Fluid Mechanics Chapter 7 – Steady Flow in Pipes P.7-26 7.5.2Branched-pipe Problemh1h3h2Jreservoir 1reservoir 3reservoir 2pipe1, k1pipe2, k2pipe 3, k3Q1Q2Q3Assume h1> h2> h3and the 3 pipes intersect at junction J. As h1is the highest head, the flow in pipe 1 must be toward J. As h3is the lowest head, Q3is flowing from J to the reservoir 3. The flow Q2’s direction is unknown because it depends on the head at junction J. If hJbe the head at junction J. There are two possible cases (i)h1> hJ> h2, or (ii) h2> hJ> h3For case (i), h1> hJ> h2, Q2is from J to reservoir 2. Q1- Q2- Q3= 0 h1– hJ= k1*Q12 hJ- h2= k2*Q22(7.24)hJ- h3= k3*Q32For case (ii), h2> hJ> h3, Q2is from reservoir 2 to J. Q1+ Q2- Q3= 0 h1– hJ= k1*Q12 h2– hJ= k2*Q22(7.25) hJ- h3= k3*Q32
Fluid Mechanics Chapter 7 – Steady Flow in Pipes P.7-27 Both sets of equations have 4 unknowns Q1, Q2, Q3and hJ. We have to determine which case controls the problem. It is determined by assuming hJ= h2, i.e. no flow from J to reservoir 2. Therefore Q1’ = hhk121−(7.26) Q3’ = hhk233−(7.27) If Q1’ > Q3’, Q2is from J to reservoir 2 - case (i). If Q1’ < Q3’, Q2is from reservoir 2 to J - case (ii).
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