- Joined
- Mar 3, 2017
- Messages
- 747
Energy is conserved. That's the first law of thermodynamics, and in the
time of James Watt, it was promulgated by the great American scientist,
Ben Thompson, or as he was known after we booted him out of the
country for his radical politics, "Count Rumford"
.... but that's a side issue, let's keep it simple.
Ben studied machining, he knew it took lots of work to bore cannon, and
the workpiece got hot (though today, we know where to buy a cure for that,
$28 a gallon). He made the connection. The work done BOTH made
chips AND heat, but duller tools made less chips and more heat
... but that's a side issue, let's keep it simple.
The 'work' aka 'energy' consumed (the input) was a conserved quantity,
you could total up the heat and chips (the output), and know how much
(1) horse feed
(2) coals from Newcastle
(3) billable electricity
(4) water volume through the flume of a given waterwheel
went in. Any of those inputs become work, produce the output.
The formula for energy in the machine tool that bored those cannon was:
Energy = Torque * Angular_speed * Time
because nothing would make chips without torque, without movement, without time.
And you can convert (because energy is conserved) from an ideal rope wrapped
around a drum, to
Energy =Rope_tension * Velocity * Time
because that rope and the drum radius make a torque, and the drum diameter
and Angular_speed = Velocity / ( 2pi * Drum_radius) :== radians per second
which follows from
Torque = Rope_tension * Drum_radius and
Velocity = 2pi * Drum_radius * Angular_speed
So, depending on the power-transmission chain, there's lots of similar
formulas, all toting up the energy, or (leaving out time which is common
to all these formulas) relating forces (and generalized force-like quantities)
and displacements (and generalized displacements) with power
(which is truly general, and needs no generalization).
Energy/ Time = Power = Rope_tension * Velocity
can also be expressed as
Watts = Newtons * Meters_per_second
and with a suitable conversion from SI units to the world of working horses,
Horsepower / (745 HP/Watt) = Newtons * Meters_per_second
Other (generalized forces) equations for power are all in the form of
a product of an intensive property (that isn't different for an ant or an
elephant, doesn't scale with power needs), and an extensive property
(which DOES scale). For economics, it's the extensive thing that costs
you more when you use more power...
Power = Voltage * Current
Power = Friction * Velocity
Power = Dam_height * Water_mass_flow
Power = Torque * Angular_speed
Power = Fuel_specific_energy_content * Fuel_delivery_rate
Power = Horse_daily_feed * Horsies_hired
Power = P40_decay_energy * (Potassium_40_atoms/P40_decay_lifetime)
but unless you are in the habit of powering Earth's volcanoes, that last one is
kinda... esoteric.
Really, I TRIED to keep it simple! That just isn't my forte.
time of James Watt, it was promulgated by the great American scientist,
Ben Thompson, or as he was known after we booted him out of the
country for his radical politics, "Count Rumford"
.... but that's a side issue, let's keep it simple.
Ben studied machining, he knew it took lots of work to bore cannon, and
the workpiece got hot (though today, we know where to buy a cure for that,
$28 a gallon). He made the connection. The work done BOTH made
chips AND heat, but duller tools made less chips and more heat
... but that's a side issue, let's keep it simple.
The 'work' aka 'energy' consumed (the input) was a conserved quantity,
you could total up the heat and chips (the output), and know how much
(1) horse feed
(2) coals from Newcastle
(3) billable electricity
(4) water volume through the flume of a given waterwheel
went in. Any of those inputs become work, produce the output.
The formula for energy in the machine tool that bored those cannon was:
Energy = Torque * Angular_speed * Time
because nothing would make chips without torque, without movement, without time.
And you can convert (because energy is conserved) from an ideal rope wrapped
around a drum, to
Energy =Rope_tension * Velocity * Time
because that rope and the drum radius make a torque, and the drum diameter
and Angular_speed = Velocity / ( 2pi * Drum_radius) :== radians per second
which follows from
Torque = Rope_tension * Drum_radius and
Velocity = 2pi * Drum_radius * Angular_speed
So, depending on the power-transmission chain, there's lots of similar
formulas, all toting up the energy, or (leaving out time which is common
to all these formulas) relating forces (and generalized force-like quantities)
and displacements (and generalized displacements) with power
(which is truly general, and needs no generalization).
Energy/ Time = Power = Rope_tension * Velocity
can also be expressed as
Watts = Newtons * Meters_per_second
and with a suitable conversion from SI units to the world of working horses,
Horsepower / (745 HP/Watt) = Newtons * Meters_per_second
Other (generalized forces) equations for power are all in the form of
a product of an intensive property (that isn't different for an ant or an
elephant, doesn't scale with power needs), and an extensive property
(which DOES scale). For economics, it's the extensive thing that costs
you more when you use more power...
Power = Voltage * Current
Power = Friction * Velocity
Power = Dam_height * Water_mass_flow
Power = Torque * Angular_speed
Power = Fuel_specific_energy_content * Fuel_delivery_rate
Power = Horse_daily_feed * Horsies_hired
Power = P40_decay_energy * (Potassium_40_atoms/P40_decay_lifetime)
but unless you are in the habit of powering Earth's volcanoes, that last one is
kinda... esoteric.
Really, I TRIED to keep it simple! That just isn't my forte.