# Fast Track NDF calculations using the

# Correction Factor method

## NDF converts Night Leakage Rate/hour to daily leakage

Leakage can be assessed either from Water Balance or from Minimum Night Flows. However, one of the most common errors in leakage calculations is the simple assumption that night leakage per hour can be simply multiplied by 24 hours per day to assess daily leakage; or that daily leakage from a water balance can be converted to hourly leakage at night by dividing by 24 hours/day. Because leak flow rates and the N1 exponent vary with the average zone pressure, a Night-Day Factor (NDF) of 24 hours/day is only valid when the average zone pressure is constant (or almost constant) for 24 hours per day. The equation relating Daily Leakage Rate to Night Leakage Rate (measured during the hour of Minimum Night Flow) is:

**Daily Leakage (Volume/day) = Night Leakage Rate (volume/hour) x NDF (hours/day)…..(1)**

In practice, the Night-Day Factor NDF (known as Hour-Day Factor HDF in the UK) can vary from less than 10 hours/day for gravity systems with high leakage and frictional losses, to more than 60 hours/day for pressure and flow modulated systems. Therefore, the assumption of a fixed NDF of 24 hours per day can introduce large systematic errors into leakage calculations based on Night Flows.

Fortunately, it is now easier to assess Night-Day Factor for any particular profile of average pressures in a Zone within a distribution system, using the Correction Factor method which allows for variable area leakage paths which change with average zone pressure. The first step is to define and identify where to measure average zone pressure.

## Define an Average Zone Point to measure Average Zone Pressures

The first essential step is to define, within each Zone, a location for pressure measurement known as the Average Zone Point (AZP), which can be considered as being approximately representative of the hourly variation of average pressure in the Zone. More information on establishing AZPs can be found in the ‘Average Zone Point’ Webpage.

It is **essential** to use the pressure at the Average Zone Point for NDF and several other calculations associated with leakage, such as Night Flow component analysis, pressure management predictions etc. If, as an attempt to short-cut the proper procedure, no AZP is established, or the inlet pressure or the critical point pressure is used for NDF calculations, the results may be incorrect and misleading to an unknown extent, and the investment of time, effort and resources will have been wasted. Establishing an AZP for each Zone is one of the best, easiest and cheapest investments in leakage and pressure data collection that it is possible to make.

The next step is to set up a pressure logger at the Average Zone Point, and record the pressures for 7 days, then calculate the 7 days x 24 hours average hourly pressure. The blue line in Figure 1 shows a 7 day average zone pressure profile in a zone supplied by gravity. When consumption is minimal (at night), the AZP pressure is highest, then fluctuates up and down during the day as consumption falls and rises. As leak flow rate is directly related to AZP pressure and N1, the leak flow rate also rises and falls as shown by the continuous red line; in this example, for demonstration purposes, a linear relationship (N1 = 1.0) between AZP pressure and Leak Flow Rate has been assumed for simplicity.

If the Leak Flow Rate (volume/hour) at the time of MNF is multiplied by 24 hours/day (as shown by the dashed red line), the daily leakage volume would obviously be over-estimated for this type of AZP pressure profile, where the ratio of daily average AZP pressure (AZPave) to AZP pressure at the time of minimum night flow (AZPmnf) is less than 1.0 (AZPave/AZPmnf < 1.0). So how can the data in Figure 1 be used to calculate the appropriate Night-Day Factor?

## Fast Track Correction Factor method of calculating NDF, for practitioners

Before the development of the fast-track Correction Factor method of assessing NDF by WLRandA Ltd in late 2017, the NDFCalc spreadsheet in the AZP&NDFCalcs software was used to calculate NDFs. Hourly AZP pressures were entered into the spreadsheet to automatically calculate the NDF for assumed constant N1 values of 0.5, 1.0, 1.5 and one other chosen N1 value. The methodology and mathematics used in the NDFCalc Spreadsheet method is explained in the previous July 2016 version of this webpage, which can be found in the Archive.

The fast-track Correction Factor method simplifies calculations considerably, even though the calculations now take account of the FAVAD concept and correct for the fact that, because the Variable Area component of leak flow rate reduces with pressure, N1 also reduces with pressure. The red dashed line example Figure 2 below, from the FAVAD and N1 Update webpage, shows how an N1 of, for example, 1.29 from an N1 test at an average AZP of 40 metres would reduce if average zone pressure is reduced.

