dor040101
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- Why is it true to use cartesian coordinates for NS equations in the small gaps? How to find ##P_2##?
There is a cylinder which is held by a rope, inside a pipe. Fluid is flowing (laminar) in the direction of Q. I'm trying to calculate the velocity profile in the gaps between the pipe and cylinder, using Navier Stokes.
First question is, if ##\frac{R_1-R}{R_1}<<1##, which means the gap width is very small compared to the cylinder, is it okay to use cartesian coordinates in NS equations? why?
Also need to find ##\frac{dP}{dz}##, assuming the pressure is constant along every horizontal plane ##P=P(z)## (##z## is up).
I know that ##\frac{dP}{dz}=const## if the flow is steady state, fully developed and constant ##\mu##. So ##\frac{dP}{dz}=\frac{P_{atm}-P_{L_2}}{L_1}##
Given everything in the diagram, how to find ##P_{L_2}##? (pressure at entrance to the gap).
First question is, if ##\frac{R_1-R}{R_1}<<1##, which means the gap width is very small compared to the cylinder, is it okay to use cartesian coordinates in NS equations? why?
Also need to find ##\frac{dP}{dz}##, assuming the pressure is constant along every horizontal plane ##P=P(z)## (##z## is up).
I know that ##\frac{dP}{dz}=const## if the flow is steady state, fully developed and constant ##\mu##. So ##\frac{dP}{dz}=\frac{P_{atm}-P_{L_2}}{L_1}##
Given everything in the diagram, how to find ##P_{L_2}##? (pressure at entrance to the gap).