I am trying to work out how much energy (ideally electrical heating) I need to put into a heater to raise the temperature of water from say 10 degrees C to 40 degrees C, if the water is flowing at 10 litres per hour.
Assume that the heater is 80% efficient.
I know that the specific heat of water comes into this at 4.18 J/g degree C but how do I work in the flow rate?
You just need to convert the volumetric flow rate to a mass flow rate by multiplying by its density. This is easy for water:
$$10\ \mathrm{l/hr} \cdot 1\ \mathrm{kg/l} = 10\ \mathrm{kg/hr} = 10^4\ \mathrm{g/hr} = \frac{10^4}{3600}\ \mathrm{g/sec} = 2.78\ \mathrm{g/sec}$$
Now you can multiply by the specific heat and the temperature rise to get the power required.
$$P = \dot m \cdot C_p \cdot \Delta T $$
Where $P$ is the power required in Watts ($Joules/sec$)
$\dot m$ is the mass flow rate ($kg/sec$) (you'll have to convert the volumetric flow given to a mass flow rate by using $\dot m = Flow_{Vol} \cdot \rho$ where $\rho$ is the density of the fluid)
$C_p$ is the specific heat of the fluid ($ \frac{Joules}{kilogram \cdot K}$)
and $ \Delta T$ is the temperature difference in $K$
This will give you the power required to heat the water as it flows. The amount of energy will, of course depend on how long the water flows.
Every second, you need to raise the temperature of 2.77 g of water by 30 °C.
Assuming 80% efficient.
You need 435 J/s.
Joules per second is a Watt
