We talked before about static head or static pressure.
Residual pressure differs from the static pressure because it accounts for friction
and minor losses between the source and a given study point.
Let’s say we are installing a new pipeline that runs between points 1 and 2 shown on
this map.
At point 1 we are connecting to an existing waterline, and at point 2 we are terminating
at a future connection point.
The tool we use to calculate the residual pressure at a given point in a system is conservation
of energy.
The energy in a pressurized pipeline can be represented as follows.
At point 1 we have the elevation of the pipeline and the pressure head accounting for the potential
energy in the pipeline.
Also at point 1 we have the velocity head which accounts for the kinetic energy in the
pipeline.
As the water travels toward point 2 energy is lost due to friction along the pipeline
as well as at the bends and fittings
in the pipeline.
In theory, the velocity head parallels the hydraulic head along the pipeline.
When we arrive at point 2, the energy is also given by the elevation, pressure and velocity
heads.
The red line represents the Energy Grade Line or EGL,
while the blue line represents the hydraulic grade line, or HGL.
The change in the HGL between point 1 and point 2 is due to the losses from friction
and fittings.
Therefore if we want to create an expression that defines the energy of the system as water
moves from point 1 to point 2 we have the elevation, pressure and velocity
heads at point 1 being equal to the elevation, pressure and velocity head at point
2 plus the headloss due to friction,
plus the summation of all the minor losses due to pipe fittings.
The headloss in this expression could be estimated using the Darcy-Weisbach or Hazen-Williams
equations.
The minor losses are found using the expression of ‘k’ times the velocity head.
where k is the minor loss coefficient which is chosen based upon the type of fitting
causing the minor losses.
Manufacturers of fittings will supply k values for their products.
But for most pipe fittings you can simply look up the k value from a trustworthy source
such as the 3rd Edition of “Pumping Station Design”, which is my preferred source.
In a situation like this the starting residual pressure, the starting and ending elevations
are all known.
The design flowrate and the pipe diameter (or diameters) are known, because you determined
them from the demand analysis and by applying the max velocity or maximum unit headloss
criteria provided by the agency.
The first step is to, once again, find the velocity in the pipeline.
Next, calculate the headloss in the pipeline using the Darcy-Weisbach or Hazen-Williams
and then the minor losses as well.
With these terms defined let me re-write our conservation of energy equation.
If the diameter of the pipe does not change, then the velocity will not change, so the
velocity heads will cancel out.
We can then solve the energy equation for the pressure head at point 2
Finally, just plug in your values and calculate the result.
I personally like to calculate the pressure head and then convert to psi after the fact,
rather than try to substitute in the unit weight of water.
Even after you calculate the result.
This still begs the question: Is the residual pressure enough?
Is it too much?
We talked about the limits to static head, but this is residual pressure.
As it turns out the minimum residual pressure can vary depending upon the demand scenario
that you are analyzing.
For example if you are analyzing for Max Day demand, your minimum residual pressure may
be 40 – 60 psi.
For the Peak hour, it may be 30 – 50 psi.
For the max day plus fire flow scenario most agencies state that this should be 20 psi.
I have not seen any other value stated.
I suppose this is because most fire fighting tools are developed to meet a certain fire
delivery requirement and this requirement is 20 psi.
The 20 psi minimum is stated in the International Fire Code (specifically, a fire hydrant must
be able to discharge 1500 gpm at a minimum pressure of 20 psi).
However, apart from the fire flow, an agency has some discretion as to how much residual
pressure they think their residents need to supply their water users for the other demand
scenarios.