Tp6 principles of siphonic roof drainage systems(dr)
Principles of siphonic roof drainage systems Marc Buitenhuis Hydraulic research engineer Akatherm International BV, Panningen, The Netherlands 17-08-2008AbstractIn this article it has been illustrated that a siphonic roof drainage system with a single roofoutlet is reasonably well understood. The governing equations are presented.The basic design of the system can be determined using single phase flow theory assumingfull bore flow of the system.The start up and two phase flow functioning of the system are more complex.In a multiple roof outlet siphonic system the interaction between the roof outlets makes it verycomplex and only skilled people can design a well functioning system. 1. Introduction explained to give a basis for the principles 1. Introduction? of a multiple roof outlet system.For drainage of large roof areas a siphonic 2. Principle of syphonic roofsystem is a well acknowledged cost saving drainagesolution. The principle of expelling airfrom the system means that only water is The principle in syphonic roof drainage isbeing transported at high speed making use the full bore flow of the system. One thusof the suction pressure created behind the has to obtain and maintain a full bore flowfull bore water column. The high speed full for optimal functioning of the system.bore flow makes smaller pipe dimensions The full bore flow is initiated by thethan in conventional systems possible. hydraulic jump (see figure 1) at theAlso the elimination of multiple downpipes entrance of the horizontal part of tail pipeand a lot of piping in the groundwork mean or collector pipe of the system. The shapea large cost saving and more architectural of the hydraulic jump depends on 2freedom for the building design. parameter:The only disadvantage is that one has to • the velocity of the flow streaming intohave a better technical background to be the horizontal pipeable to properly design a siphonic system. • and the resistance of the pipe beyondA multiple roof outlet siphonic system is a the entrance of the collector pipe.complex system that needs to be carefullyoptimized to function properly.In this article the theory of a single roofoutlet siphonic roof drainage will be
pronounced, delaying the onset to priming of the system. 3. Theoretical background In fluid dynamics the Navier-Stokes equations are the general form of the momentum equations that account for fluidfigure 1. forming of the hydraulic jump at start up of siphonic motion and are written as: roof drainage system DρV = ρg − ∇p + µ∇2VThe principle can be compared to the Dtstream of vehicles on highways or racetracks. Vehicles can accelerate optimally For incompressible inviscid flow theyon roads that are straight and keep on become: being straight for miles. As soon as there is DV ρ = ρg − ∇pa curve in the road the vehicles have to Dtslow down. When the first vehicle and are known in this form as Euler’sdecelerates the one behind him has to equations.decelerate also and the distance between p The headloss ΔH is defined as ΔH = ρ . gthe vehicles is decreasing. This is veryoften the moment for accidents to happen: Substituting this in the above Euler’sthere is an increasing chance for collision. equations and dividing by ρ gives: Exactly this is the case for fluid particles in DV = g − g∇Ha stream. When particles are redirected Dtfrom the vertical downfall to horizontal In streamline coordinates along the x-axisflow the fluid is decelerated. As fluid and taking the z-direction the direction ofparticles have no brakes they will collide gravity: and the only way they can go is up, DV ∂Vx ∂Vxcreating height and thus a hydraulic jump. = +Vx = −g∇ − g∇ = z H Dt ∂t ∂xThe above explains 2 things: first of all ∂Hwhy an increasing length of vertical tail − g ⋅ sin β − g ∂xpipe leads to earlier priming, second why With a constant diameter of the pipe andan increasing resistance in the collector thus constant cross section, A, this can bepipe leads to this same result. further rewritten to:An increasing length of tail pipe leads to DQ ∂Q Q ∂Qmore time to accelerate the fluid coming = + = −A ⋅ g∇z − A ⋅ g∇H =from the roof, thus to higher velocities in Dt ∂t A ∂xthe bend to the horizontal pipe. This will ∂H − A ⋅ g ⋅ sin β − A ⋅ glead to a higher hydraulic jump when the ∂xflow is decelerated in the horizontal pipe.Also the more the flow is decelerated in with β the angle between the streamline xthe horizontal pipe, thus the higher the and the direction perpendicular to theresistance downstream of the bend, the gravity (β positive when the streamlinehigher the hydraulic jump will be. ascends).The higher the hydraulic jump is the earlier For a descending collector pipe the angle βthe full pipe diameter will be closed off by thus is negative, the term with thiswater and priming will start. parameter thus positive, driving the speedWhen the horizontal pipe is (slightly) in the collector pipe up and thus making itinclined the water will run off easier and decelerate less, producing a lessthus the hydraulic jump will be less pronounced hydraulic jump and thus
delaying priming (full bore flow) in the The basic design of the system can besystem. determined using single phase flow theory assuming full bore flow of the system.In a steady incompressible inviscid full The start up and two phase flowbore flow integration of Euler’s equations functioning of the system are moreover a streamline gives the well known complex.Bernoulli equation: In a multiple roof outlet siphonic systemp V2 the interaction between the roof outlets + gz + = constρ 2 makes it very complex and only skilledThis equation is often referred to to easily people can design a well functioningexplain the principle of siphonic roof system.drainage. 5. ReferencesThe head loss in pipe systems consists oflosses due to the friction coefficient of the - Robert W. Fox, Alan T. McDonald,pipe walls, losses due to the fittings (bends, Introduction to fluid mechanics, thirdknees, T-pieces and the roof outlet) and edition, 1985, School of Mechanicallosses due to the additional roughness Engineering Purdue University, Johncaused by welding of pipes and Wiley & Sonsfittings.The head loss due to friction along - Scott Arthur, John A. Swaffield, Siphonicthe pipe walls can be described by the roof drainage: current understanding, 2001,equation: Water research group, Department of civil L Vx2 and offshore engineering, Heriot-WattH = f University, Edinburg, Scotland (UK) D 2g - G.B. Wright, S. Arthur, J.A. Swaffield,with f the friction factor. For the Numerical simulation of the dynamicdetermination of the friction factor the operation of multi-outlet siphonic roofColebrook-White equation is most widely drainage systems, 2005, Drainage andapplied: water supply research group, School of the 1 k 2.51 build environment, Heriot-Watt University, = 0.25log s + 3.7 D Re f f Edinburg, Scotland (UK)with ks the equivalent sand grain - Scott Arthur, The priming focused designroughness. A good estimation for f is: of siphonic roof drainage, drainage −2 research group, School of the built k 5.74 environment, Heriot-Watt University, f 0 = 0.25log s + 0.9 3.7 D Re Edinburg, Scotland (UK)The head losses of fittings and roof outlets - S. Arthur, G.B. Wright, Siphonic roofcan be approximated in a similar way by: drainage systems – priming focused design, 2006, School of the built Vx2 L V2H =ξ = f e x environment, Heriot-Watt University, 2g D 2g Edinburg, Scotland (UK)with ξ a coefficient specific for each fitting - S. Arthur, J.A. Swaffield, Siphonic roofof a certain diameter and Le an equivalent drainage system analysis utilizing unsteadylength of pipe. flow theory, 2000, Department of building engineering and surveying, Heriot-Watt 4. Conclusions University, Edinburg, Scotland (UK)In this article it has been illustrated that asiphonic roof drainage system with a singleroof outlet is reasonably well understood.The governing equations are presented.