Non-turbulent oil pipeline operated by gravity.. maximum flow rate and optimum angle?

[khfrekek92]

1. The problem statement, all variables and given/known data

You wish to design an oil pipeline such that the flow rate under gravity alone will be as large as possible while remaining non-turbulent. the diameter is .45m, the viscosity is .385 n-sec/m^2, and the reynolds number is 2000.

(a) what is the maximum flow rate you can achieve?
(b) what should be the slope of the pipeline (m/km)?
(c) is this a feasible way to design a pipeline?

2. Relevant equations

Vc=Rn/rho(D) (critical velocity)

3. The attempt at a solution

By using the above reynolds equation I've found that the maximum velocity before turbulence to be 2.01 m/s. Then I assume that I multiply this by the area (pi(.45/2)^2) to get the maximum flow rate? Is that right? Then I have no idea how to find slope of the pipeline afterwareds.. any help is much appreciated!

[yus310]

It depends on what tools you have rather what tools you can use/comfortable with. Basic theory & computations, via the bernoulli's equation for inviscid flow, can get you a basic answer based on raw calculates for pressure, density, elevation, etc.

If you also add factors like minor head loss, major head loss, fricitional losses, changes in head,

you can easily make some raw pipeline designations for this .. if you don't know the equations.. see attached.. they are given in these examples...

If you are a grad. student, then things like computational work, navies stokes, etc. will do equally as well and better..

best

[khfrekek92]

Oh wow that all looks so complicated, probably too much so for my physics class, which is just an honors-level 2nd year physics major class.. Is flow rate simply just Av?

[yus310]

no it is pretty simple like those equations...