# Flow rate loss

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1. Jun 27, 2017

### InvEngineer

I have a diesel pump doing 900 lpm with a hose reel 30 meters long, the inside diameter of the hose is 32mm. The frictional loss for 30 meters of hose is 461.04 kPa. The Viscosity of Diesel is 4.5 mPas. I would like to know the final flow rate.

2. Jun 27, 2017

### Staff: Mentor

Welcome to PF!

You gave the flow rate in the explanation of your problem, but seem to be asking about two different flow situations, which you don't seem to have defined (I only see one case). Could you explain in more detail the two cases?

3. Jun 27, 2017

### InvEngineer

thanks for the reply, when you are unloading from a truck thru a pump and hose reel system, the pump's discharge has 900lpm, but the hose end will not be 900 lpm, it will be less. I am trying to calculate the lpm lost in the hose.

4. Jun 27, 2017

### InvEngineer

wondering the below formula is correct and will provide me the lpm lost, since I know the Δ P of the hose

Δ P = 128 μ L Q/ π d 4

5. Jun 27, 2017

### Staff: Mentor

I'm sorry, but this doesn't make sense to me: if the diesel fuel doesn't come out the end of the hose, where does it go? It can't just disappear.

6. Jun 27, 2017

### Staff: Mentor

That looks like a form of a friction equation:
https://en.wikipedia.org/wiki/Darcy–Weisbach_equation#Pressure-loss_form

The formula is valid, but it won't provide you with actual flow by the method you are using because your method is circular: you appear to be using the flow to calculate the friction to calculate the flow -- so the flow should be the same flow you plugged in to the equation!

I think you need to model the system in more detail using the actual performance of the pump. Do you have a pump curve? Also, if the system is open, do you have the elevation difference between inlet and outlet pipes?

7. Jun 27, 2017

### InvEngineer

not all pumping systems work in Q=A1V1=A2V2... in this case the pump keeps running unable to push diesel out the other end. you might remember that a pump does "x lpm @ "y" meters head at its discharge... but you get "zero" flow at "y" meters vertical elevation"

To keep it simple the practical flow we achieve after the hose reel is about 400lpm... all i am trying to do is theoretically calculate it, so we can provide some solution to customers that a pump with 900 lpm discharge will give you "X" lpm with 20 meter or 30 meter or 60 meter hose reel.

8. Jun 27, 2017

### Staff: Mentor

They must unless they have a leak. The extra diesel doesn't just disappear.
Doesn't that mean that the flow rate at the pump is lowered? If not, where is the extra flow going?
In what you describe, x=0. The pump is dead-headded in both situations.
I think what you are really intending to say is that the pump will produce 900 lpm at one pressure, but 400 lpm at a certain, higher pressure. So what is needed is to define the two scenarios as specifically as you can, so you can calculate the missing piece of information.

So:
It produced 900 lpm at what head?
The frictional loss of 461 kPa happens at what flow rate?
The 400 lpm is an actual measurement? At what head?
Which pipe lengths and elevations do these scenarios correspond to?

9. Jun 27, 2017

### Staff: Mentor

I agree with what Russ is saying. Is the 900 lpm the discharge rate of the pump with no back pressure? Are you asking, "how do I determine the flow rate in a hose if the pressure drop is 461 kPa?" Or, "what is the pressure drop-flow rate relationship for the hose with diesel fluid flowing through it?" Does the unit mPa signify milli-Pascals?

10. Jun 27, 2017

### InvEngineer

900 lpm at 7 bar.
hose loss 461kPa at 7m/sec velocity (diesel flow thru pipe/hoses velocity limiting factor to avoid static electricity generation) about 337.8 lpm.
pump and hose are at same elevation with a meter in between them.

11. Jun 27, 2017

### Staff: Mentor

So, at 7 bars, 900 lpm and at 4.6 bars, 338 lpm?

12. Jun 27, 2017

### InvEngineer

900 lpm 7 bar at pump discharge... yes

30 meter hose loss is 4.6 bar... (338lpm is the max allowed flow thru 32mm internal dia hose, anything over we have to restrict it with valves)

13. Jun 27, 2017

### Staff: Mentor

I estimate that at 338 l/m, the Reynolds number will be about 44000. This is an indication of turbulent flow. If I use the Blasius equation to calculate the fanning friction factor, I get: $$f=\frac{0.079}{Re^{0.25}}=0.00545$$Knowing the fanning friction factor, one can calculate the shear stress at the wall: $$\tau=\frac{\rho v^2}{2}f=\frac{(0.885)(700)^2}{2}(0.00545)=1182\ \frac{dynes}{cm^2}$$I am using cgs units in these calculations. The pressure drop in the hose is then estimated from $$\Delta p=4\frac{L}{d}\tau=\frac{(4)(3000)}{3.2}1182=4.43\times 10^6\ \frac{dynes}{cm^2}=443\ kPa$$This compares with your value of 461 kPa.

