[myv65]

Originally posted by unregistered
separate aspect: I can speak to pump heat generation (but not quantification)
by placing an oil cooled aluminum bodied pump within a heat bath, its heat generation can be observed at different flow rates
- restricting the pump's output causes it to 'create' MUCH more heat than in a 'free flowing' condition

myv65
care to comment on the heat balance aspects of the wb pressure drop ?

On your "separate aspect", what you're seeing is the difference in where the energy goes. I guess a little more definition may be required here. A classical setup is to have a pump drawing liquid from a stilled reservoir and pumping it somewhere. In such a case, the power input to the pump impeller shaft will go up with flow rate. Fortunately, a pump has no knowledge other than the conditions that exist at its inlet and outlet. For this reason, the same is true for an inline setup and its power also increases with flow rate.

What will vary as flow changes is how the energy put into the impeller shaft shows itself within the liquid. In the simplest sense, the "useful" work of the pump would be defined as the pressure difference on either side of the pump multiplied by the flow rate through the pump. True engineering types may complain that "work" has units of force*distance while flow rate multiplied by pressure has units of force*distance/time (power). Whatever. When you look at a centrifugal pump's efficiency curve, you'll find that they define efficiency as flow*delta-P/shaft power.

At zero flow, efficiency is zero. Likewise is true for zero delta-P. In the former, all energy goes into churning the water, ie directly into heat. You immediately see this in your example. As soon as you have some flow, the energy gets split between ineffectual churning of the water and producing flow. Efficiency climbs from zero and starts marching towards its peak. The peak efficiency will occur at some nominal flow that lies between zero flow/peak head and peak flow/nearly-zero-head. Even at peak efficiency, some of the shaft power doesn't generate any useful flow and produces heat directly. Point here is that the portion showing directly as heat is inversely related to the pump's efficiency.

The rub for a closed system is that all the energy put into the water eventually turns to heat. This is the result of pressure drops through the remainder of the system. In a truly open system you can have some energy storage if you indefinitely pull water from a low elevation and pump it to a high elevation. Note that our "open systems" really aren't open from an energy perspective.

Another thing that comes into play with submerged pumps like your example is the motor behavior. A split capacitor, single phase, four-pole motor will have a peak efficiency in the range of 65%. The efficiency curve looks like a parabola. So as you move away from the "full rated load", the efficiency will drop off dramatically. A dead head condition will tend to drop the motor output load, but will also bump the motor some along its efficiency curve. I have done absolutely zero work in this area to measure the effects, so I can't say positively how significant this is. All I would point out is that energy input to the motor does not drop as rapidly as the shaft output power drops due to the efficiency curve of the motor.

In your example above, this translates to lower total energy input when dead-headed, but 100% of that energy coverting immediately to heat. In a free-flow case, more energy is input to the fluid, but a smaller amount is directly converted to heat.

*Warning: Engineering geek-speak ahead*

I'm not quite sure where you are headed with your request to "comment on the heat balance aspects of the wb pressure drop". I try to break down problems into one of two conditions. Either you define a control surface or a control volume. In the former, you analyze everything that crosses a given surface. In the latter, you analyze everything that happens to a given volume. Our systems generally lend themselves to the control surface approach.

In any analysis like this, you have a fundamental equation that governs life: Input + Created = Output + Stored + Destroyed. For our simple systems when energy is the topic, there is no "Created" or "Destroyed" terms. The "Stored" term only relates to transient conditions and can be ignored when one is only interested in examining steady-state operation under extreme load.

In this respect, I would consider drawing the imaginary box around the block, cutting the inlet and outlet lines where they meet the box and cutting the interface between the bottom of the block and interface material. Energy gets into the control surface as thermal energy from the interface material and thermal, kinetic, and potential energy in the fluid stream. Energy gets out of the control surface as thermal, kinetic, and potential energy in the outlet fluid stream. There are also minor (perhaps ignorable?) effects on the remaining block surface as it may be warmer or cooler than the surrounding ambient air as well as radiation (almost certainly ignorable due to emissivity, view factors, and surrounding absolute temperatures in comparison).

The difficulty that I know you face is one of quantification. A control surface is only as good as one's ability to measure the properties at that surface. Tell you something you don't already know, eh?

*End engineering geek-speak*

OK, no guarantees it's all 100% accurate. That's what you get for writing off-the-cuff without proofing.