Optimum Oil Pipeline Flow Rate & Angle

[khfrekek92]

Homework Statement

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?

Homework Equations

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

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...

 

[paranormal]

Yes, your calculation for the maximum flow rate is correct. Multiplying the critical velocity by the cross-sectional area will give you the maximum flow rate for the pipeline.

To find the slope of the pipeline, you can use the Bernoulli's equation, which states that the sum of the pressure, kinetic energy, and potential energy per unit volume is constant along a streamline. In this case, we can ignore the potential energy term since the pipeline is horizontal.

Therefore, the slope of the pipeline can be calculated using the following equation:

m = (1/ρg) (P2 - P1) / (Lsinθ)

Where m is the slope, ρ is the density of the oil, g is the acceleration due to gravity, P2 is the pressure at the end of the pipeline, P1 is the pressure at the start of the pipeline, L is the length of the pipeline, and θ is the angle of the pipeline with respect to the horizontal.

Using this equation, we can determine the slope of the pipeline that will result in the maximum flow rate while remaining non-turbulent.

Lastly, whether or not this is a feasible way to design a pipeline depends on various factors such as cost, terrain, and environmental impact. It is important to consider all these factors in addition to the technical aspects when designing a pipeline.