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I was recently looking at two immiscible fluids in a 2-D Poiseuille Flow with two immiscible fluids of different densities. Let the total distance of the channel be ##L+\epsilon L##, where the dividing line between the two flows is ##L##. I was thinking of the possible flow profiles and finally decided to solve the problem. When I did, I noticed the maximums of the two fluids' velocities always occurred at the same height (keep in mind I'm talking mathematically, as ##v_1 \in [0,L]## and ##v_2 \in [L,\epsilon L]##). The implication being the flow could never have two maximums.

Can someone explain why we cannot have two maximums?

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# Channel Flow Fluids

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