On-Demand Water Heaters. Conventional hot-water heaters...

On-Demand Water Heaters. Conventional hot-water heaters consist of a tank of water maintained at a fixed temperature. The hot water is to be used when needed. The drawbacks are that energy is wasted because the tank loses heat when it is not in use and that you can run out of hot water if you use too much. Some utility companies are encouraging the use of on-demand water heaters (also known as flash heaters), which consist of heating units to heat the water as you use it. No water tank is involved, so no heat is wasted. A typical household shower flow rate is $2.5 \mathrm{gal} / \mathrm{min}(9.46 \mathrm{~L} / \mathrm{min})$ with the tap water being heated from $50^{\circ} \mathrm{F}\left(10^{\circ} \mathrm{C}\right)$ to $120^{\circ} \mathrm{F}\left(49^{\circ} \mathrm{C}\right)$ by the on-demand heater. What rate of heat input (either electrical or from gas) is required to operate such a unit, assuming that all the heat goes into the water?

Transcript

00:01 Here we're going to look at how much energy it takes to heat up the water as you're taking a shower.

00:07 That is one of the highest energy usages in the home.

00:13 Our thermodynamic relationship is q, the heat added.

00:18 It could be subtracted, but here we want to heat up the water, is equal to the mass of the water times the specific heat capacity.

00:35 Times the difference in temperature.

00:45 This relationship works if you are far away from a phase change, such as water turning to ice or vapor.

00:54 But the application is an on -demand water heater, which is a little unit that either takes electricity or propane, and as water starts to flow through that source of energy, allows for the water flowing in at a certain temperature to come out the other side at a higher temperature.

01:26 And really what matters is how quick the water flows through this system.

01:32 So we will have a certain mass flow rate, delta m by delta t, where t is time.

01:42 And that's related to the power that the box utilizes dq by dt, the amount of energy used per unit time, heat absorbed per unit time, is equal to that mass flow rate, time, times c, times the difference in temperature.

02:09 So we're simply rewriting the equation above, but we need our mass flow rate, we need the specific heat of water, which we can look up.

02:27 It is 4 ,186 joules per kilogram degree centigrade.

02:36 To get some of the parameters, we will consider a typical shower application.

02:44 There, the volume flow rate, which is the volume coming through the box per unit time, can be of the order of 9 .46 liters.

03:10 So about 10 coke bottles every minute.

03:15 I'll write that in 60 seconds.

03:20 The unit of power that we're going for is based on the lot, which uses seconds.

03:29 And we are going to assume that the change in temperature that we are looking for is 120 degrees fahrenheit, which is 49 degrees centigrade, minus roughly 10 degrees centigrade.

03:57 And that is the temperature usually from the city power, the water supply from the city.

04:06 It could be a little bit warmer than that, but we will go with 10 degrees centigrade.

04:21 So now we just need a mass flow rate.

04:23 And for that, we are going to have to use the volume flow rate.

04:28 So mass equals density times volume.

04:36 Density of water is 1 ,000 kilograms per cubic meter.

04:47 And doing the same trick, the mass flow rate will be the density times the volume flow rate...

Question

Please give Ace some feedback