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#  # Cost of a Shower

So how much does it cost to have a 4 minute shower? And which is the cheaper fuel source, electricity or natural gas? Read on to find out.

 Assumptions

• using a 3 star shower head with a flow of 9 litres/min
• average cold water temperature of 15 °C in Tasmania
• water temperature at the shower head is 42 °C (this may seem a bit high, however water temperature drops significantly as it falls from the shower head)
• a hot water system efficiency of 85% where an electric hot water cylinder is used, and 70% where a 5 star instantaneous gas hot water unit is used. These efficiencies take into account piping losses, cylinder losses (for electric hot water), and the thermal efficiency of the heat exchanger (for gas hot water).
• hot water cylinder thermostat setting is 60 °C (minimum allowed for hot water cylinders to prevent microbial growth)
• tariff 41 (hot water) energy rate of 16.757 c/kWh
• tariff 41 daily charge of 19.089 c/day
• natural gas energy rate of 2.98 c/MJ (10.75 c/kWh)
• natural gas daily charge of 21.3 c/day
• average total hot water use per day is 200 litres per household
• approximately 30% of natural gas consumption in an average home is for hot water, with the majority for heating and some for cooking
• note tariff rates are current as of February 2013

 Calculations

• Total water requirement is 36 litres (4 minutes x 9 litres/min).
• Amount of 60 °C hot water required to achieve 42 °C shower head temperature is 21.6 litres (mixed with 14.4 litres of 15 °C cold water).

Electricity

• To raise 21.6 litres from 15 to 60°C takes 1.33 kWh (based on the energy required to heat water (J) = mass of water (g) x specific heat of water (4.18 J/g/°C) x temp difference between hot water cylinder temp and supply water temp (°C), converting J to kWh using 3.6 MJ = 1 kWh, and allowing for the 85% hot water system efficiency factor, and assuming 1 ml water = 1 g water).
• Therefore energy rate cost = 22.29 cents (1.33 kWh x 16.757 c/kWh).
• And daily charge component = 2.06 cents (21.6 litres / 200 litres x 19.089 c/day).
• This gives a total of 24.35 cents.

 Natural Gas

• To raise 21.6 litres from 15 to 60 C takes 5.8 MJ (based on the energy required to heat water (J) = mass of water (g) x specific heat of water (4.18 J/g/°C) x temp difference between hot water temp and supply water temp (°C), and allowing for the 70% hot water system efficiency factor, and assuming 1 ml water = 1 g water).
• Therefore energy rate cost = 17.28 cents (5.8 MJ x 2.98 c/MJ).
• Daily charge component = 0.69 cents (21.6 litres / 200 litres x 30% x 21.3 c/day).
• This gives a total of 17.97 cents.

So it costs around 24 cents to have a 4 minute shower if you are using an electric hot water cylinder and around 18 cents if you are using an instantaneous natural gas water heater.