Educate me on fluid dynamics

[Chevy-SS]

I replaced two rear brake lines with nickel/copper tubing. I love this stuff as its easy to bend and double-flare.

HOWEVER, my brake pedal now requires substantially more effort to stop the car. The pedal is good and firm and high. And I bled the **** out of the brakes after installing the new lines. My theory is that I must have created smaller openings in the brake lines where I formed the double-flared ends. Fluid is still getting through OK, as it was easy to bleed the brakes at the calipers.

What exactly is happening when a slight restriction is placed in a brake line?????? Bernoulli's Law or something to that effect?

There's gotta by a few fluid dynamics folks in here. Help me out.

Thanks

 

[a_thiel24]

I think you are correct in that it involves Bernoulli's equation. The caliper/wheel cylinder, depending on what you're working on, still requires the same amount of fluid to do its job. If you have indeed decreased the cross sectional area of the brake line, the brake fluid will flow slower and require more pressure. I should know more about this as I just took the class last fall, but I'm sure someone else will gladly chime in if I am wrong lol.

 

[lbperry]

If you displace a certain volume of fluid at the head (master cylinder) of the tubing, wouldn't the same volume of fluid be displaced at the caliper/wheel cylinder end of the tubing regardless of the diameter of the tubing itself?

 

[kerrynzl]

If you displace a certain volume of fluid at the head (master cylinder) of the tubing, wouldn't the same volume of fluid be displaced at the caliper/wheel cylinder end of the tubing regardless of the diameter of the tubing itself?

Correct
Pressure is pressure and volume is volume.

Restricting volume will slow down the pedal movement [both ways] but if it is now too firm there is another issue

 

[bsaint]

Yea since brake fluid isn't really "flowing" through the system. Its a near static system.

 

[EdT]

Yes, if you displace an amount of fluid at one end of the system the same amount will be displaced at the other end. The question here appears to be how long does it take for the pressures and volumes to equalize. If the diameter of the tube is significantly reduced the flow will be correspondingly reduced and it will take more time for the system to reach equilibrium. I the most simplistic example, the flow through a hole changes as the fourth power of the diameter of the hole. That is, if you made the hole effectively half as big as it was your flow would be 1/16th as much as it was. So, that might be noticeable. Again, the brakes would still be applied with just as much force, eventually. Imagine a syringe with a large diameter needle. Press on the plunger with a known force and the fluid inside will be squirted out in an amount of time. The same syringe with the same fluid and the same force with a little skinny needle on it and it will take longer to get the fluid out and if you put a pressure gauge on it it would be the same in both cases. IMHO the flares would have to pretty "wrong" for this to occur.

 

[pancho400cid]

Bernoulli's eq is just a re-statement of the law of conservation of energy. It says that the summed energy due to elevation, pressure and flow is constant everywhere in the system. You can exchange one form of energy for another. Makes sense.

Did you use the same size brake lines (I'm guessing "yes") or change out other components (master cyl, etc.)?

Honestly - I would be surprised that lines would make that much difference unless the new lines were significantly smaller or more restricted.

You didn't reverse connections at the proportioning valve or something like that?

What kind of car? Is there a vacuum booster and is it working right?

Not being a jerk - just asking....

 

[larry_g]

Bernoulli's eq is just a re-statement of the law of conservation of energy. It says that the summed energy due to elevation, pressure and flow is constant everywhere in the system. You can exchange one form of energy for another. Makes sense.

Did you use the same size brake lines (I'm guessing "yes") or change out other components (master cyl, etc.)?

Honestly - I would be surprised that lines would make that much difference unless the new lines were significantly smaller or more restricted.

You didn't reverse connections at the proportioning valve or something like that?

What kind of car? Is there a vacuum booster and is it working right?

Not being a jerk - just asking....

Tell us all you can about why your replaced the lines, any other brake or engine work done about the same time. Have you confirmed that the rear brakes are even working? Like Pancho said it's hard to believe just a line change would cause problems. What make and model would help.

