Pressure drops in hydraulic dampers

[Tommtb]

Homework Statement

Hi there, I am having a theoretical dillema which does not involve a specific problem, rather I am thinking of this scenario in my head and I am not sure how to go about it.

I am unsure whether to calculate P2 using the head loss or using the bernoulli equation. Because in textbook examples they disregard the fact that a chamber may have a reduced diameter compared to the one before and so the pressure will be lower due to the higher velocity of the fluid as shown in the picture. Hence the only pressure drop is due to the orifice.

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Is the textbook example too simplified or am I missing a key concept?

Homework Equations

The Attempt at a Solution

No specific problem so no solution.

Thank you in advance!

 

[haruspex]

calculate P2 using the head loss or using the bernoulli equation.

I don't think that is quite the right dichotomy. As I understand it (but I am not an expert so I could have this wrong), head loss is the drop in pressure by whatever cause. Flowing through an orifice into a narrower section there will be kinetic head loss (Bernoulli) and frictional head loss. These will add together. Flowing into a wider section there will be kinetic head gain, but maybe some frictional head loss again.
In many circumstances, one or other cause will dominate.

 

[Tommtb]

I don't think that is quite the right dichotomy. As I understand it (but I am not an expert so I could have this wrong), head loss is the drop in pressure by whatever cause. Flowing through an orifice into a narrower section there will be kinetic head loss (Bernoulli) and frictional head loss. These will add together. Flowing into a wider section there will be kinetic head gain, but maybe some frictional head loss again.
In many circumstances, one or other cause will dominate.

I'm assuming you also mean pressure drop (P1-P2) is different to head loss? The bernoulli equation does take into account friction losses with delta(P_st) and also the change in velocity with the kinetic velocity terms. But how does the discharge coefficient do the same?

 

[haruspex]

I'm assuming you also mean pressure drop (P1-P2) is different to head loss? The bernoulli equation does take into account friction losses with delta(P_st) and also the change in velocity with the kinetic velocity terms. But how does the discharge coefficient do the same?

I'm seeing some disagreement on these terms between different authors.
Nearly everyone writes that the Bernoulli equation assumes work conservation, so does not allow for friction. Yes, you can add a frictional term to make it more complete, but then it is no longer Bernoulli's equation.
Some write that head loss is simply the pressure difference, as I thought, while others say it is restricted to loss due to friction. I now think you are right to say it is only that due to friction.

Anyway, this is just terminology. Your original question is what terms should be in the equation.
Since there is a diameter change, you must use the work-conserving elements of Bernoulli as a starting point. Whether you need to add a frictional term depends on whether it will be large enough to matter. You can only determine that by estimating how much difference it makes.

 

[Tommtb]

I'm seeing some disagreement on these terms between different authors.
Nearly everyone writes that the Bernoulli equation assumes work conservation, so does not allow for friction. Yes, you can add a frictional term to make it more complete, but then it is no longer Bernoulli's equation.
Some write that head loss is simply the pressure difference, as I thought, while others say it is restricted to loss due to friction. I now think you are right to say it is only that due to friction.

Anyway, this is just terminology. Your original question is what terms should be in the equation.
Since there is a diameter change, you must use the work-conserving elements of Bernoulli as a starting point. Whether you need to add a frictional term depends on whether it will be large enough to matter. You can only determine that by estimating how much difference it makes.

I appreciate the reply, that does make a bit more sense. What's very confusing however is that every shock absorber modelling I come across, the pressure inside a port hole before a shim stack is never calculated, the pressure in the main chamber is always used even though its diameter is much larger than the port's leading to the shims.

Does the discharge coefficient only take into account the reduced area? There is nothing in the formulas that proves it addresses losses, though K can be calculated directly from Cd

 

[Tommtb]

Think I worked it out! The pressure on the valve isn't only the static pressure but also the dynamic (duh!), so when the fluid enters the port, even though the static is reduced, the dynamic is increased therefore the same pressure on the shim as if there wasn't a port.