Load on leaf blower as function of outlet shape

[Swamp Thing]

Would a leaf blower see a different load (in terms of back pressure and flow) depending on whether the outlet tube ends in, say a 1" nozzle, versus a flared out horn of 6" diameter? I am not thinking of viscosity effects here, but rather of Bernoulli type considerations.

In the case of the horn, I believe Bernoulli leads to a sub-atmospheric pressure in the narrow part of the tube where it exits the blower proper. (Is that correct?) But I am not sure about the nozzle: Would the jet of air after leaving the nozzle effectively form a "virtual horn" spreading to a larger effective diameter, or would the physical tip of the nozzle see atmospheric pressure right away?

 

[russ_watters]

No, the exit pressure is atmospheric and yes, additional static pressure is needed, which is converted to dynamic pressure in the nozzle, pet Bernoulli.

 

[Swamp Thing]

Sorry, I'm not sure which part of your response refers to which part of my question -- maybe I should have made the questions clearer. My bad.

Here are the two cases :

In the first case, define $P_{NOZZLE}$ as the pressure say 1 cm back from the tip of the spout. Will this be pretty close to atmospheric?

Define $P_{BACK}$ as the pressure at the center of the blower spout for both cases.

In the second case (with the horn attached), will $P_{BACK}$ be less than atmospheric by $1/2 \rho v^2$ ? In other words, will the blower see a lighter load with the horn attached?

 

[russ_watters]

Sorry, I read the OP backwards (the drawing helps), thinking it was a 6" duct with 1" nozzle.

But for a horn(diffuser) it is just the opposite. Bernoulli's principle still holds, so total pressure is the same at the mouth and back in the duct. So, working backwards the higher velocity pressure back in the duct means you have a lower and yes, potentially sub-atmospheric static pressure. The increase in the diffuser is often called "static regain".

 

[erobz]

Bernoulli's is valid for what happens on a streamline (steady flow) for purely hypothetical inviscid flow, which approximates real viscous flow only over very short distances. I don't believe (could be wrong) sub-atmospheric pressure in the discharge is a possible result here for any real leaf blower.

Working with inviscid flow, the leaf blower can supply any flow you desire at zero differential pressure across a straight tube. So, if you are beginning at the nozzle entrance at atmospheric pressure, and the duct is converging then you could get any sub-atmospheric nozzle exit pressure you desire...

Bernoulli's has limited applicability; this is not one of the applications for which it works to give meaningful results IMO. I think we have to look at it in a framework which at the very least considers viscosity. I would like to see that kind of an analysis before I change my mind.

 

[russ_watters]

Working with inviscid flow, the leaf blower can supply any flow you desire at zero differential pressure across a straight tube. So, if you are beginning at the nozzle entrance at atmospheric pressure, and the duct is converging then you could get any sub-atmospheric nozzle exit pressure you desire...

How would that be physically possible? It sounds like you are describing the suction side of the fan having a higher pressure than the discharge.

 

[erobz]

How would that be physically possible? It sounds like you are describing the suction side of the fan having a higher pressure than the discharge.

Yeah, inviscid flow...where Bernoulli's is applicable produces absurd results:

If I have a straight (horizontal) section of pipe, one end open to atmospheric conditions and inviscid flow and we apply Bernoulli's we get for the pipe $\Delta P = 0$ across the pipe independent of flowrate in the pipe.

In otherwords it fails pretty spectacularly at describing reality.

 

[erobz]

To me it doesn't make sense that some point (in either nozzle) the SP could dip below atmospheric pressure. It can go sub inlet-pressure at some point in either nozzle, but that is not sub atmospheric pressure. The exit ( of discharge side) being maintained a 0 gage implies the pressure at any location inside the pipe for any real viscous flow be greater than atmospheric (as far as I can tell).

 

[erobz]

After much back and forth with myself and my fluids textbook I have changed my mind. It can happen.

This is how cavitation can occur in a system. It slipped my mind because usually we are concerned with cavitation on the suction side of pumps, but it can occur on discharge side in scenarios like above.

Hopefully the diagram shows that if the kinetic head increases to the total available head at the contraction, the static head must become increasingly negative (gage pressure) as we progress in the direction of flow such that the available head at a certain position is conserved.

Sorry if I caused any confusion.

 

[russ_watters]

After much back and forth with myself and my fluids textbook I have changed my mind. It can happen.

Sorry if I caused any confusion.

I've been going back and forth as well (rereading my posts, I'm arguing against myself). What I think happens on a nuts and bolts level is the centrifugal fan throwing the air out is effectively pulling the molecules apart, and providing velocity pressure in part at the expense of static pressure.

Either that or the system must be exceptionally lossy (which it may also be).

 

[256bits]

After much back and forth with myself and my fluids textbook I have changed my mind. It can happen.

View attachment 321962

This is how cavitation can occur in a system. It slipped my mind because usually we are concerned with cavitation on the suction side of pumps, but it can occur on discharge side in scenarios like above.

Hopefully the diagram shows that if the kinetic head increases to the total available head at the contraction, the static head must become increasingly negative (gage pressure) as we progress in the direction of flow such that the available head at a certain position is conserved.

Sorry if I caused any confusion.

Are you describing a thick orifice inserted into a pipe.

 

[erobz]

Are you describing a thick orifice inserted into a pipe.

I wasn't trying to describe any specific geometry in particular. Its was just an example of how the pressure could be reduced below atmospheric in a flow.

 

[Dullard]

'Eductors' operate (very well) on this principle.