Calculating Speed of fuel travel in new pipeline

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

15 September 2019

Geofrey Mwangangi says that he read in the newspapers that the new oil pipeline connecting from Mombasa to Nairobi has the capacity to deliver one million litres per hour. So, he wonders: at what speed does the fuel travel in the pipe?

First of all, I checked from the Kenya Pipeline Company website and it is true that the line is operating at one million litres per hour. But that’s not its full capacity. To keep up with demand, the flow rate will be gradually increased up to about 2.6 million litres per hour by the year 2044.

To find out the speed of the fuel in the line, we ask ourselves this question: what length of this pipe would be required to enclose one million litres? To get the answer, we need to know the size of the pipe.

It is referred to as a 20-inch pipe which translates to 50cm in diameter. To calculate volume, we multiply the cross-sectional area of the pipe by length.

The area is found by multiplying the square of the radius (half of the diameter or 25cm) by pi (3.14). The answer is 1,963 square centimetres.

So, what length of pipe is needed to enclose one million litres? Before jumping to the calculator, we need to think about the units first. Since we have an area in square centimetres, we need to convert the volume to cubic centimetres (cc) and then divide the two to get an answer in centimetres.

One litre is equal to 1,000cc; so, one million litres is one billion cubic centimetres. Dividing this volume by the cross-sectional area (1,963 sq.cm) we find that we need about 500,000cm of pipe; that is 5,000m, or 5km!

Now; if the pipe is delivering one million litres per hour, it means that every hour, all the fuel in the last 5km of the pipe will be emptied. In other words, the fuel is travelling at 5km/h.

Since the pipe is 450km long, then it takes about 90 hours (almost four days) for fuel to travel from Mombasa to Nairobi.

But that should not be of any bother to us as fuel consumers since what we are concerned about is the volume that we get each day –24 million litres per day.

The older pipeline was 14-inch diameter and was operating at 880,000 litres per hour. Doing similar calculations reveals that the fuel was transported at a speed of about 10km/h. So, even though the volume flow rate was lower, the speed of the fuel was about twice the current one. How is that possible: that slower speed transports more fuel?

Well, the answer is in the size of the pipe. Increasing the diameter has a much greater impact on the volume carried (litres per hour) than changing the speed of flow (km/h).

Incidentally, before any fuel can be passed through, the pipe needs to be filled up along the entire 450km. The new line needed about 88 million litres of fuel. At the current price of about Sh100 per litre, this fill-up cost almost Sh9 billion!