The relative magnitudes of pipe losses and fittings loss in practical pipe lines.
We now
have the Darcy expression to be used with the Moody diagram, and the
expressions for losses in fittings. We know that the Moody diagram must be used
on the basis that the figures are all good approximations. Now we have
expressions for losses that may well involve similar approximations. We need to
have some idea of the use of these expressions in practice. This involves
making some calculations for a typical pipeline by way of illustrative example.
Let us take as an example a simple system of a new copper pipe of 32 mm diameter connecting two tanks filled with water with a valve in the pipe to control the rate of flow between the tanks. The system is shown in figure 8-5 and it can be seen that there are four bends in the pipe and these can be taken to be swept bends. Let us suppose that the pipe has a total length of 70 m, that the velocity of water in the pipe is to be 3 m/s, and attempt to find the minimum difference in level between the tanks that would be required to maintain this velocity. We can apply the total head equation to points 1 and 2 in the free surfaces and write :
+ the loss between 1 and 2.
As and this reduces to :
= the loss between 1 and 2
The minimum loss between 1 and 2 is the sum of the loss in the pipe, the loss at entry to the pipe, the loss in four bends, the loss in the open valve and the loss at exit from the pipe. We have expressions for all these losses, so we can write :
The loss between 1 and 2 = .
Clearly we need a value for but we do not know Re or the relative roughness . However, for water, = 1000 kg/m3 and can be taken to be 0.001 kg m/s2 and then :
Re = . For new copper pipe is 0.0015 and then the equivalent sand grain roughness for the pipe = .
From these figures = using the Moody diagram. Then :
the loss between 1 and 2 = = =
In this calculation the suspect figure is that for . Had we used a higher value of of, say 0.002, the calculated value of the loss in the pipe would be 21.07m. The difference of 0.8m is more than a half of the calculated value of the other losses. There is nothing unusual in the outcome of these calculations and it is not surprising that engineers decide to ignore the loss caused by fittings when they see that the context of the calculation makes this justifiable. The loss in the fittings is then frequently referred to as a minor loss.