help me out of a muddle

[Stephen Bowman]

Hi I'm looking for a mathematician amongst you all.
one of my engineers on a new build first fix has install a hot running toilet, easilly resolved but the customer wants compensation for the water he's heated within the flush. its 3/4 l flush, he's had it installed for five years and its a heat only gas boiler and megaflo.
can anybody work out what the cost is to heat the water he may have used.
will be eternally grateful

 

[Deleted member 120897]

Why has it taken 5 years to resolve? It would all depend on how many times they’ve flushed it, what the cost of gas was at the time, and they would have the water heated anyway being a cylinder.

 

[snowhead]

It's an impossible calculation without a lot more information.

How many people were there in the house over the period, including visitors and what were the average hours of occupation.
How many times did they use and flush the toilet?
Did they always flush the toilet after every use?

Do any of them have medical conditions such that they would need to use the toilet more often, if so how many more times than average do they flush the toilet.

etc, etc,,

The customer is claiming compensation so should be supplying an estimate and the method of calculating it, including the charges for gas that they were paying over the period.
Then the company who caused the issue should be employing an expert to contest / supply a counter proposal.

 

[Ben-gee]

Presumably this is a joke. Either on your behalf or your customer’s.

 

[fowlerboi]

It would have been noticed within a month of living there and after maybe 4-5 flushes at most. If the customer has failed to report the problem until 5 years later then that's their problem. Fix the toilet and offer them £100 to say sorry.

If it was reported early on and still not been fixed within 5 years then who ever was in charge of snagging or organising it needs to pony up £500 as good will. At 4 flushes a day my maths had it at £200

 

[Chuck]

Okay, I'll give it a go. I'll assume a single person living in the house.

First estimate how much water was used by flushing each year and how many kW hr of gas was need to heat it.

Vol_short = 3 (litres),
Vol_long = 4.5 (litres),

— Typical values

N_brown = 1 (per day),
N_yellow = 4 (per day)
T_mains = 15 °C
T_hot = 60 °C

— Constants

dpy = 365.25 (days/year)
SHC_water = 4200 / (3600 * 1000) (kW hr / °C)

— Formulae

Litre_per_day = ( N_brown * Vol_long ) + ( N_yellow * Vol_short )
Litre_per_year = Litre_per_day * dpy
T_delta = T_hot - T_mains
Energy_per_year_kWhr = Litre_per_year * SHC_water * T_delta

— Values

T_delta: 45.00
Litre_per_day: 16.50
Litre_per_year: 6027
Energy_per_year_kWhr: 316.4

For the price, I've found the GB annual average domestic gas prices published here:

Average unit costs and fixed costs for gas for GB regions (QEP 2.3.4):

https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/1146289/table_234.xlsx

Using the 'Direct debit: Average variable unit price (£/kWh)' column and adding 5% APR interest I make the total £77.56p per occupant.

 

[Gasmk1]

To be honest I would tell the customer that I would go back put right and call it that,the amount of extra heated water is negligible Less than £100.00 Over 5 years, Should have been noticed a lot sooner than 5 years. So some onus is on the customer.

 

[Chuck]

Then the company who caused the issue should be employing an expert to contest / supply a counter proposal.

Claimant: "We seek £1500+VAT costs for our expert's fees."
Judge: "To settle a £100 dispute? No."