Skip to 0 minutes and 4 secondsSo we're going to solve a little problem now, the hand dryer used in public toilets. And what we're asked to find is the energy used by the dryer to dry our hands and the manufacturer's claim, it'll dry your hands in 12 seconds. So let's draw a little picture of the arrangements, a schematic diagram, doesn't need to be very precise. So it's got two air streams that come out, which are fed from a single inlet. So these are my two air streams out. And the flow comes out here at the velocity of 200 metres per second. And the inlet here has a volume flow rate, so I'll use capital V for that, of 32 litres per second.
Skip to 0 minutes and 57 secondsAnd we're told that the air surrounding it is at room temperature, and that the difference in height between the intake here and the outlet is 30 centimetres. So we're going to solve this using the steady flow energy equation. So let's start out by saying we're going to apply the steady flow energy equation. And I'm going to make an assumption, first of all, I'm going to assume air is an ideal gas.
Skip to 1 minute and 44 secondsAnd so we can write down that m dot, for the mass flow rate, times the change in enthalpy between outlet and inlet, plus the change in kinetic energy between the outlet and the inlet, plus the change in potential energy between the outlet and the inlet will be equal to Q dot, the heat transfer rate, minus W dot, the work rate. OK, so that's our standard result for the steady flow energy equation. And we can say that this is adiabatic. There's no heat transfer going on, so no heat transfer, brackets, adiabatic.
Skip to 2 minutes and 39 secondsTherefore, Q dot equals 0. So that removes that term. And if we look at these terms here, then the air is coming in at room temperature. And it's going out at room temperature. There's no heating inside our air dryer. And so we can say that the process is isothermal.
Skip to 3 minutes and 2 secondsHence, there's no change in the enthalpy. So h2 equals h1. And so we can say that delta h equals 0. So this term will disappear, as well. And then, if have a very large inlet here, we can assume that the velocity of the inlet is 0. So let's assume a large inlet. Therefore, v1 is approximately equal to 0. And so we lose part of this term here. And so, the remaining thing we need to look at is m dot here. And we can find m dot. So we could say now, m dot will be equal to the density times the volume flow rate. And we're told what that is.
Skip to 3 minutes and 54 secondsSo we can calculate this as 1.2 for the density of air, times the flow right over here, which is 32. And we'd like that in terms of a cubic metre. So divide by 1,000, and that will come out as 0.0384 metres cubed per second. I'm sorry, that should be kilogrammes per second. OK, so we can now substitute all these values into this expression up here. So let's call that equation one. So substituting in equation one, we're going to have W dot is equal to what's left over on this side here. So let's write it out in symbols. First of all, m dot, we still have, and this term here has disappeared. We're just left with one term here.
Skip to 4 minutes and 57 secondsSo it's v2 squared over 2. And we're left with this term, as well, plus g z2 minus z1, close brackets. And so we can put some values in here now. And we can say that m dot we just found is 0.0384, times the velocity here. That's this value at the top. So that's 200 squared over 2, plus g, which is 9.81 times the height difference here, which is 0.3 of a metre. And if you get your calculator out and you work that out, you'll find that W dot equals 768.1 watts. So that's the rate of doing work. And so over a 12 second period, the energy used equals W dot times time. And so that's 768.1 times 12.
Skip to 6 minutes and 14 secondsAnd that's 9217 joules. And that's our final answer.
Hand dryer (worked example)
A hand-dryer, designed for use in public toilets, generates two 200m/s sheets of air at approximately room temperature and at about 30cm above the air intake. The total flow rate is 32 litres/second and the manufacturers claim it will dry your hands in 12 seconds. Calculate the energy used by the dryer to dry your hands, stating any assumptions made.
Try solving this question yourself and then watch the video or check your answer against the solution PDF at the bottom of the page.
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