calculating head loss between two nodes on a pipe network

[ketanco]

on a pipe network analysis problem, when comparing the heads between the two adjacent points, when writing the energy equation, they took into account only the elevation and pressure heads. why didnt they take velocity head into account?

This is the question In the 13th edition of practice problems for civil engineering PE exam, on page 17-21 (solution to problem 17-11), when writing the energy equation, they took into account only the elevation and pressure heads. why didnt they take velocity head into account?

 

[fel3]

The universal practice in water system modeling is for the pipe segment between two nodes to have a consistent diameter and a uniform flow. Otherwise, an intermediate node or nodes is required. Nodes exist to separate changes in pipe sizes, to represent connections with multiple pipes (e.g. tees and crosses), and to consolidate where demands are extracted from the system or supplies are introduced into the system. It's not worth the effort, for example, to model each residential service on a street, let alone in an entire city. Instead, we geographically group several to several dozen homes that surround (usually) a node and assign the total demand from this group to the node. We geographically group other types of demands (e.g. apartments, commercial, industrial, etc.) in a similar fashion.

Back to the heart of the matter: Because the pipe segment between two nodes will have one diameter and one flow rate, it will have one velocity and thus one velocity head along its entire length. So, in applying Bernoulli's equation, the velocity head at one end of the pipe will cancel out the velocity head at the other end. Because we know this cancellation will happen when we start the problem, there is no reason to even mess with the velocity head. The same is not true for the elevation and pressure heads.

In addition, in typical water distribution systems, the velocity head is too small to worry about. For example, for a velocity of 5 ft/s, the velocity head, (V^2)/2g = 0.4 ft. The net result of the error bars for the other data used to prepare the model is generally several times larger than this. Also, compare this velocity head to a water system that operates in the 50 to 60 psi range: the HGLs range from 115 to 138 ft. The velocity head is thus a fraction of 1% of the HGLs and can be safely ignored. In water system modeling, we pay attention to the hydraulic grade line and not the energy grade line, but in other fluid mechanics applications it might be important.

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"Is it the only lesson of history that mankind is unteachable?"
--Winston S. Churchill

 

[BigInch]

Velocity head may be added when in need of slightly more net positive suction head at a pump input, but it is usually ignored there as well. I never depend on it when designing a system, but when evaluating total NPSHA in a system that is very close to NPSHR, it could make a difference in the results.

Independent events are seldomly independent.