I ask about the motor work in case the vacuum signal to the booster has changed.

lg
no neat sig line

 

[rsanter]

When you bent the tubing did you reduce the cross section area at all?
One reason for using actual bender tools verses bending with your hand is that it helps keep from partially collapsing the tubing. If you reduce the cross sectional area , depending on how much you may have a localized increase in pressure due to the restriction and that may be causing the problem

Bob

 

[kerrynzl]

The OP should check the tamdem M/C , the floating piston has probably bottomed out.
It will appear much stiffer because clamping pressure is only on one circuit

Just crack the bleed screws on the the front, and let it gravity bleed for a while.
The floaring piston should centralize itself [it is spring loaded]

 

[Chevy-SS]

Bernoulli's eq is just a re-statement of the law of conservation of energy. It says that the summed energy due to elevation, pressure and flow is constant everywhere in the system. You can exchange one form of energy for another. Makes sense.

Did you use the same size brake lines (I'm guessing "yes") or change out other components (master cyl, etc.)?

Honestly - I would be surprised that lines would make that much difference unless the new lines were significantly smaller or more restricted.

You didn't reverse connections at the proportioning valve or something like that?

What kind of car? Is there a vacuum booster and is it working right?

Not being a jerk - just asking....

Good questions, thanks. It's a '03 Cadillac DeVille. Same size brake lines. NOTHING else was touched in the system. I simply replaced lines on both sides, and bled the brakes. The Ni/Cu line bends very easily with no kinks.....

Tell us all you can about why your replaced the lines, any other brake or engine work done about the same time. Have you confirmed that the rear brakes are even working? Like Pancho said it's hard to believe just a line change would cause problems. What make and model would help.

I ask about the motor work in case the vacuum signal to the booster has changed.

lg
no neat sig line

Replaced two brake lines that were badly rusted, that's it. NOTHING else done to anything. Bleeding the system seemed to go smoothly.

When you bent the tubing did you reduce the cross section area at all?
One reason for using actual bender tools verses bending with your hand is that it helps keep from partially collapsing the tubing. If you reduce the cross sectional area , depending on how much you may have a localized increase in pressure due to the restriction and that may be causing the problem

Bob

Yep, good comment about the tubing bender. I have a pretty good one, but the small Ni/Cu brake lines bend very easily without kinking at all. However, I will double check the lines for kinks.


Thanks for all comments! I plan on putting the car back on my lift this afternoon and taking the two lines off, and checking them out carefully. If I can post pics of any obvious issues, I will.

I'll post my observations later, and hopefully I'll have it fixed too!

 

[rlitman]

...If you have indeed decreased the cross sectional area of the brake line, the brake fluid will flow slower and require more pressure...

At the point where it is restricted, you will increase the velocity and decrease the pressure. But as pointed out above, that's not relevant in a brake hydraulic system as the flow rate is way too low.

The question I'd ask is how the **** was bled out of the system? If good flow was seen while bleeding (and the **** cannot be bled out of a system without decent flow), then certainly flow will be good enough for normal operations (which is much lower than the flow seen when bleeding).

I believe kerrynzl is pointing in the correct direction.

 

[Chevy-SS]

At the point where it is restricted, you will increase the velocity and decrease the pressure. But as pointed out above, that's not relevant in a brake hydraulic system as the flow rate is way too low.

The question I'd ask is how the **** was bled out of the system? If good flow was seen while bleeding (and the **** cannot be bled out of a system without decent flow), then certainly flow will be good enough for normal operations (which is much lower than the flow seen when bleeding).

I believe kerrynzl is pointing in the correct direction.

In other words, I have no brakes in the rear?? That is a possibility, but I didn't do anything that would have shifted the internal M/C components. That is, I never pumped the M/C when bleeding, I simply let them gravity bleed. However, I may indeed be operating with front brakes only. That will be the first thing I check....

