Parallel pipeline problem
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When the fluid passes through the two parallel pipelines 1 and 2, flow stagnation occurs in both pipelines. If the lengths of the two pipes are L1=2L2 and the diameters are d1=2d2, then the volume flow rate ratio V1/V2 is ( ). A、0.5 B、0.25 C、0.125 D、0.0625. I got 8 as the answer, but it’s not among the options?
Has anyone skilled at calculating it figured it out? How is it calculated?
It should be 4. In parallel pipes, the pressure difference is equal: deltaP=λ(L1/d1)(u1)^2/2=λ(L2/d2)(u2)^2/2; hence, u1=u2, meaning the flow velocities in the two pipes are the same. The flow ratio is (A1×u1)/(A2×u2) = A1/A2 = (d1)^2/(d2)^2 = 4
Wrong; the resistance losses in parallel pipelines are equal, but λ is not necessarily equal – λ = 64/Re (stagnation)
The pressure differences across the parallel pipes are equal: h(f1) = h(f2). h(f) = λ(L/d)(u1)^2/2 = 64*μ/d/u/ρ*L/d*u*u/2 = (32μ/ρ)*(4/π)*(L*V/d^4). Therefore, v1/v2 = (d1^4*L2) / (d2^4*L1) = 8. The answer might be incorrect
The original poster is being overly fixated on this issue. If λ also needs to be substituted, then there are several solutions. The original poster only calculated the λ value for laminar flow. There are also turbulent cases, for which the formula is more complex and varies logarithmically with the pipe diameter. Moreover, in engineering practice, laminar flow is rarely seen in the pump outlet piping; the vast majority are in a turbulent state, as otherwise it would not be economical. Is what the original poster is doing a bit theoretical?
Please read the question carefully, but the formula I used is this: V1/V2 = (d1^5 / (√(coefficient of friction 1 * (L1 + Le1)))) : (d2^5 / (√(coefficient of friction 2 * (L2 + Le2))))، where Le1 = Le2 = 0 and the coefficient of friction equals 64/Re; this is even simpler than the formula above. Last edited by grandf on 2009-3-10 08:54.]
I think the friction coefficient λ should be taken into account for this problem; after all, the question states that the flow condition is stagnant, and thus the formula λ=64/Re needs to be used. If we are in a region of complete turbulence, that is, in the regime where resistance is proportional to the square of velocity, then there’s no need to consider this factor. After making the calculations, I think the answer should be 8, just like the original poster
By directly applying Hagen’s leaf formula, it is possible to calculate that u1=u2; and by using V=Au, the answer can be determined. For 8
u1=2u2, I just made a mistake. It must be 8