14. Jun 27, 2017

### JBA

Are either the flow rates you have listed actual values measured by a flow meter while operating your delivery system; or are they the pump manufacturers published delivery of 900lpm @ 7 bar and your desired delivery of 338lpm?

15. Jun 27, 2017

### InvEngineer

Hi Chester, thanks for the calcs, I did get the same values while doing the calc verification on the hose reel pressure loss.

Hi JBA,
Its a positive displacement pump (one revolution is 900 cc and the pump rotates at 1000 rpm = 900lpm).
Once you go over 7 bar the in the pump - the bypass valve will open the suction and discharge for re circulation.
If nothing attached to the pump discharge it will pump out 900lpm.

When we pump diesel/petrol we have to limit the velocity to 7m/sec which is that 338 lpm.
But in actual case we get a max of 288 lpm (sometimes even less upto 227 lpm) when we trigger the nozzle at the end of the hose reel.
Each and every truck with same setup yields different final flow rates. All I am trying figure out is how much is this hose reel eating up.
The same pump yielded in one truck 404lpm at the nozzle with 38mm internal dia 30m hose.
These are the previous values recorded by the company that I am working for now. I have no other details.
I also tried Δ P = C*Q^2, which gave some crude approximation with the C value 140. This one doesn't consider diameter and length.

16. Jun 28, 2017

### Staff: Mentor

You seem to have left out some important information in your earlier posts, but finally, a more clearcut picture seems to be developing. (It also was not clear what values were calculated and what values were actually measured).

You mention a nozzle on the hose. Do you have any idea what the pressure drop is across the nozzle with the oil flowing. If the pressure drop across the nozzle is significant, the combined pressure drop of the hose and nozzle might be high enough to trigger the bypass, even at lower flow rates. Can you measure the pressure in the hose at the location just before the nozzle?

17. Jun 28, 2017

### gmax137

The bypass may be coming in sooner or later on the different units. The bypass flow itself could also be higher or lower between units. The pumps could be different (worn/leaky valves, etc.) Are these engine or motor driven pumps? The speeds could be different. Are you using the same instrument to measure the flow from each pump? Or does each pump have its own measuring instruments? They could be out of calibration.

18. Jun 28, 2017

### JBA

What controls the point at which the pump starts, i.e. if there is a valve on the nozzle at the end of the hose does the pump start before or after the valve is open?

19. Jun 29, 2017

### InvEngineer

to JBA - Truck's engine idle's at 700 rpm, there will be a PTO fitted to the truck's gearbox, its output is a constant 1000 rpm, the PTO drives a hydraulic pump which in turn runs the hydraulic motor at 1000 rpm. Once you mechanically engage the PTO, the pump will be running until you disengage it. (remember once you go over the 7 bar in the system, the pumps bypass will open to recirculate) So nozzle triggering will not run the pump, that only happens in retail bowsers (service stations), the trucks we make here are the ones supply bulk fuel to those service stations.

to gmax137 - the bypass is set to open at 7 bar for the pump and tested and certified. the same pumps I have used them for "aviation refuelling" pretty accurate with their settings, as I mentioned earlier, hydraulic motor drives the pump constantly at 1000 rpm. yes... a qualified calibrator uses his certified instrument (NATA certified) to calibrate both petrol and diesel, he then issues a certificate that these were the flow rates achieved with the pump and hose size and length, yes... each truck has its own flow measuring metering equipment with a printer, all those are the calibrated by the qualified calibrator.

to chester - I am only interested in converting the hose pressure loss to flow loss, now I have nearly explained the whole system, the nozzle loss is 50 kPa. like I mentioned before, with or without nozzle it doesn't worry me, I just want to know how to convert the pressure loss into flow loss.

20. Jun 29, 2017

### Staff: Mentor

Maybe we underestimated the friction factor. Maybe the hose can't be treated as being very smooth, in which case the friction factor would be higher. This would lead to a higher pressure drop at a given flow rate, and trigger the bypass at a lower flow rate.

21. Jun 29, 2017

### InvEngineer

yes... some customers don't get any flow on a 60 meter hose reel (even all 60 meters is unwound), but the same pump and hose reel length for another customer is delivering 150lpm. the hose loss i mentioned earlier is laid out in a straight line (brand new from the factory), but after couple of uses, the hose out of shape.

22. Jun 30, 2017

### Asymptotic

Is there any possibility of partial hose failure with a delaminated section of the ID acting as a pinch valve?

23. Jun 30, 2017

### JBA

I have run a piping loss program I have using your values and its results for your hose size etc. indicate that the maximum hose discharge flow with 9 bar at the pump discharge will be 490 lpm; which means you would be return bypassing 410 lpm of your pump output. (See Screen print below)

24. Jul 1, 2017

### InvEngineer

no rupture or failure, the hoses just bend and twist after couple of uses, i am trying to get the flow rate on brand new hose

25. Jul 2, 2017

### JBA

During the above calculation I wrongly remembered the pressure value for the recirculation valve opening as being 9 bar. Below is the corrected calculated flow rate for the 7 bar pump limit.