Head Loss Calculations - are gallons standardized?

[MinnesotaSlinger]

Suppose you're calculating head loss within a piping system for radiative or reheat piping, for which the water flowing through it will be 150-180 F. When you refer to a flow of 1 gpm, does that generally mean 1 gallon (i.e., 0.1337 cubic feet) of volume at 150-180 F or does it mean 1 gallon at standard conditions (like 60 F) that would actually take up more than 0.1337 cubic feet at the higher temperature. Because of the expansion of water, 1 cubic foot of water at 60 F will take up about 1.025 cubic feet at 165 F. So, 1 gpm at 60 F will have to flow 2.5% faster at 165 F. Given that head loss is roughly proportional to velocity squared (it is except for the change in friction factor, which would be small in this case), that means that head loss would be 5% more. That's not a huge difference, but it does seem significant enough to consider for proper pump selection.

So basically, when referring to a flow of x gpm, are those gallons standardized to, say, 60 F or is a gallon the amount of water that occupies 0.1337 cubic feet at whatever temperature it's at?

Thanks.

 

[CountOlaf]

I haven't checked your numbers to see if the 5% is correct or not, but I would say that the piping friction loss charts for water ARE typically based on 60 deg F, and therefore you could do some additional tweaking/inflating of your numbers based on operating temperature. Presumably, there are plenty of other opportunities within your sysetm head loss calculations to thow in some fudge factors/saftey factors (e.g., fitting losses, lengths, valves, etc.).

 

[GMcD]

And then the reality of the installing contractor doing whatever it takes in terms of additional offsets, elbows, and "on-site" revisions to the piping system makes anything less that a 5% variation in the calculated conditions moot anyway. I keep chiding the youngsters here that calculate head losses and pump sizing criteria to one or two decimal places. The real world is where you add 10% to a rounded-up calculated value anyway. There are still a lot of variations in how the hydronic system and piping is installed that at best, a 10% margin of error needs to built into the systems sizing anyway.

 

[MintJulep]

From a quick glance at my copy of Cameron, friction loss is a function of kinematic viscosity.

The kinematic viscosity of water changes by a factor of 6 from freezing to boiling.

 

[CountOlaf]

Yeah, but there is not a 6-fold increase or decrease in friction loss due to this viscosity change. I don't feel like going through the whole Reynolds # chart, but it looks to me like the rise in temperature causes a decrease in viscosity which should result in a decrease in pipe friction.

At any rate, using the the different methods (Manning formula, Hazen-Williams, Darcy-Weisbach, etc.) to calcualte friction loss for a particular scenario will give a variation of +/- 10% alone, hence I agree with GMcD that this 5% variation (if it is in fact an increase) can be ignored as long as the other safety factors (10% seems appropriate) are added into the final numbers.

 

[RossABQ]

I keep chiding the youngsters here that calculate head losses and pump sizing criteria to one or two decimal places. The real world is where you add 10% to a rounded-up calculated value anyway.

LOL, I've had that conversation too....

 

[katmar]

I agree totally that any errors should be taken care of by the safety margin, but this is an interesting question with which to occupy a bit of time on a Friday afternoon....

It is correct to say that the velocity will increase in direct proportion with the increase in specific volume for a fixed mass flow rate. It is also correct to say that the head loss will increase with the square of the velocity. But it must be remembered that this head loss is in terms of the flowing fluid. If you want to calculate the pressure drop in (say) psi then you need to multiply by the density of the fluid, i.e. pressure drop is proportional to [ρ]v². Since the density is decreasing as the velocity is increasing the pressure drop in psi would increase in proportion to the specific volume change and not to the square of that change (for a fixed mass flow). Plugging the numbers into my software confirms this theory!

But centrifugal pumps develop head and not pressure, so your conclusions are correct for pump sizing. Oh well, back to work now...