Thanks

 

[rlitman]

In other words, I have no brakes in the rear?? That is a possibility, but I didn't do anything that would have shifted the internal M/C components. That is, I never pumped the M/C when bleeding, I simply let them gravity bleed. However, I may indeed be operating with front brakes only. That will be the first thing I check....

Thanks

Could be in the MC, or it could be in any place where there are two pistons in parallel. You didn't say it was pulling, so I wouldn't guess that one of a pair of caliper pistons was seized. Maybe something happened in a proportioning valve (I'm not familiar with your vehicle's particular plumbing arrangement)?

But yeah, no brakes in the rear would be the first thing that comes to mind.

Do you happen to have an IR temp gun? You could measure the rotor temperature after a drive and quickly see if they're working.

 

[Chevy-SS]

Could be in the MC, or it could be in any place where there are two pistons in parallel. You didn't say it was pulling, so I wouldn't guess that one of a pair of caliper pistons was seized. Maybe something happened in a proportioning valve (I'm not familiar with your vehicle's particular plumbing arrangement)?

But yeah, no brakes in the rear would be the first thing that comes to mind.

Do you happen to have an IR temp gun? You could measure the rotor temperature after a drive and quickly see if they're working.

Well, put the car on lift and then stuck a short 2x4 from seat to brake pedal, and the brakes seem to be working fine.

Then disconnected the lines to check connections and all flares were spot-on, so no restrictions in those areas. Bled the brakes with pressure bleeder.

Interesting issue. I think the IR gun is great idea, thanks. I will do some rather hard braking then shoot IR at all four wheels and see what kinds of temps I am getting.

Thanks for all comments gents!

 

[HoosierBuddy]

In other words, I have no brakes in the rear?? That is a possibility, but I didn't do anything that would have shifted the internal M/C components. That is, I never pumped the M/C when bleeding, I simply let them gravity bleed. However, I may indeed be operating with front brakes only. That will be the first thing I check....

Thanks

You only gravity bled the system?

I finally broke down and bought a power bleeder. Last car I worked on (Subaru WRX) I gravity bled first and then switched over to the power bleeder. Amazing how much air was still in there.

Phil

 

[Chevy-SS]

You only gravity bled the system?

I finally broke down and bought a power bleeder. Last car I worked on (Subaru WRX) I gravity bled first and then switched over to the power bleeder. Amazing how much air was still in there.

Phil

I power bled the **** out of brakes today. I have a super-duper power bleeder....

 

[Milton Shaw]

If the lines were restricted enough to cause a hard pedal the brakes would never release as the brake springs(or caliper release) would not push fluid back through the restriction. I think you have power booster problems from what it sounds like.

 

[aggierailroad]

Going back to your original fluids question, you've got a few fluid dynamics things happening. One, in a hydraulic system, you are working with Pascal's law. basically, the pressure at each end is equal. This means the pressure of the brake master cylinder piston is the same as the pistons at the brake drums/calipers. The only things that change are the areas (piston diameters) which then gives you more force. P1=P2 (assuming no friction losses) and pressure is force/area.

You don't get a work multiplier in hydraulic systems - combined with your friction losses from a smaller line, you feel a firmer pedal. Those friction losses are caused by a reduction in your brake line diameter. You still are flowing the same volume through a smaller hole. A smaller hole has a greater surface area per cross sectional area. So, combine Pascal's law with some work on friction factors by Darcy and Weisbech and you get a nice law from Poiseuille.

If we assume that the fluid doesn't become turbulent (it probably is, but this gets us going) we get that volume flowrate = (pressure difference [pedal to brake] * radius^4) / ( 8/pi * viscosity * length)

It's getting crazy but we can simplify. The bottom half, pi and viscosity and length are the same in your pre and post tubing change. The big difference is in the radius. It is an exponent to the 4th power. If you decrease it by a size, that's multiplied 4 more times. We are interested in the pressure, so, divide the flowrate by the new radius^4th power and you can see that it makes a big difference.