This may seem quite complex, but it is the reality of pressure:leak flow relationships, and needs to be recognized as such. Despite this complexity, the Correction Factor method of calculating NDF is designed to be simpler, faster and more reliable than the previous AZP&NDFCalcs spreadsheet method which assumed a constant N1 that does not vary with pressure.

## NDF Fast-Track Approximate Method

If you only want an approximate quick answer for NDF, use the graph in Figure 3. Using Figure 1 data as an example, calculate the ratio of AZPave/AZPmnf = 62.1 m/72.4 m = 0.86.

Then, in Figure 3 below, read upwards from AZPave/AZPmnf = 0.86 on the X axis. For any value of N1 at the AZPave, choose the corresponding curved line and read the NDF from the Y axis. The curved line for N1 = 1.0 at AZPave is highlighted in red.

• If N1 at AZPave is 0.5, NDF for Figure 1 data is around 22 hours per day

• If N1 at AZPave is 1.0 NDF for Figure 1 data is around 20 hours per day

• If N1 at AZPave is 1.5, NDF for Figure 1 data is around 19 hours per day

## NDF Fast-Track Correction Factor method

The FAVAD equation for NDF is

**NDF (hours/day) = CF x 24 x AZPave/AZPmnf …(2)**

where CF is the Correction Factor which can be interpolated from Figure 4 below. The curved line for N1 = 1.0 at AZPave is highlighted in red.

For the AZPave/AZPmnf value of 0.86 in Figure 1, the interpolated CF values are:

• If N1 at AZPave = 1.30, interpolated CF = 0.95, NDF = 0.95 x 24 x 0.86 = 19.6 hours/day

• If N1 at AZPave = 1.00, interpolated CF = 1.00, NDF = 1.00 x 24 x 0.86 = 20.6 hours/day

• If N1 at AZPave = 0.70, interpolated CF = 1.05, NDF = 1.05 x 24 x 0.86 = 21.7 hours/day

Alternatively, the CF values can be interpolated from Look-Up Table 1 below. For the AZPave/AZPmnf value of 0.86 in Figure 1, the interpolated CF values are:

• If N1 at AZPave = 1.30, interpolated CF = 0.954, NDF = 0.954 x 24 x 0.86 = 19.7 hours/day

• If N1at AZPave = 1.00, interpolated CF = 0.996, NDF = 0.996 x 24 x 0.86 = 20.6 hours/day

• If N1at AZPave = 0.70, interpolated CF = 1.045, NDF = 1.045 x 24 x 0.86 = 21.6 hours/day

which are very close to the NDF values calculated using CF values read from Figure 4.

**Look-Up Table 1: Correction Factors for AZPave/AZPmnf vs N1 at AZPave**

The most accurate calculations of NDF are obtained by using the equation for the Correction Factor CF, which can be used for Smart System automatic processing of data from multiple Zones. For further information on the Correction Factor equation, Contact Us.

## Average Zone Point Pressure Profiles where AZPave/AZPmnf exceeds 1.0

Figures 3 and 4 show that, when the ratio AZPave/AZPmnf is close to 1.0, for example in the range 0.9 to 1.1, the NDF will be always be close to 24 hours per day. But what if the AZP pressure profile in the Zone in Figure 1 is modified by reducing the pressures at night to 40 metres, as shown in Figure 5? This type of pressure management is increasingly popular in many countries; the overnight leak flow rates are reduced, and because the maximum pressure is also reduced, there is often a reduction in burst frequency on mains and services, leading to an extension of asset life.

If the Leak Flow Rate (volume/hour) at the time of MNF in Figure 5 is multiplied by 24 hours/day (as shown by the dashed red line), the daily leakage volume would obviously be under-estimated for this type of AZP pressure profile, where AZPave (55.3 metres) is more than AZPmnf (44 metres), and AZPave/AZPmnf exceeds 1.0.

### Now check if you can now calculate NDFs for Figure 4 data yourself

Calculate the ratio AZPave/AZPmnf = 55.3/44 = 1.26 and then use Figures 3, 4 and the CF Table 1 to calculate:

a) From Figure 3, the maximum and minimum possible values of NDF for N1 = 1.5 and 0.5

b) From Figure 4 and the CF Table, values of the N1 at AZPaverage are 1.3, 1.0 and 0.7.

