The speed of fuel in the pipeline

 By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

12 December 2010

How fast does a liquid flows through a pipe? This question occurred to James Wainaina when he was driving from Mombasa to Nairobi recently: “Can I drive faster than the fuel in the petroleum pipeline?”

To get the answer, we need some basic information about the pipeline. The Mombasa to Nairobi section has a 14-inch diameter and a total length of about 450km. Now this is slightly shorter than the 500km distance along the highway. The reason is that the pipe runs over a straighter path than the road.

Before working out the speed of the fuel in the pipeline, an interesting fact comes out the parameters: this is that, at any one time, there is a huge volume of product inside the pipe.

The pipeline can be seen as a very long cylinder of 14-inch diameter and 450km in length. The volume of such a shape is equal to the cross-sectional area multiplied by the length.

The area is simply pi-r-squared. Now the radius of the pipe is 7 inches (half the diameter). Converting that to centimetres yields 17.78cm; therefore the area is about 1,000 square-cm.

What then, is the volume of fuel contained in 1km of the pipeline? Well; one kilometre is equal to 1,000m and one metre is 100cm; therefore, 1km has 100,000cm. Since volume is area (1,000sq-cm) x length (100,000cm), the answer comes to 100,000,000 cubic centimetres (cc).

But one litre (L) is 1,000cc; so, one kilometre of the pipeline contains 100,000L of fuel…therefore the entire 450km Mombasa-Nairobi section has 45,000,000L at any one time. Yes; 45 million litres!

Of course this fuel doesn’t just sit there: it is in constant flow. However, when the pipeline was first installed, this “initial” fill had to be pumped in before any output could be discharged at the Nairobi outlet.

This initial fill is a hidden installation cost for any pipeline. Some one must pay to fill up the pipeline before it can begin pumping. At today’s prices of Sh90 per litre, filling the pipeline would cost about Sh4 billion.

Now the pumping rate of the Mombasa-Nairobi section is 440,000L per hour. There was talk of increasing the capacity to 880,000 some time back, but I checked the Kenya Pipeline Company website and it says 440,000L/h. So I will use the old figure.

At this pumping rate, it would take about 100 hours (4 days) to pump out all the 45,000,000L in the pipe. This must be the time it took to fill the line after installation. It is also the speed of flow of the fuel; that is, 450km in 100h, or 4.5km/h. So yes, James; you were driving much faster than the fuel in the pipeline.