Flow

[rswolff]

ok.....so here's a little process question for all of you out there.......an oreo (doublestuff) and a glass of milk for any correct answers......no secrets...no hidden tricks....its a straightforward process application.....or is it? first a small teaser just for giggles...... you're in a small boat in a lake with your wife (or girlfriend) or conversely your husband (or boyfriend)....one of your children (or just some kid off the street)....a toaster and a bowling ball. The kid takes the bowling ball off the floor of the boat....what happens to the lake? the kid then throws the bowling ball into the water....now what happens to the lake.....no its not a trick bowling ball, an upside down boat, there are no aliens, nor giant squid in the answer (unless you'd like to include them) now the tuffie...... you have a 30hp pump supplying a 3" diameter pipe, 500ft long (basically horizontal) loop with water at a rate of 80gpm. Water returns to a tank and the pump pulls from the tank. Tank is 3000 gallons and is full. At one point in the loop you have an Endress Hauser flow meter. Further down the loop you have another Endress Hauser flow meter. Both flow meters give a pulse every 0.1 liters. Accurarcy of the flow meters is specified as 0.1%. Between the flow meters you have a use point being controlled by a valve. Control is simply open or closed. Use point flows 5gpm. So if you know who much water passed the first flow meter, and subtract from the amount of water that passed the second flow meter is this the amount of water that was dispensed? Minimum water dispensed is 5 gallons. End user wants an accuracy of water dispensed from the use point of 0.5%. Is this possible? Is so why. If not why? go ahead and knock me out.....this was an actual application..... ----------------------------------------------------------------------------------------------------------------------- wow.......lots of looks.....not even a single answer? must be tougher than I thought..... Edited March 27, 2011 by rswolff

[paulengr]

The fact that you asked on a weekend means answers probably are slow in coming.

[rswolff]

i'll answer the first one first.....sorta places things in perspective.....as I stated its a normal everyday bowling ball....in the boat or being suspended by the boat, its displacing its weight....since a bowling ball sinks (no its not hollow or has a cork core) in the water its displacing its VOLUME. Since the volume of water it displaces weighs less than the bowling ball it sinks......so when you throw it into the water....the level of the lake goes down....the ball is displacing less water then it did in the boat.....physics for the merry....i'll give the second one a bit more time before I respond......again....no tricks or treats in the answer.... and no, the first part had nothing to do with the second except to stimulate the brain cells a bit....... and so far your second part is good...but not quite there.....as for the flowrate at the use point its not calculated from the flow meters and for the sake of this discussion there are no erroneous 'clicks' or lost signals. And we'll take for granted that the specified accuracy is achievable in the field. At the given pressure (i didn't specify but lets say 20psi) and at 80gpm, the use point valve was set to dispense 5gpm (it was a mechanically adjustable valve. No, not a hand valve). Again, for the sake of this discussion we'll agree that it is in fact 5gpm unless you can convince me, in mathematical (or possibly theoretical) terms why is should not be so. And I think I explained this possibly incorrectly. The question is not whether you can dispense at the rate of 5gpm accurately, that would be controlled by the valve opening. Can you dispense by weight (or liters/gallons) accurately? So could I dispense 100 liters or 25 gallons within the required specification of 0.5%? or better, can I determine how much was dispensed with the required accuracy? Does that help? Edited March 28, 2011 by rswolff

[paulengr]