For example. Let's say the flow is 1 cubic inch/s (let's get rid of the second because that's a unit in viscosity) and say force now. Divide that by your old tubing diameter (let's say 3/8 inch to the 4th power) and you get 0.0198. 1 divided by that is about 50 lbs of "pedal" force.

If you changed to quarter inch tubing, that 50 lbs now becomes 300!

This is a really rough example but shows you how fluids don't like to go through small diameters. The big reason is friction losses along the walls of the tube or pipe. In brakes, you want big tubes for an easy push, but no so easy that you are stomping the floor.

Hope this long, nerdy post helps.

 

[zable9]

Going back to your original fluids question, you've got a few fluid dynamics things happening. One, in a hydraulic system, you are working with Pascal's law. basically, the pressure at each end is equal. This means the pressure of the brake master cylinder piston is the same as the pistons at the brake drums/calipers. The only things that change are the areas (piston diameters) which then gives you more force. P1=P2 (assuming no friction losses) and pressure is force/area.

You don't get a work multiplier in hydraulic systems - combined with your friction losses from a smaller line, you feel a firmer pedal. Those friction losses are caused by a reduction in your brake line diameter. You still are flowing the same volume through a smaller hole. A smaller hole has a greater surface area per cross sectional area. So, combine Pascal's law with some work on friction factors by Darcy and Weisbech and you get a nice law from Poiseuille.

If we assume that the fluid doesn't become turbulent (it probably is, but this gets us going) we get that volume flowrate = (pressure difference [pedal to brake] * radius^4) / ( 8/pi * viscosity * length)

It's getting crazy but we can simplify. The bottom half, pi and viscosity and length are the same in your pre and post tubing change. The big difference is in the radius. It is an exponent to the 4th power. If you decrease it by a size, that's multiplied 4 more times. We are interested in the pressure, so, divide the flowrate by the new radius^4th power and you can see that it makes a big difference.

For example. Let's say the flow is 1 cubic inch/s (let's get rid of the second because that's a unit in viscosity) and say force now. Divide that by your old tubing diameter (let's say 3/8 inch to the 4th power) and you get 0.0198. 1 divided by that is about 50 lbs of "pedal" force.

If you changed to quarter inch tubing, that 50 lbs now becomes 300!

This is a really rough example but shows you how fluids don't like to go through small diameters. The big reason is friction losses along the walls of the tube or pipe. In brakes, you want big tubes for an easy push, but no so easy that you are stomping the floor.

Hope this long, nerdy post helps.

#fistbump....make me have flashbacks to college....;-)

 

[kerrynzl]

Going back to your original fluids question, you've got a few fluid dynamics things happening. One, in a hydraulic system, you are working with Pascal's law. basically, the pressure at each end is equal. This means the pressure of the brake master cylinder piston is the same as the pistons at the brake drums/calipers. The only things that change are the areas (piston diameters) which then gives you more force. P1=P2 (assuming no friction losses) and pressure is force/area.

You don't get a work multiplier in hydraulic systems - combined with your friction losses from a smaller line, you feel a firmer pedal. Those friction losses are caused by a reduction in your brake line diameter. You still are flowing the same volume through a smaller hole. A smaller hole has a greater surface area per cross sectional area. So, combine Pascal's law with some work on friction factors by Darcy and Weisbech and you get a nice law from Poiseuille.

If we assume that the fluid doesn't become turbulent (it probably is, but this gets us going) we get that volume flowrate = (pressure difference [pedal to brake] * radius^4) / ( 8/pi * viscosity * length)

It's getting crazy but we can simplify. The bottom half, pi and viscosity and length are the same in your pre and post tubing change. The big difference is in the radius. It is an exponent to the 4th power. If you decrease it by a size, that's multiplied 4 more times. We are interested in the pressure, so, divide the flowrate by the new radius^4th power and you can see that it makes a big difference.

