainage and water supply research group, School of the build environment, Heriot-Watt University, Edinburg, Scotland (UK) 4. Scott Arthur, The priming focused design of siphonic roof drainage, drain 5. age research group, School of the built environment, Heriot-Watt University, Edinburg, Scotland (UK) 6. S. Arthur, G.B. Wright, Siphonic roof drainage systems – priming focused design, 2006, School of the built environment, Heriot-Watt University, Edinburg, Scotland (UK) 7. S. Arthur, J.A. Swaffield, Siphonic roof drainage system analysis utilizing unsteady flow theory, 2000, Department of building engineering and surveying, Heriot-Watt University, Edinburg, Scotland (UK)
- 4. pronounced hydraulic jump and thusdelaying priming (full bore flow) in the 4. Conclusionssystem. In this article it has been illustrated thatIn a steady incompressible, inviscid, full other then for conventional roof drainagebore flow integration of Euler’s equations systems an inclination of the collector pipeover a streamline gives the well known in a siphonic roof drainage system is notBernoulli equation: advantageous and will delay the priming ofp V2 the system. Thus it is advised to install the + gz + = constρ 2 collector pipes horizontally for properThis equation is often referred to to easily siphonic functioning.explain the principle of siphonic roofdrainage. 5. References 1. Fox, Robert W., McDonald, Alan T. Introduction to fluid mechanics, third edition, 1985, School of Mechanical Engineering Purdue University, John Wiley & Sons 2. Scott Arthur, John A. Swaffield, Siphonic roof drainage: current understanding, 2001, Water research group, Department of civil and offshore engineering, Heriot-Watt University, Edinburg, Scotland (UK) 3. G.B. Wright, S. Arthur, J.A. Swaffield, Numerical simulation of the dynamic operation of multi-outlet siphonic roof drainage systems, 2005, Drainage and water supply research group, School of the build environment, Heriot-Watt University, Edinburg, Scotland (UK) 4. Scott Arthur, The priming focused design of siphonic roof drainage, drain 5. age research group, School of the built environment, Heriot-Watt University, Edinburg, Scotland (UK) 6. S. Arthur, G.B. Wright, Siphonic roof drainage systems – priming focused design, 2006, School of the built environment, Heriot-Watt University, Edinburg, Scotland (UK) 7. S. Arthur, J.A. Swaffield, Siphonic roof drainage system analysis utilizing unsteady flow theory, 2000, Department of building engineering and surveying, Heriot-Watt University, Edinburg, Scotland (UK)
- 5. pronounced hydraulic jump and thusdelaying priming (full bore flow) in the 4. Conclusionssystem. In this article it has been illustrated thatIn a steady incompressible, inviscid, full other then for conventional roof drainagebore flow integration of Euler’s equations systems an inclination of the collector pipeover a streamline gives the well known in a siphonic roof drainage system is notBernoulli equation: advantageous and will delay the priming ofp V2 the system. Thus it is advised to install the + gz + = constρ 2 collector pipes horizontally for properThis equation is often referred to to easily siphonic functioning.explain the principle of siphonic roofdrainage. 5. References 1. Fox, Robert W., McDonald, Alan T. Introduction to fluid mechanics, third edition, 1985, School of Mechanical Engineering Purdue University, John Wiley & Sons 2. Scott Arthur, John A. Swaffield, Siphonic roof drainage: current understanding, 2001, Water research group, Department of civil and offshore engineering, Heriot-Watt University, Edinburg, Scotland (UK) 3. G.B. Wright, S. Arthur, J.A. Swaffield, Numerical simulation of the dynamic operation of multi-outlet siphonic roof drainage systems, 2005, Drainage and water supply research group, School of the build environment, Heriot-Watt University, Edinburg, Scotland (UK) 4. Scott Arthur, The priming focused design of siphonic roof drainage, drain 5. age research group, School of the built environment, Heriot-Watt University, Edinburg, Scotland (UK) 6. S. Arthur, G.B. Wright, Siphonic roof drainage systems – priming focused design, 2006, School of the built environment, Heriot-Watt University, Edinburg, Scotland (UK) 7. S. Arthur, J.A. Swaffield, Siphonic roof drainage system analysis utilizing unsteady flow theory, 2000, Department of building engineering and surveying, Heriot-Watt University, Edinburg, Scotland (UK)

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