Here are the first few calculations to get you started; answers can be found at the end of this article.

### Figure 3: imagine drawing a line up from AZPave/AZPmnf = 1.26 on the X axis.

If N1 at AZPave = 1.5, NDF = around 34 hours/day.

If N1 at AZPave = 1.0 (red line), NDF = around 30.5 hours/day.

If N1 at AZPave = 0.5, NDF = around 27 hours/day.

**Figure 4:** draw a line up from AZPave/AZPmnf = 1.26 on the X axis.

If N1 at AZPave = 1.30, interpolated CF = 1.06, NDF = 1.06 x 24 x1.26 = 32.0 hours/day

If N1 at AZPave = 1.00, interpolated CF = ????, NDF = ???? x 24 x1.26 = ???? hours/day

If N1 at AZPave = 0.70, interpolated CF = ???? NDF = ???? x 24 x 1.26 = ???? hours/day

**From CF Table 1: **Interpolate CF values from columns for AZPave/AZPmnf of 1.2 and 1.4.

If N1 at AZPave = 1.30, interpolated CF = 1.066, NDF = 1.066 x 24 x 1.26 = 32.2 hours/day

If N1 at AZPave = 1.00, interpolated CF = ?????, NDF = ????? x 24 x 1.26 = ???? hours/day

If N1 at AZPave = 0.70, interpolated CF = ?????, NDF = ????? x 24 x 1.26 = ???? hours/day

If you get the correct answers, you now know how to calculate NDF using the Correction Factor method, in 3 different ways. Congratulations! …. but don’t forget that you must use pressures at the Average Zone Point!

Given the range of NDF values for N1s between 0.7 and 1.3, if you were using NDFs to calculate daily leakage from night flows, you would be satisfied to use an estimated or average value of N1 for the calculation? If you are not satisfied, you need to do an N1 Test, following the N1 Test Protocol.

## More extreme cases of High Ratios of AZPave/AZPmnf

Figure 6 shows a low pressure gravity system with pressure reduction at night. The ratio of AZPave/AZPmnf is 16.61 m/8.7 m = 1.91.

The approximate estimate method in Figure 7 below is adequate in this case to show that the NDF could be anywhere between 33 and 64 hours/day, depending upon the N1 at the AZPave of 16.6 metres. Clearly, in this case, an N1 test was essential to be reasonably sure of the correct NDF to use (and was in fact carried out).

## Summary:

This updated version of the Night Day Factor Webpage will, it is hoped, encourage more practitioners to calculate NDF values, now that they can use the more technically correct Fast Track Correction Factor approach incorporating FAVAD concepts, rather than having to assume a constant N1 and enter data into the NDF Calcs Worksheet in the AZP&NDFCalcs software (which will now no longer be issued through LEAKSSuite).

The fastest approximate method of assessing NDF is the graph in Figure 3 (and Figure 7 above). A more reliable estimate based on assessment of Correction Factor CF can be made from Figure 4 or Table 1. The most accurate calculations of NDF are obtained by using the equation (not shown here) for the Correction Factor CF, which can be used for Smart System automatic processing of data from multiple Zones. For further information on the CF equation, Contact Us.

Allan Lambert

12th November 2011

Answers to example questions:

**Figure 4:** draw a line up from AZPave/AZPmnf = 1.26 on the X axis.

If N1 = 1.3, CF = 1.06 and NDF = CF x 24 x AZPave/AZPmnf = 1.06 x 24 x 1.26 = 32.0

If N1 = 1.0, CF = **0.99** and NDF = CF x 24 x AZPave/AZPmnf = **0.99 **x 24 x 1.26 = 29.9

If N1 = 0.7, CF = **0.92** and NDF = CF x 24 x AZPave/AZPmnf = **0.92** x 24 x 1.26 = 27.8

**From Table:** interpolate CF values between columns for AZPave/AZPmnf of 1.2 and 1.4.

If N1 = 1.3, CF = 1.066 and NDF = CF x 24 x AZPave/AZPmnf = 1.066 x 24 x 1.26 = 32.2

If N1 = 1.0, CF = **0.993** and NDF = CF x 24 x AZPave/AZPmnf =** 0.993** x 24 x 1.26 = 30.0

If N1 = 0.7, CF = **0.930** and NDF = CF x 24 x AZPave/AZPmnf =** 0.930** x 24 x 1.26 = 28.1