For example. Let's say the flow is 1 cubic inch/s (let's get rid of the second because that's a unit in viscosity) and say force now. Divide that by your old tubing diameter (let's say 3/8 inch to the 4th power) and you get 0.0198. 1 divided by that is about 50 lbs of "pedal" force.

If you changed to quarter inch tubing, that 50 lbs now becomes 300!

This is a really rough example but shows you how fluids don't like to go through small diameters. The big reason is friction losses along the walls of the tube or pipe. In brakes, you want big tubes for an easy push, but no so easy that you are stomping the floor.

Hope this long, nerdy post helps.

Going by all this ********, the pedal will still be hard if he removed the bleed screws

Look for the obvious issues

 

[Chevy-SS]

Going by all this ********, the pedal will still be hard if he removed the bleed screws

Look for the obvious issues

LOL, I agree about looking for the obvious. But the professor did exactly what I asked in the title of the thread: "Educate me on fluid dynamics".

 

[Zeke]

When you bent the tubing did you reduce the cross section area at all?
One reason for using actual bender tools verses bending with your hand is that it helps keep from partially collapsing the tubing. If you reduce the cross sectional area , depending on how much you may have a localized increase in pressure due to the restriction and that may be causing the problem

Bob

I'm thinking this. I once did some calcs that I didn't believe. Take a round tube and make it an oval or ellipse, the area is reduced.

 

[CarBikeGuy70]

This whole post takes me back to my days in college. A small diameter or change in a radius makes a huge difference in performance of a fluid that is performing a function. I had a prof. in college who was a retired engineer involved in the hydraulics field and he could make your head spin on this exact subject. Larger diameter lines and larger radius smooth bends are the easy way to make life great with fluids ( everything else being the same).

 

[aggierailroad]

Going by all this ********, the pedal will still be hard if he removed the bleed screws

Look for the obvious issues

This is wrong in so many ways. If you open it right up it would just be harder to push by a fraction. I guess it's not obvious to think about what changed and to ask why that made a change.

If you take out the bleeders then p1 does not equal p2, master cylinder pressure does not equal brake cylinder pressure. Sure, you can set the equation to zero but then all you can solve for is fluid velocity. What that will show you is that it speeds up from the smaller area. When a high speed fluid suddenly finds itself stopping on a dime you get pressure.

 

[pancho400cid]

Brake systems are only "barely" dynamic fluid systems. I can assure you that you can beat a brake line half flat with a hammer and no one could tell a difference in the pedal feel or performance.

 

[aggierailroad]

Brake systems are only "barely" dynamic fluid systems. I can assure you that you can beat a brake line half flat with a hammer and no one could tell a difference in the pedal feel or performance.

Which is why we used equations for static systems.

 

[Superbec]

If the lines were restricted enough to cause a hard pedal the brakes would never release as the brake springs(or caliper release) would not push fluid back through the restriction. I think you have power booster problems from what it sounds like.

this !

 

[Superbec]

Going back to your original fluids question, you've got a few fluid dynamics things happening. One, in a hydraulic system, you are working with Pascal's law. basically, the pressure at each end is equal. This means the pressure of the brake master cylinder piston is the same as the pistons at the brake drums/calipers. The only things that change are the areas (piston diameters) which then gives you more force. P1=P2 (assuming no friction losses) and pressure is force/area.

You don't get a work multiplier in hydraulic systems - combined with your friction losses from a smaller line, you feel a firmer pedal. Those friction losses are caused by a reduction in your brake line diameter. You still are flowing the same volume through a smaller hole. A smaller hole has a greater surface area per cross sectional area. So, combine Pascal's law with some work on friction factors by Darcy and Weisbech and you get a nice law from Poiseuille.

