Aquarium Turbines

Some background about aquarium pumps is needed. An aquarium pump and filter are shown in typical operation. Water, originally at the surface in the filter box (1) passes upward through the pump to jet into the aquarium with properties; (2). Water of the aquarium returns to the filter box by action of a siphon (3).

Calculate the least wattage of the pump.
♦ The flow of the pump is steady. The energy equation is:

(1) The "signage" on frictional work assured that it
is a "loss" of fluid energy mechanical energy.

To shorten writing, we calculate the mass and enter its number.

(2) 2

Next, entering and exiting temperatures and pressures of the water are the nearly the same, so (h_in - h_out) equals zero. The system is in thermal equilibrium so ΣQ = 0. Least power occurs when friction work is zero.

(3)3

Aquarium Turbines: My brother, into nano-technology, has built an "Aquarium Turbine" that will take ALL of the available power out of the flow of water back to the filter box. His system "entrance" is at the aquarium free surface, (3), and the exit is at the filter water free surface, (1). Water returns to the filter box at the same rate it is delivered to the aquarium and going either way, h_in - h_out = 0, and ΣQ-dot = 0. An energy equation for that flow (with and/or without his turbine) is:

(4) 4

So if my brother defeats friction, his "Aquarium Turbine" will return 0.021 watts to the power grid.

So what is the efficiency of our operating aquarium pump? If 0.021 watts can be gotten from the flow coming back, done right, 0.021 watts ought to enough power to get it there - with no friction. Our cheap pump eats 1.9 watts. Pump efficiency is "least work divided by actual work times 100," or [(0.021/1.9)x100] = 1.09%! Wow, are these lousy pumps or what?. There has got to be a market for my brother's Aquarium Turbine.

Aquarium Turbines

Calculate the least wattage of the pump.