Bernoulli's theorem of conservation in a nozzle spraying to atmosphere

[MVerrall]

Hi there, I'm having a problem behind the theory of bernoulli's theorem. Can it be applied in an application where water flows from a pump into a pipe with x diameter and out of a nozzle with y diameter to atmosphere. There is a pressure gauge on said pipe. There is a nozzle screwed into this pipe with no pressure gauge on it.

Is the gauge pressure at the nozzle atmospheric pressure, 0 or is it what can be calculated using bernoulli's theorem of conservation of energy?

 

[BigInch]

Yes, if you include the nozzle coefficient, which tells you how much pressure is lost due to friction exiting the nozzle and by extension the remaining amount that is converted to velocity.

Learn from the mistakes of others. You don't have time to make them all yourself.

 

[MVerrall]

That's what I'm trying to find out, the Cd. I've tested the nozzles and documented all the 'actual' flows at different pressures, read from the gauge. So to get the 'theoretical' flow rate should I use the specs from my pump to calculate that. These nozzles are newly developed, so they have no calculated coefficients yet.

 

[MVerrall]

I've found a worked example on the net. Does the theory of P2=0 apply in my application.

 

[BigInch]

If you are working in gauge pressures, same as the example problem, and discharging to atmosphere, atmospheric pressure is usually taken as 0 psig, or 0 barg.

Learn from the mistakes of others. You don't have time to make them all yourself.

 

[MVerrall]

This might be a stupid question. So gauge pressure is the pressure read on the actual pressure gauge on my pipe. Should I do it this way or should I use absolute pressure, which includes atmospheric pressure?

 

[zdas04]

YOU CANNOT SOLVE BERNOULLI'S EQUATION IN GAUGE PRESSURE. Was I shouting? The reason that the solved example you posted worked is because (P1+P(atm))-(P2+P(atm))=P1(which is in gauge). That particular bit of coincidence is unique to atmospheric discharge and should never become a habit (or you'll try to solve P2≠P(atm) problems in gauge and get very wrong answers.

MVerrall, not only is that a stupid question, it calls into question your fundamental understanding of the phenomena you are purporting to evaluate.

David Simpson, PE
MuleShoe Engineering

Law is the common force organized to act as an obstacle of injustice Frédéric Bastiat

 

[MVerrall]

My application is unique to atmospheric discharge as the nozzles spray onto an open screen. Sorry if I sound nieve, I just graduated 3 months ago.

 

[BigInch]

You can use either gauge or absolute, as long as you are consistent.

Since the only type of pressure mentioned in the example is gauge, I assume both pressures are given in gauge (that is the only thing that makes sense).
However, if you assume the 400 is absolute and convert the other, that other is said to be gauge, to atmospheric, you can also solve the problem. It's just a different answer.

Learn from the mistakes of others. You don't have time to make them all yourself.

 

[zdas04]

Well, there are a couple of forms of the equation. The first is that the three energy terms are added together to equal a constant. In this form pressures must be in absolute.

The other form compares conditions at one place to conditions at another. If you have both pressures then you are calculating a differential pressure and gauge or absolute doesn't matter as long as you are sure what you are using.

Even in this form if you are solving for a missing pressure, then the one provided must by in absolute.

So, in 2 of the 3 ways that people use this equation you have to have absolute pressure. The third way is probably the most common form and it can be in either. My approach is to always work in absolute because then I can't get tripped up using gauge in the first or third form.

David Simpson, PE
MuleShoe Engineering

Law is the common force organized to act as an obstacle of injustice Frédéric Bastiat

 

[BigInch]

Agreed. Absolute is ALWAYS much better. Gauge readings are only for convenience of use in the field.

Learn from the mistakes of others. You don't have time to make them all yourself.

 

[MVerrall]

Thanks very much for your help on this gentlemen. So,basically, if I wanted the pressure in the nozzle itself before the orifice I would use absolute pressure, but in terms of my application, whereby it's discharging to atmoshere, use of the gauges reading is acceptable.

 

[zdas04]

If that is all you got from the discussion, then sure, use the upstream gauge as the differential pressure.

David Simpson, PE
MuleShoe Engineering

Law is the common force organized to act as an obstacle of injustice Frédéric Bastiat

 

[cvg]

So to get the 'theoretical' flow rate should I use the specs from my pump to calculate that?

in order to estimate flow rate with a pump curve, you need TDH. If you were to install a pressure gauge and measure the suction pressure, you could get the TDH. without that, you cannot accurately estimate the flow through the pump (assuming a centrifugal pump). However, even if you did have that it would still only be an estimate. much better to install a flow meter and actually measure the discharge. I can see no reason to go through this exercise to estimate the nozzle coefficient using only estimated flow rates.