If we assume that the fluid doesn't become turbulent (it probably is, but this gets us going) we get that volume flowrate = (pressure difference [pedal to brake] * radius^4) / ( 8/pi * viscosity * length)

It's getting crazy but we can simplify. The bottom half, pi and viscosity and length are the same in your pre and post tubing change. The big difference is in the radius. It is an exponent to the 4th power. If you decrease it by a size, that's multiplied 4 more times. We are interested in the pressure, so, divide the flowrate by the new radius^4th power and you can see that it makes a big difference.

For example. Let's say the flow is 1 cubic inch/s (let's get rid of the second because that's a unit in viscosity) and say force now. Divide that by your old tubing diameter (let's say 3/8 inch to the 4th power) and you get 0.0198. 1 divided by that is about 50 lbs of "pedal" force.

If you changed to quarter inch tubing, that 50 lbs now becomes 300!

This is a really rough example but shows you how fluids don't like to go through small diameters. The big reason is friction losses along the walls of the tube or pipe. In brakes, you want big tubes for an easy push, but no so easy that you are stomping the floor.

Hope this long, nerdy post helps.

wow... in all that sciency stuff you forgot there are at least 2 pistons in the front brakes ...

 

[aggierailroad]

wow... in all that sciency stuff you forgot there are at least 2 pistons in the front brakes ...

They were there before he changed the lines, they were there after he changed the lines. Net/net is zero. Regardless, it's just a back of the napkin calculation to show the cause and effect of putting a smaller line in a piping system.

My previous job was as a construction superintendent building refineries and petrochemical plants. I've done quite a few piping systems. I'm not an industry expert but I've got a lot of real world troubleshooting experience. Believe it or not I'm not trying to fan any flames here - just add my knowledge to this great forum where I've learned so much.

 

[Evilunclegrimace]

No one mentioned bleeding the ABS system. Some of these new units do not like to be run out of fluid and they have very specific procedures to flush the air out of the if I am not mistaken.

 

[kerrynzl]

No one mentioned bleeding the ABS system. Some of these new units do not like to be run out of fluid and they have very specific procedures to flush the air out of the if I am not mistaken.

Good point,
My dad had a Toyota pickup that had a really hard pedal and no stopping power.
It had an axle bearing leaking oil over the rear brakes. The ABS was doing what it was programmed to do, and equalized all the wheel speeds.

I think the "professor" has the early stages of the "Dunning Kruger Effect"

There is a shitload of a difference between flow in pipings systems and clamping pressure in a brake system [where the calliper piston only moves 5 thou maximum]
If there was a restriction in the brake lines [not a blockage] as he is claiming ,the rear brakes would remain on for a while after the brakes are released.



There is quite a bit of math in designing a brake system [I do this a lot for race cars] but the diameter of bundy tubing isn't one of the neccessary calculations

 

[aggierailroad]

I guess I'm the dummy. I didn't invent scenarios that the OP never mentioned such as oil on an ABS sensor. Again, I answered his original question - "What exactly is happening when a slight restriction is placed in a brake line?????? Bernoulli's Law or something to that effect?"

There is absolutely no difference in the two systems. None. Hydraulic pressure doesn't change for incompressible fluids. It's also conceivable that the rear brakes would stay on until the pedal is released. The brake fluid would then flow, slowly, back into the low pressure side of the system - the master cylinder.

You also state that you do a lot of math designing braking systems for race cars. The reason "bundy" tubing diameter never comes into play is because everyone says the same thing - use 3/16" or 1/4" line. Even Wilwood recommends this. By fixing a variable you eliminate big chunks of that "brake system math". The question is why do they say 3/16" or 1/4"? The same reason your intake line to a pump is larger than your exhaust - you wan't to ensure there is enough liquid available. Brake fittings are 1/8" - by using a larger line you ensure that there is sufficient supply fluid in a line size that balances friction losses with expansion losses caused by pressuring up a larger diameter tubing.

