Working out the speed of water supplied to Nairobi

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

03 November 2019

After reading the article about the speed of fuel in the Mombasa – Nairobi pipeline, a reader asked me if the water supplied to Nairobi moves faster or slower. At that time, we found that the fuel travels at about 5km per hour.

In the case of Nairobi’s water, things are a lot more complicated. First of all, there are a number of pipelines supplying water to the city. A sketch map on the Nairobi Water Company website shows a total of nine lines – five carrying raw, untreated water and four bringing clean, treated water.

But don’t worry: the raw water is treated on arrival before being poured into the supply lines comes to your house. Drink it without fear.

The main supply comes from the Ng’ethu treatment works in Kiambu. This source provides about 433 million liters, representing over 80 per cent of all the water consumed in Nairobi. Three quarters of that (330 million litres) comes from the Ndakaini Reservoir in raw form and then treated at Ng’ethu.

The remaining 103 million liters of the Ng’ethu water is tapped on site from the Chania River. From here, all the water is delivered to Nairobi in three parallel pipelines of different sizes – 1.4m, 1.0m and 0.7m in diameters. The length of these pipes is about 40km.

Since the water from Ng’ethu is not pumped – it flows by gravity – the speed in the three pipes is the same. So, to find the speed, we simply divide the volume supplied by the total cross-sectional.

The largest pipe has a cross-sectional are of about 1.54 square metres. The next one is 0.785 and the smallest is 0.385 square metres. Thus, the total cross-sectional area comes to about 2.71sq.m.

This source supplies 433 million litres per day; that is an average of 18 million litres per hour. Since one million litres are equal to 1,000 cubic metres, this flow rate is equivalent to 18,000 cubic metres per hour.

This water is passing through a combined cross-sectional area of 2.71 square metres; therefore, the speed comes to 18,000 divided by 2.71. That is, 6,64 metres per hour. In other words, 6.64km/h. It turns out that, just like the fuel in the pipeline from Mombasa, the water coming to Nairobi is also quite slow.

To verify these numbers, I checked the design specifications for the water pipelines and found that the maximum speed is 2 metres per second. Since there are 3,600 seconds in one hour, this works out to 7,200m/h. That is, 7.2km/h. Thus, the system is operating at about 80 per cent capacity.

The final question, then, is: why do the engineers limit the speeds to such slow levels? The answer has to do with cornering. Have you ever noticed that when a car goes around a corner, you feel a force pushing you to the outer direction? The faster the car, the stronger the force

The same effect is experienced by a liquid in a pipe. If it moves too fast round bends and corners, the outward force can be big enough to break the pipe.