This is to continue the discussion on the heat transfer and efficiencies of aquarium pumps, from the thread on Tunze/closed loop.
Say a submerged pump uses 100 watts. And we'll say it's 40% efficient. That means 40 watts are utilized as transfer to kinetic energy of the water.
When started up, the tank flow takes 5 seconds to reach steady-state flow. Roughly, there are 200 (40J/s x 5s) joules of kinetic energy stored in the water. For the next 1000 seconds, the pump runs normally. So, we've used 200 + (1000 x 40) ~ 40,000J in this time, just transferring to the motion of water. What happened to this energy, which, as we know, is conserved? It didn't go to increasing the kinetic energy (mass x velocity^2), as the mass of the water has remained the same, as has its velocity. This energy went to thermal energy in the water, or heat.
The other 60%, or ~60,000J, also heated the water, as conduction from the pump body to the water. Initially, the temperature of the water will rise, but will stop rising at the point where the temperature gradient across the glass or acrylic reaches a steady-state profile.
After the initial start up, the pump is transferring a net 100J/s to the water, in the form of thermal energy. After the temperature gradient across the tank material reaches steady state, the tank will be transferring 100J/s of thermal energy to the room around it.
The pump needs to use energy on a continual basis (power, 40J every second) in order to overcome resistive losses in the water column, which stores a constant amount of energy over time (200J). No net energy is transferred to the water at steady state, as it takes no net energy to keep a mass moving at a constant velocity (object in motion tends to stay in motion, etc. etc.)
Right before the pump turns off, 1005 seconds after startup, we've used 100,200J, 100,000 as heat to the water, and 200 that are stored as kinetic energy in the water. Then the pump turns off, and is no longer using power. When the water stops moving, it dissipates its 200J to heat in the water column. We've used 100,200J, and all of it went to heat the water.
Electrons in a conductive metal present a similar analogy. They collide with defects in the material, including phonons, and the kinetic energy is converted to heat. You need to continue to apply a potential (voltage) difference to keep them moving at the same rate, and when you take the potential difference away, the current stops. If you had a defect-free metal at 0 Kelvin, it would behave like a superconductor if it wasn't for lattice vibrations (that scatter the electrons) that exist at 0 Kelvin. Superconductors will continue to pass current even after the voltage difference is removed, indefinitely.
There is no superconducting analog to fluids like saltwater. These fluids are resistive, and require a constant supply of power to maintain a constant velocity (equivalently, energy). This energy doesn't change, so after a few seconds of startup, the energy input goes to heat.
Hope this helps explain why a 50W submerged powerhead transfers the same thermal energy per time to the water, as does a 50W submerged resistor, which is what aquarium immersion heaters are.
I think the other issues were related to efficiencies. A more efficient pump will store a greater amount of kinetic energy in the water, but will transfer the same thermal energy to the water over time.
The way to avoid transferring all of the pump's power to heat in the water is to mount it externally. Then, most of the heat resulting from the inefficiencies will heat the air around the pump. The 40% to maintain the fluid velocity still goes to heat the water, however.
In thermodynamics, the work that goes to move a fluid is called stirring or shaft work. In a perfectly insulated (adiabatic) box, a propeller inside (even motor outside) will continually raise the temperature inside, forever. In a non-perfectly insulated box, the temperature will reach a steady state value (isothermal), which will be higher than if the propeller were not turning. This temperature increase depends on the dimension of the box, and the thickness and thermal conductivity of the material.
G1
Say a submerged pump uses 100 watts. And we'll say it's 40% efficient. That means 40 watts are utilized as transfer to kinetic energy of the water.
When started up, the tank flow takes 5 seconds to reach steady-state flow. Roughly, there are 200 (40J/s x 5s) joules of kinetic energy stored in the water. For the next 1000 seconds, the pump runs normally. So, we've used 200 + (1000 x 40) ~ 40,000J in this time, just transferring to the motion of water. What happened to this energy, which, as we know, is conserved? It didn't go to increasing the kinetic energy (mass x velocity^2), as the mass of the water has remained the same, as has its velocity. This energy went to thermal energy in the water, or heat.
The other 60%, or ~60,000J, also heated the water, as conduction from the pump body to the water. Initially, the temperature of the water will rise, but will stop rising at the point where the temperature gradient across the glass or acrylic reaches a steady-state profile.
After the initial start up, the pump is transferring a net 100J/s to the water, in the form of thermal energy. After the temperature gradient across the tank material reaches steady state, the tank will be transferring 100J/s of thermal energy to the room around it.
The pump needs to use energy on a continual basis (power, 40J every second) in order to overcome resistive losses in the water column, which stores a constant amount of energy over time (200J). No net energy is transferred to the water at steady state, as it takes no net energy to keep a mass moving at a constant velocity (object in motion tends to stay in motion, etc. etc.)
Right before the pump turns off, 1005 seconds after startup, we've used 100,200J, 100,000 as heat to the water, and 200 that are stored as kinetic energy in the water. Then the pump turns off, and is no longer using power. When the water stops moving, it dissipates its 200J to heat in the water column. We've used 100,200J, and all of it went to heat the water.
Electrons in a conductive metal present a similar analogy. They collide with defects in the material, including phonons, and the kinetic energy is converted to heat. You need to continue to apply a potential (voltage) difference to keep them moving at the same rate, and when you take the potential difference away, the current stops. If you had a defect-free metal at 0 Kelvin, it would behave like a superconductor if it wasn't for lattice vibrations (that scatter the electrons) that exist at 0 Kelvin. Superconductors will continue to pass current even after the voltage difference is removed, indefinitely.
There is no superconducting analog to fluids like saltwater. These fluids are resistive, and require a constant supply of power to maintain a constant velocity (equivalently, energy). This energy doesn't change, so after a few seconds of startup, the energy input goes to heat.
Hope this helps explain why a 50W submerged powerhead transfers the same thermal energy per time to the water, as does a 50W submerged resistor, which is what aquarium immersion heaters are.
I think the other issues were related to efficiencies. A more efficient pump will store a greater amount of kinetic energy in the water, but will transfer the same thermal energy to the water over time.
The way to avoid transferring all of the pump's power to heat in the water is to mount it externally. Then, most of the heat resulting from the inefficiencies will heat the air around the pump. The 40% to maintain the fluid velocity still goes to heat the water, however.
In thermodynamics, the work that goes to move a fluid is called stirring or shaft work. In a perfectly insulated (adiabatic) box, a propeller inside (even motor outside) will continually raise the temperature inside, forever. In a non-perfectly insulated box, the temperature will reach a steady state value (isothermal), which will be higher than if the propeller were not turning. This temperature increase depends on the dimension of the box, and the thickness and thermal conductivity of the material.
G1