It's fine not to believe me, after all, I'm apparently a disenchanted novice. Try checking out the work done here: http://www.sciencedirect.com/science/article/pii/S2090447912000135

Experimental evidence showing that line sizes matter in a braking system.

Not enough?

You're right again - line diameter isn't normally a huge deal because everyone knows to use the correctly sized line - of which you can only get two sizes from the big speed shops. But somebody had to figure out what size line to use at one time or another.

http://www.engineeringinspiration.co.uk/brakecalcs.html

Look at the steep pipe expansion section towards the bottom. Yep - you got me again. It says that it's "unlikely to be of interest" but take a second of your time to look at the equation. The diameter of the tube is the leading driver of the volume of fluid displaced. Again - it's the leading factor of the system's fluid dynamics by a factor of 3.

It matters. A line restriction is no different than using an orifice plate in any other line, tubing or pipe. They drop pressure on one side and raise it on the other.

But again, I'm just a primadonna "professor".

 

[kerrynzl]

I guess I'm the dummy. I didn't invent scenarios that the OP never mentioned such as oil on an ABS sensor. Again, I answered his original question - "What exactly is happening when a slight restriction is placed in a brake line?????? Bernoulli's Law or something to that effect?"

There is absolutely no difference in the two systems. None. Hydraulic pressure doesn't change for incompressible fluids. It's also conceivable that the rear brakes would stay on until the pedal is released. The brake fluid would then flow, slowly, back into the low pressure side of the system - the master cylinder.

You also state that you do a lot of math designing braking systems for race cars. The reason "bundy" tubing diameter never comes into play is because everyone says the same thing - use 3/16" or 1/4" line. Even Wilwood recommends this. By fixing a variable you eliminate big chunks of that "brake system math". The question is why do they say 3/16" or 1/4"? The same reason your intake line to a pump is larger than your exhaust - you wan't to ensure there is enough liquid available. Brake fittings are 1/8" - by using a larger line you ensure that there is sufficient supply fluid in a line size that balances friction losses with expansion losses caused by pressuring up a larger diameter tubing.

It's fine not to believe me, after all, I'm apparently a disenchanted novice. Try checking out the work done here: http://www.sciencedirect.com/science/article/pii/S2090447912000135

Experimental evidence showing that line sizes matter in a braking system.

Not enough?

You're right again - line diameter isn't normally a huge deal because everyone knows to use the correctly sized line - of which you can only get two sizes from the big speed shops. But somebody had to figure out what size line to use at one time or another.

http://www.engineeringinspiration.co.uk/brakecalcs.html

Look at the steep pipe expansion section towards the bottom. Yep - you got me again. It says that it's "unlikely to be of interest" but take a second of your time to look at the equation. The diameter of the tube is the leading driver of the volume of fluid displaced. Again - it's the leading factor of the system's fluid dynamics by a factor of 3.

It matters. A line restriction is no different than using an orifice plate in any other line, tubing or pipe. They drop pressure on one side and raise it on the other.

But again, I'm just a primadonna "professor".

I hope you realize the OP is refering to pedal pressure not pedal movement.

The total volume hasn't changed, and there isn't a significant change in restriction.
There is another issue that has caused the problem [eg: Tandem M/C only on the front circuit, or ABS pump not equalizing ]

 

[Chevy-SS]

LOL, now now professors, let's not quibble over the details. I am truly grateful for the help.

I posted the question with "fluid dynamics" in the title because I was fairly confident that particular phrase would draw in some of the more knowledgeable folks that peruse this forum, and my 'bait' worked, haha.

kerrynzl did pick up on an important issue though, that is, it took increased pedal pressure to stop the vehicle. Actual pedal travel is/was always minimal.

Now, interestingly, I dis-assembled all the lines, checked all line openings to make sure within spec (they were all fine), then carefully put everything back together, and used my super-duper Motive power bleeder, and it all seems good now.

So gentlemen, I salute you all and say a hearty "THANK YOU"" for the fine help!