You have 2 flow meters that give a "click" type output for a totalizer. You want to measure the DIFFERENCE between them and state something about the accuracy of this. Pressure, flow rates, etc., aren't really important if the key measurement is the difference between two totalizers (it's a dispensing application), and again, I'm assuming the flow meters are on the "loop" and not the output itself (which is not being measured). If it's on the measurement line, then things get very simple because we can simply ignore all other meters and only look at the meter on the dispensing line. The "click" type output is at a rate of 0.1 liters/click. The absolute accuracy of both meters is 0.1%. There are four sources of error on your output: 1 & 2. Each meter is accuracte to 0.1%. Since we have 2 meters and it is definitely possible for them to deviate in opposite directions. 3 & 4. The "click" causes quantization errors. The degree that this is a problem depends on the size of the output...with more "clicks" (bigger volume), this error quickly averages out. If we are dispensing 5 gallons, converting from gallons to liters, this amounts to 0.0264 / 5 = 0.528%. But if we are talking about 100 liters, it dies down to only 0.1%. These are absolute numbers. The error in reality is that anything within +/- those values is equally likely, so the average error is exactly half of that, or 0.264% for 5 gallons, or 0.05% for 100 liters. Now we get to the tricky part. You have to decide how to add the errors together. It will give you an absolute worst case to add errors, but the reality is that most of the time, errors aren't correlated and worst case doesn't happen...it is highly unlikely that all the errors will be worst case in opposite directions enough to drive the error rate to over 0.5%. You can add errors exactly by taking their actual probability plots and doing a cross-correlation to get the exact result but there's a simpler way. As you add more and more error sources together, and look at the result, it quickly resembles a gaussian curve. Gaussians are really easy to add...just take the square root of the sum of squares. This actually happens if the error sources are independent, which is generally true in this case. So in this case, the result is sqrt(0.1^2+0.1^2+0.264^2+0.264^2) = 0.4% for the 5 gallon case, or 0.16% for the 100 liter case. I've given you enough rope to calculate out various other cases yourself.

[rswolff]

over some infinite period of time the errors should equal out, but for a finite time period the errors could be at their relative peaks, or near them. So its would be theoretically possible for the errors to be skewed in opposite directions during any particular dispensing operation. You'd need to determine the rate that the error moves inside of each device to determine the actual possible overlap. That however, would still not get you out of the 0.5% range, if how you stated the dispensing calculation was correct. Its not. Yes, the flow meters are in the loop. The use point valve is roughly mid point. Valve position in the loop does not actually make a difference. And we can compensate for any losses in the piping from the dispensing valve into the tank. I can categorically state that its mathematically impossible to achieve 0.5% accuracy. In fact you couldn't achieve 1.0%. Its a process problem plain and simple. And the flow meters are high precision Coriolis type units. Calibration and testing determined that they were indeed roughly close to the factory specified 0.1%. I wouldn't design to that spec but it was confirmed in the field. Can no one else even offer some opinion, technical insight or just a plain guess? remember there's an oreo doublestuff for any correct answers. Correct guesses win the cookie too, though I will admit the probability of a correct guess is mighty low.

[robh]

The answer is 46.

[Ken Moore]

It's a bad design, I would never install a system like this, so the challenge does not really grab my interest.

[Mickey]

46 ?? It's 42.

[robh]

You forgot to add 4.

[RussB]

I thought it was Add -4?

[DanW]

Are you sure that the installed meters are Coriolis meters? for water service? I thought immedieately that they were vortex meters, because any vortex installtion faces a low flow drop out for the conditions you cite. The 5gpm diversion flow rate is less than 10% of the 80 gpm nominal flow rate and likely falls into the low velocity range in which vortices are not produced at a sufficient rate and the meter reading is forced to zero. All commercial Vortex meters have a low flow drop out for this reason.

[DanW]

The expected 0.5% error on the 5 gallons of diverted flow is 0.025 gallons. However, the flow meter's error is a percentage of its instantaneous flow rate. The upstream meter passes 85 gallons over some period of time at the stated 0.1% error or ±0.085 gallons. The downstream meter passes 80 gallons over that same period of time at the stated 0.1% error or ±0.08 gallons. The diverted flow is the difference of upstream minus downstream = 5 gallons over that period of time. Even if the flowmeter errors are not in opposite directions, but the same direction, each flow meter's error based on percentage of flow rate is 3+ times the expected error of the diverted flow: - the upstream meter's error of ±0.085 gallons is 3.4 times the ±0.025 gallons expected error. - The downstream meter's error of 0.080 gallons is 3.2 times the ±0.025 gallons expected error on the diverted flow. At a total of 17 gallons of diverted flow, one approaches the point where the error approaches the expected 0.5% error. 0.5% of 17 gallons = 0.085 gal Edited May 5, 2011 by DanW