What is an N^1.85 Graph?

MeyerFire University | FX106.03

By Franck Orset

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TRANSCRIPT

What is an N^1.85 (N to the 1.85 power) graph? 

​We need to be able to quantify the flow and pressure for a water supply.  

Generally for a water supply, the lower the flow rate, the higher the available pressure. 

As more water moves through a pipe network, the faster movement creates more friction at the pipe walls, and this additional friction decreases the pressure along the length of the pipe. 

So, as more water moves through a pipe network, more friction loss happens, and less pressure is available at the point where it is used. 

In order to quantify the pressure and flow available from a water supply, we create a graph that shows how much pressure is available at different flow rates. 

So to graph this, with flow rate on the horizontal x-axis, and available pressure along the vertical y-axis, then our relationship might look something like this. 

However, this relationship is not linear. Pressure and flow are related, but not linearly. 

If we graph the actual relationship along a normal graph, our relationship would look like this. It’s an exponential relationship. 

What is that relationship? Why is the exponent 1.85? 

The Hazen-Williams formula related friction losses inside a pipe to the flow and pressure of the pipe.  

Pressure (p) equals 4.52 times flow rate (Q) to the 1.85th power, divided by c-factor (C) to the 1.85th power, and pipe diameter (d) to the 4.87th power. 

For a given system, where the friction loss coefficient of the pipe and the diameters of the network remains consistent across different flow rates… 

then the Hazen William can be simplified to P = Constant times Q to the 1.85th power. 

This doesn’t change how the water supply provides water, it just shows that the relationship between flow rate, represented here as “Q”, is related to pressure by a 1.85 exponent. 

To make our lives a whole lot easier when graphing this relationship, we use a graph that is called a Log Graph, or N to the 1.85th power, or Q to the 1.85th power graph sheet. 

This graph takes the x-axis and scales it according to the 1.85th power. 

Now, instead of our relationship showing a curve, this graphed relationship now becomes a straight line, because the x-axis has been adjusted. 

This visualization is very helpful to extrapolate the expected residual pressure at a larger flow rate.  

This is also helpful when analyzing what a system demand will be and comparing it against the available water supply. A sprinkler system or standpipe system will demand a flow rate and pressure. With this graph, we can easily compare the available water supply against the system demand. 

In the old days we would hand-graph our curve knowing two points – a static pressure, with no flow, and a residual pressure at a measured flow rate. Using the log graph, we were then able to connect these two points with a straight line and could interpolate or extrapolate at any point on the supply line. 

With twenty first century technology, we very well understand this non-linear relationship and could graph our results along a traditional x- and y-axis with a calculated curve shown. However, our simplified tradition of the log graph has kept reading the water supply results quick and consistent. 

So what is a log graph, or N to the 1.85th power graph, or Q to the 1.85th power graph? 

It’s a graph with a scaled x-axis that allows us to quickly and easily see available pressure across different flow rates in a hydraulic water supply curve  

For Franck Orset I’m Jeff Kelm, this is MeyerFire University