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The flow in manifolds is extensively encountered in many industrial processes when it is necessary to distribute a large fluid stream into several parallel streams and then to collect them into one discharge stream, such as fuel cells, plate heat exchanger, radial flow reactor, and irrigation. Manifolds can usually be categorized into one of the following types: dividing, combining, Z-type and U-type manifolds. A key question is the uniformity of the flow distribution and pressure drop.
Traditionally, most of theoretical models are based on Bernoulli equation after taking the frictional losses into account using a control volume. The frictional loss is described using the Darcy–Weisbach equation. One obtains a governing equation of dividing flow as follows:
where
∆X = L/n. The n is the number of ports and L the length of the manifold. This is fundamental of manifold and network models. Thus, a T-junction can be represented by two Bernoulli equations according to two flow outlets. A flow in manifold can be represented by a channel network model. A multi-scale parallel channel networks is usually described as the lattice network using analogy with the conventional electric circuit methods. A generalized model of the flow distribution in channel networks of planar fuel cells. Similar to Ohm's law, the pressure drop is assumed to be proportional to the flow rates. The relationship of pressure drop, flow rate and flow resistance is described as Q = ∆P/R. f = 64/Re for laminar flow where Re is the Reynolds number. The frictional resistance, R = 128 μ L π d 4 {\displaystyle \,R\,={\tfrac {\,128\mu \,L}{\pi \,d^{4}}}} using Poiseuille's law. Since they have same diameter and length in Fig. 3, their resistances are same, R2 = R3. Thus the velocities should be equal in two outlets or the flow rates should be equal according to the assumptions. Obviously this disobeys our observations. Our observations show that the greater the velocity , the more fluid fraction through the straight direction. Only under very slow laminar flow, Q2 may be equal to Q3.