Increasing flow rate makes pressure drops larger

[fysik]

hello

In venturi meters, orifice plate meters and generally when there is a neck, constriction at a point in a pipe there is, at that point, a drop in pressure and an increase in velocity, so that the whole energy is preserved (theoretically)

my question is, why if we increase the flow rate (which means we increase the pressure in the pipe?) we have a much larger drop in pressure at the constriction?

that drop in pressure is larger, going through the same restricted hole, but why? what is the cause of this?

I could expected the drop in pressure to be the same, as the diameter of the hole is the same

but it seems that MORE energy becomes from pressure energy into kinetic energy with increased flow rate

but why?

thanks

 

[russ_watters]

Welcome to PF!

How familiar are you with Bernoulli's principle and equation? What does it say about this situation?

 

[Chestermiller]

hello

In venturi meters, orifice plate meters and generally when there is a neck, constriction at a point in a pipe there is, at that point, a drop in pressure and an increase in velocity, so that the whole energy is preserved (theoretically)

my question is, why if we increase the flow rate (which means we increase the pressure in the pipe?) we have a much larger drop in pressure at the constriction?

that drop in pressure is larger, going through the same restricted hole, but why? what is the cause of this?

I could expected the drop in pressure to be the same, as the diameter of the hole is the same

but it seems that MORE energy becomes from pressure energy into kinetic energy with increased flow rate

but why?

thanks

At the higher flow rate, the fluid is experiencing greater acceleration (the difference in velocities between upstream and at the contraction is greater) so you need to apply more net force (i.e., a higher pressure difference).

Chet

 

[russ_watters]

Well, my take on questions like this is "larger" in what sense? The equation is what it is and is exactly the same for a low flow rate as for a high flow rate. The pressure change in psi or torr may be different at different flow rates, but the equation dictates that the pressure change in % is exactly the same. That's why I'm looking for the OP to dig into the equation.

 

[fysik]

well, the equation clearly states that the difference in pressure (drop in pressure) is proportional to the flow rate

but I am asking why

why fastest water through an orifice causes larger pressure drop through that orifice

 

[Chestermiller]

Well, my take on questions like this is "larger" in what sense? The equation is what it is and is exactly the same for a low flow rate as for a high flow rate. The pressure change in psi or torr may be different at different flow rates, but the equation dictates that the pressure change in % is exactly the same. That's why I'm looking for the OP to dig into the equation.

I'm a little confused. Doesn't the Bernoulli equation say that the pressure difference increases in proportion to the square of the flow rate?

My understanding of Bernoulli is that the work done by the pressure forces is equal to the change in kinetic energy of the fluid (neglecting potential energy changes). Or equivalently, larger pressure differences are required to accelerate the fluid more.

Chet

 

[russ_watters]

I'm a little confused. Doesn't the Bernoulli equation say that the pressure difference increases in proportion to the square of the flow rate?

Yes. So a doubling of velocity always yields four times the pressure change, whether the first velocity was 1 or 7 or 200 m/s or ft/sec.

It's just an opinion, but I think it is more useful because it is more specific that way.

 

[fysik]

but what about my question?

 

[Chestermiller]

but what about my question?

Russ and I answered your question in two different, but consistent, ways. I'm just trying to figure out why you still feel that neither of these answers your question.

Chet

 

[russ_watters]

well, the equation clearly states that the difference in pressure (drop in pressure) is proportional to the flow rate

but I am asking why

why fastest water through an orifice causes larger pressure drop through that orifice

I see two different and perhaps new questions there:
1. Why does pressure change at all? A: Conservation of energy requires it and the pressure is the force that causes the speed change.
2. Why is it a square function? Dimensions: velocity is one dimension (length) and area is two (length and width). So when one affects the other, it must be a square function.