# I think I understood Bernoulli principle but I need to clarify one thing quickly

1. Jan 6, 2010

### sameeralord

Ok after hours of contemplating I think I finally understood the concept(hopefully ). However I still need 1 quick clarification.

When water flows suddenly from a larger to a small dimater
Bernoulli says

1. Pressure decreases
2. Velocity of fluid increases

I'll put numbers just for easy understanding

This is according to Bernoulli assuming no loss
Energy in large diameter (Hydrostatic pressure=4 Kinetic energy=2)
Energy in small diameter(Hydrostatic pressure=2 Kinetic energy=4)

Ok in real life when you consider resistance in the smaller tube is it the K.E that is lost to create lower fluid velocity. If hydrostatic pressure is the pressure that exerts on the walls, why isn't that decreased instead. I mean resistance from walls only affect molecules hitting against it which is H.P. I just like to know what type of resistance decreases K.E in real life. Thanks a lot

2. Jan 6, 2010

### Staff: Mentor

Bernoulli's equation assumes no resistance from walls at all. Bernoulli's equation is a conservation of energy statement where the sum of the various pressures (static, velocity, perhaps gravitational) is constant.

3. Jan 6, 2010

### gmax137

Following up Russ's comment, 'in real life' we add head loss terms to the Bernoulli equation to account for friction and to account for unrecovered losses due to geometry. These head losses are typically based on empirical formulas tabulated in books like Crane 410, Cameron hydraulic manual, I'del chik, etc.

Your question "Ok in real life when you consider resistance in the smaller tube is it the K.E that is lost to create lower fluid velocity" doesn't make sense to me. The velocity is just flow rate divided by area (for incompressible flow, constant density fluids like water). The velocity in the smaller diameter must be higher in order for the mass flow rate to be constant along the pipe.

4. Jan 6, 2010

### rcgldr

In the ideal case and real world case, once a flow is established, the mass flow across any point along a pipe is constant. In a real world situation, the pressure decreases with distance due to wall friction and viscosity, and the overall mass flow is reduced, but remains constant at every point in the pipe (otherwise mass would be accumulating at some point).

5. Jan 6, 2010

### sameeralord

Thanks for all the replies. I couldn't express my question properly until now. Why is the mass flow reduced in the real world?. If the answer is simple as small diameter smaller flow why didn't Bernoulli consider this mass flow? I'm also confused why mass flow is reduced when velocity increases. Higher velocity and lower volume would still create the same flow right? I'm having this feeling that in real life particles move slower inside a contraction due to resistance? Is this wrong?

Last edited: Jan 6, 2010
6. Jan 6, 2010

### Staff: Mentor

Reduced from what? As already said, mass flow is constant in any pipe....it must be - and that's reflected in the equations. Did you read Jeff's post? Do you understand that Bernoulli's equation only deals with one pipe at a time?

Your questions don't make much sense to me.

7. Jan 7, 2010

### rcgldr

The overall mass flow is reduced because of friction with the walls of the pipe. The larger the amount of wall friction, the more the mass flow is reduced, given the same initial pressure differential at the ends of a pipe. In a pipe of constant diameter, the pressure decreases with distance, but the mass flow at any point in the pipe is the same.

The overall mass flow is reduced due to friction (and viscosity), but the mass flow at all points in a pipe will be the same, regardless of higher velocities in narrower sections of the pipe and/or lower velocities in wider sections of the pipe.

The friction in a smaller diameter pipe creates more of an opposing force to the flow than it does in a larger diameter pipe. However, the reduction in flow at the narrowest section of pipe affects the flow at all points in the pipe. Other than startup, once a flow is established, the flow same at all points in a pipe.

8. Jan 7, 2010

### sameeralord

Thanks for all the replies but I'm still bit confused.

When a blood vessel constricts, the heart's response is to increases its heart rate, thus increasing blood pressure? Is the reason behind this because total hydrostatic pressure lost is higher when an artery is constricted.

-----------------constriction----------------------------

Does the constriction act like a wall to particles left of it creating higher pressure loss, inside the constriction the pressure would obviously be lost as well.

Did I get the pressure loss thing right?

