# What is the Night-Day Factor NDF and why is it important?

## NDF converts Night Leakage Rate (per hour) to Daily leakage, and vice-versa

Leakage can be assessed either from Water Balance or from Minimum Night Flows. However, one of the most common errors in leakage calculations is to simply assume that daily leakage from a water balance can be converted to hourly leakage at night by dividing by 24 hours/day; or that night leakage per hour can be simply multiplied by 24 hours per day to assess daily leakage. These assumptions would only be correct if the average pressure in the Zone is constant for 24 hours per day, because leak flow rates vary with the average pressure and N1 exponent in the Zone, as described in __FAVAD N1__.

In practice, the multiplier in Hours/day, known as the Night-Day Factor NDF (or Hour-Day Factor HDF in the UK) can vary from less than 12 hours/day for gravity systems with high leakage and frictional losses, to more than 30 hours/day for pressure and flow modulated systems, so the assumption of a fixed NDF of 24 hours per day, can introduce large systematic errors to leakage calculations.

Figure A below shows Zone Inflow (split into customer use and leakage) and Average Zone Pressure, for a system supplied by gravity. The Average Zone Pressure is highest at night, but reduces during daytime when consumption increases, resulting in a reduced leakage rate for most of the 24 hours. In this situation, it is evident thatif the Night Leakage Rate in volume/hour were to be multiplied by 24 hours/day, the Daily Leakage volume would be over-estimated. The Night-Day Factor for a system supplied by gravity with a reasonably steady inlet pressure is therefore normally less than 24 hours/day.

Figure B below shows Zone Inflow (split into customer use and leakage) and Average Zone Pressure, for a pressure controlled system, in which the pressure at night is deliberately reduced by pump scheduling, or by a pressure reducing valve with time modulation or flow modulation. The Average Zone Pressure is now lower at night than during the rest of the day, resulting in an increased leakage rate for most of the daytime hours. In this situation it is evident that if the Night Leakage Rate in volume/hour were to be multiplied by 24 hours/day, the Daily Leakage volume would be under-estimated. The Night-Day Factor for this type of pressure management is therefore normally more than 24 hours/day.

Fortunately, it is quite a straightforward matter to assess the Night-Day Factor for any particular Zone within a distribution system.

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 ‘Pressure Measurements’ Slide of the explanatory Power Point AZP&NDFCalcsPPTJuly2016 and in __Guideline 2013L__ on calculation of Average Pressure.

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 will generally be incorrect and misleading, 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, record the pressures for 7 days, calculate the 7 days x 24 hours average hourly pressure. Then follow the instructions in the ‘**Calculate NDF**’ Worksheet of the __AZP&NDFCalcs__ free software and enter the data as shown in Table 1 below. Any units can be used for pressure provided they are consistent.

It can be seen from the lowest part of Table 1 that the NDF varies from day to day. Also, the leak flow rates of leaks with higher N1 exponents are more sensitive to pressure, resulting in a lower NDF in the Zone in Table 1 where AZP pressures are higher at night than during daytime hours. The average weekly NDF is not 24 hours per day, but between 18.6 and 21.9 hours per day depending on the assumed N1 exponent. For an assumed average N1 exponent of 1.0, the NDF is 20.1 hours.

**Table 1: Example calculation in AZP&NDFCalcs Free Software; AZP Pressure highest at night.**

Table 2 shows the effect of reducing overnight AZP Pressures to 50 metres between 00 and 01 hours, and 05 and 06 hours; and to 44 metres from 01 to 05 hours.

**Table 2: Example calculation in AZP&NDFCalcs Free Software; AZP Pressure lowered at night.**

The NDF continues to vary from day to day, but in contrast to Table 1, higher N1 exponents result in a higher NDF in the zone when AZP Pressures are lower at night than during daytime hours. The average weekly NDF is not 24 hours per day but between 26.8 and 34.1 hours per day depending on the N1 exponent. For an assumed average N1 of 1.0, the NDF is 30.2 hours.

**The mathematical calculation of NDF** uses the __FAVAD N1__ assumptions. A baseline hour of the night is selected (in this case 03 to 04 hrs) and copied down to the yellow (data entry) ‘MNF hour’ row..

- Suppose L(03 to 04) is the minimum night leakage rate at 03 to 04 hrs, at pressure AZP(03 to 04)
- Then leakage rate at 04 to 05 hrs is L(04 to 05) = L(03 to 04) x {(AZP(04 to 05)/AZP(03 to 04)}
_{N1} - Then leakage rate at 05 to 06 hrs is L(05 to 06) = L(03 to 04) x {(AZP(05 to 06)/AZP(03 to 04)}
^{N1}

And so on for the remaining hours.

- Night-Day Factor NDF = {sum of 24 hourly leakages}/ L(03 to 04)
- L(03 to 04) cancels out from the NDF numerator and denominator, so ….
- NDF = sum of 24 values of {(AZP(00 to 01)/AZP(03 to 04)}
^{N1}…..to {(AZP(23 to 24/AZP(03 to 04)}^{N1} - As the calculation of NDF is based on ratios of AZP Pressure, any consistent units can be used for pressure.
- So it is not necessary to measure night flows to assess Night-Day Factors!
- Seasonal variations of NDF can occur in many systems, so this type of 7-day calculation can be repeated at different times of the year to assess the seasonal changes which may occur in NDF

**Illustration of Errors introduced by assuming Night-Day Factor = 24 hours/day**

In Table 3, if NDF of 24 hours/day is assumed for the system in Table 1 (NDF = 20 hours/day), then error in assessed daily leakage is 168 – 140 = 28 m3/day, or +20%

The lower part of Table 3 shows that if an NDF of 24 hours/day is assumed for a system with AZP Pressure reduced at night and NDF of 30 hrs per day, then the error in assessed daily leakage is: 168 -210 = – 42 m3/day, or +20%

**Illustration of Errors in predicted daily leakage reductions from pressure management if assumed Night-Day Factor = 24 hours/day**

Table 4 shows the effect of introducing pressure reduction at night. The minimum night flow has reduced from 10 m3/hour to 6 m3/hour, and Night Leakage Rate has reduced from 7 m3/hour to 3 m3/hour. NDF (as measured at the Average Zone Point) has increased from 20 hours/day to 30 hours/day.

If an NDF of 24 hours/day is assumed for both the ‘before’ and ‘after’ calculations, Table 3 shows that the Predicted Daily Leakage volume would reduce by 168 – 72 = 96 m3/day or 57%.

However, if the calculation is done correctly, with measurement of NDF at the AZP point before and after the pressure management, the assessed daily leakage would reduce by 140 – 90 = 50 m3/day, which is approximately half of the predicted reduction based on assuming constant pressure and NDF of 24 hours per day.

I have seen these types of errors repeated so many times, by practitioners and analysts who were not aware of the importance of NDFs, that I decided that a Night Day Factor Webpage and the explanatory Power Point AZP&NDFCalcsPPTJuly2016 needed to be added to the existing free AZP&NDFCalcs software and Guideline 2013L on calculation of Average Pressure. I hope that Users of the website will find it helpful, and notify their colleagues of this important concept.

Allan Lambert, 28th July 2016