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Date: Wed, 31 Mar 1993

Newsgroup: rec.aquaria

In article <27915-at-hacgate.SCG.HAC.COM> larisa-at-tcville.edsg.hac.com writes: >Could someone please remind me of the formula which computes total >equivalent vertical head based on measurements of vertical and horizontal >runs? I seem to recall something like this: "a horizontal run takes as >much work to pump through as a vertical run of 0.4 times its length." > >I need to find the equivalent vertical head of my overall plumbing. Also, >if you remember how to compute pressure at arbitrary head based on a >pressure measurement at a given head, feel free to include the info. > >Follow-ups to rec.aquaria unless you select otherwise. > >-- Larisa >larisa-at-tcville.edsg.hac.com > These formulas may help: HEAD = 2.31*pressure head is in units of feet pressure is in psi Bernoulli's Equation can be used to determine the total head of a system: Bernoulli's Equation: pres(1)/spwt + vel(1)^2/2GR + EL(1) + WI ==== pres(2)/spwt + vel(2)^2/2GR + EL(2) + WO + TFHL where: pres(1) = pressure at point 1 [Pascals] pres(2) = pressure at point 2 [Pascals] spwt = specific weight of fluid, typically water [Fresh H2O=9782 N/m^3 -at-20degC] vel(1) = fluid velocity at point 1 [m/s] vel(2) = fluid velocity at point 2 [m/s] EL(1) = Elevation at point 1 relative to a chosen datum(EL=0), [m] EL(2) = Elevation at point 2 [m] WI = work in; solving for this will produce total head required by a pump WO = work out, usually ignored unless there are devices in system which are storing energy, ie accumulators, etc... GR = 9.806 m/s^2, the acceleration of gravity TFHL = the total fluid head loss due to frictionary forces [m] FHL(I) = FF*TEPL*VEL^2/(2GR*DIA) where: FF = friction factor for ith section of pipe TEPL = total equivalent pipe length for ith pipe section; this includes the total straight pipe length plus equivalent pipe lengths from pipe components such as elbows, reducers, etc... [m] VEL = velocity through ith pipe section [m/s] DIA = diameter pf ith pipe section (id) [m] TFHL = FHL(1)+FHL(2)+...+FHL(n-1)+FHL(n) ---> total fluid head loss Friction factors are determined through the use of a moody's diagram. In order to determine the friction factor from the graph, the reynold's # must be calculated, as well as the relative roughness of the pipe. RE=VEL(I)*DIA(I)/KIVIS where: KIVIS=kinematic viscosity of fluid, use 1.3E-6 N/m^2 for freshwater -at-20C. if RE<2000 then FF=64/RE else use a moody diagram. Most people won't have a moody diagram handy;) therefore, if RE>2000 use a FF of 0.04 for calculations. This is a conservativevalue for FF for most applications. RELATIVE ROUGHNESS, RR=0.00006/DIA(I) for steel pipe. For copper pipe use the smooth pipe line on the moody diagram. Volumetric Flow=AREA(I)*VEL(I) All of this is very simple....NOT! ;) Friction plays a very key role in plumbing applications. Once the total head is calculated, (WI=Total Head, from bernoulli's EQN) the pump can be selected. This is also a very complicated process, but for the sake of brevity, choose a pump which will is rated for a head close to the calculated total head. Don't oversize the pump too much, as this will result in a less efficent pump setup. ############################################################# # # # o___ Stephen H. White # # _ *> / _ Internet (swhite-at-brahms.udel.edu) # # (_) \ (_) University of Delaware # # # #############################################################

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