On 11-06-21 10:35 AM, Stephen A. Lawrence wrote:
Jed sez a 150 watt hose wouldn't be very hot. GoatGuy says it would.
Well, let's do a little plausibility calculation, and see whose
ballpark we wind up in.
Now, let's just slow down here. There's another plausibility check we
can do, and it comes out a little differently. Let's try to calculate
how much heat the surface of the hose might be dumping into the air,
using a lightbulb for a "standard", and assuming the hose is really
quite hot.
Assume a 100 watt bulb is a sphere 2" in diameter, or 5 cm. (That
ignores the stem, of course, but it's not too far off, I think. Note
that making this value too small will be "conservative", which is the
direction in which we want to err here.)
Assume it dumps ALL of its energy to convection with the air. (That's
an overestimate, which is conservative, as you will see.)
Assume, further, that its envelope temperature is 200 C above ambient
(which is in the ballpark, according to Wiki, and according to what I'd
guess based on how they feel).
Bulb area is then 4 * pi * 2.5^2 = 79 cm^2.
Now, let's assume the hose has a surface temp of 100C. The rubber is an
insulator, so it'll really be a bit cooler than that; consequently this
is a "conservative" assumption.
So, hose temp is about 80 C above ambient (which I'm assuming is 20 C).
Hose radius is 1 cm.
The 3 meter hose has area = 2 * radius * pi * length = 2 * 1 * pi * 300
= 1885 cm^2.
Convective loss rate of the hose, relative to the bulb, will be
(area(hose) / area(bulb)) * (temp above ambient(hose) / temp above
ambient(bulb)
or
(1885/79) * (80/200) = 9.6
The bulb is assumed to be losing 100 watts, so that's a loss rate of 960
watts for the hose.
That's a loss of 38% of the output power, which was stated to be 2.5 kW.
Furthermore, that's (probably) a liberal estimate: An incandescent bulb
actually radiates away something like 20% of its energy (if I recall
correctly), while the hose, being a lot cooler, will radiate away quite
a bit less. Furthermore, the hose is made of an insulator (rubber) so
its outside surface temp will certainly be cooler than its inside temp;
consequently, its outside temperature must actually be *less* than 80C
above ambient. Furthermore, room temperature is often higher than 20,
rarely lower, which would reduce the relative temp of the hose further.
These effects combine to reduce the power being dumped by the hose to
something less than 38% of the output power of the device.
Consequently, it seems to me that the end of the hose should still be
putting out a steam plume which carries away on the order of 1.5 kW.
That may still be enough energy to carry GoatGuy's main conclusion,
which is that the hose should have been a lot livelier than it appeared
on the video.