Ok my question is what does exactly this loss of hydrostatic pressure mean, are the molecules that are lost converted into heat leading into less mass? Why does a loss in hydrostatic pressure create a response where the heart beats faster?

Last edited: Jan 7, 2010
9. Jan 7, 2010

### Darmog

The blood pressure proposition has incorrect assumptions eg following artery constriction heart beats faster. Why not slower? Having been an anaesthetist used to considering these variables I would say heart output would likely fall even while systolic pressure perhaps increased. I recommend we stick to simpler models.
Darmog

10. Jan 7, 2010

### rcgldr

Regarding blood pressure, the vascular system is a closed system, so when the vascular walls constrict, it would seem that the static pressure is increased. Also, isn't blood a mixture of liquid and gas (and some solids like platelettes)?

11. Jan 7, 2010

### sameeralord

Thanks Jeff but I still got a question

---------------------------<
A(If pressure at point A is 100 mg Hg)

There is no fluid yet in the < region(which is a dilated part). When the tube tries to reach equilibrium 100 mg/Hg everywhere, why does the according to Bernoulli the pressure inside the dilated tube is higher? Shouldn't it be 100 mg/Hg. Also before fluid flows to < region, why isn't <region compressed due to to higher pressure outside?

Also you didn't address what pressure loss mean? What happens to the particles when they lose pressure? Do the particles remain stationary?

12. Jan 8, 2010

### rcgldr

Bernoulli principle applies to established flows. It doesn't explain what happens during the transition from zero flow to non-zero flow.

Once a state of equilibrium is reached where mass flow is constant at all points along a pipe, then the speed of the fluid will be faster in the narrower sections of the pipe, and slower in the wider sections of pipe. The changes in speed coexist with pressure gradients that accelerate of decelerate the fluid in a pipe. In the real world, mass flow remains constant at all points within a pipe, but the pressure decreases with distance due to wall friction, viscosity and related turbulent factors. If the pipe diameter varies, you still have the pressure gradients that accelerate or decelerate the fluid, but the overall reduction of pressure over distance remains a factor.

The pressure loss versus distance occurs because the walls of the pipe peform "negative" work on the fluid, reducing it's total kinetic energy over distance. The overall mass flow is also reduced due to this "negative" work, but the reduced mass flow is constant at all points within the pipe, with the pressure decreasing over distance.

Last edited: Jan 8, 2010
13. Jan 8, 2010

### sameeralord

Thanks for giving a nice detailed response. Ok so from what I understand when there is a constriction there is reduced constant mass flow all along the tube(meaning even in the non constricted area) . That makes sense so heart increases pressure to create a greater flow? Ok now let's say there is a tube and a dilated part? Does the dilation account for higher constant mass flow all along the tube? So heart decreases pressure to counter this? Did I finally get this? If what I'm saying is right your response was awesome and I got it.

14. Jan 8, 2010

### Darmog

This began with request to clarify one thing quickly! Bloodpressure may be most complex model and guaranteed to confuse as is evident already.
Sorry, BP not quite enclosed system as apart from blood loss, donation, and transfusion, there is substantial daily variation in blood volume by interchange with other body fluids. And the gases are in solution or in chemical combination unless you are suffering from the Bends (nitrogen bubbles). Also with all the corpuscles and platelets the viscosity is substantial.
Before Bernoulli causes an aneurism in my brain to pop may I plead for return to simply models for illustration and understanding of Bernoulli.
From Darmog

15. Jan 8, 2010

### rcgldr

Correct. Think of a constriction like the spigot on your tap or garden hose.
The heart rate also increases flow. It's a series of jerks in the flow rather than a continuous flow. Also the vascular system branches out to a huge number of parallel paths down to the tiny capillaries, all of which can compress or expand, blood has high viscosity, and this is not a good model for Bernoulli principle.

16. Jan 11, 2010

### Darmog

Loss of mass flow? Bernoulli then will no longer apply - there must be leak in your pipe.
This happens often to oil pipes in Nigeria I've heard.(Theft)
Where pressure is reduced the energy is manifest in another form ie kinetic.
Darmog

17. Jan 11, 2010

### rcgldr

I don't see any mention of loss of mass flow, only reduced overall mass flow due to restrictions in a pipe.