Pascal's Principle vs. Bernoulli's Principle

In summary, Pascal's principle states that the pressure in a fluid acts equally in all directions at a given point, and is only applicable in static situations where there is no difference in height. Bernoulli's equation, on the other hand, is a conservation of energy equation for fluids and describes how pressure, velocity, and elevation of the fluid vary with location in non-static cases. It is also only applicable in steady state situations and when viscosity can be ignored.
  • #1
Isaac0427
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Hi,

There is a basic problem I am having with fluid dynamics that has been really confusing me.

I have been told that as a result of conservation of energy and Pascal's principle, for an incompressible fluid Pin=Pout, or pressure is constant.

However, pressure is not necessarily constant in Bernoulli's equation (as if it were, pressure wouldn't even be in the equation).

Is it that pressure is constant if the fluid is static and there is no height difference? If so, textbooks say that it applies in that weird U-shaped container where there is definitely a height difference. How does this work?

Thanks in advance!
 
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  • #2
Pascal's principle doesn't involve acceleration of the fluid; it describes a static, equilibrium situation. Bernoulli's equation is based on the fact that the same volume of fluid has to leave as the volume leaving. If there's a change in cross sectional area then liquid has to change velocity, which requires a force imbalance to accelerate the fluid.
 
  • #3
Isaac0427 said:
Hi,

There is a basic problem I am having with fluid dynamics that has been really confusing me.

I have been told that as a result of conservation of energy and Pascal's principle, for an incompressible fluid Pin=Pout, or pressure is constant.

However, pressure is not necessarily constant in Bernoulli's equation (as if it were, pressure wouldn't even be in the equation).

Is it that pressure is constant if the fluid is static and there is no height difference? If so, textbooks say that it applies in that weird U-shaped container where there is definitely a height difference. How does this work?

Thanks in advance!
Pascal law state that if pressure in a liquid is changed at aparticular point,the change is transmitted to the entire liquid without being diminished in magnitude
And u shape has always same height on either side if there is no any external pressure and difference in cross sectional areas
 
  • #4
Pascal's law just says that, at a given location in a fluid (that is either static or flowing), the pressure acts equally in all directions at that point. This says nothing about how the pressure changes from location to location. Bernoulli's equation is a conservation of energy equation for the fluid, and describes how the variations of pressure, velocity, and elevation of the fluid vary with location.
 
  • #5
So, Sal Kahn said that Pin=Pout--when is that applicable?
 
  • #7
Isaac0427 said:
So, Sal Kahn said that Pin=Pout--when is that applicable?
Who’s Sal Khan?
 
  • #8
Isaac0427 said:
So, Sal Kahn said that Pin=Pout--when is that applicable?

Basically only when talking about static (non-moving) fluids where change in pressure due to height effects is negligible.
 
  • #9
cjl said:
Basically only when talking about static (non-moving) fluids where change in pressure due to height effects is negligible.
This is not correct. Certainly, in the standardTorricelli problem, the inlet and outlet pressures are atmospheric.
 
  • #10
Chestermiller said:
Who’s Sal Khan?
From Kahn Academy. Here's the link:
 
  • #11
Isaac0427 said:
From Kahn Academy. Here's the link:

Do you have a specific problem that you are having trouble understanding and that you would like to focus on? If so, please state it.
 
  • #12
Chestermiller said:
Do you have a specific problem that you are having trouble understanding and that you would like to focus on? If so, please state it.
No, I'm just confused, as it seems as though the equation Sal gave is inconsistent with Bernoulli's equation.
 
  • #13
Isaac0427 said:
No, I'm just confused, as it seems as though the equation Sal gave is inconsistent with Bernoulli's equation.
Please write out the equation for us that is causing you confusion and how you feel that it is not consistent with the Bernoulli equation.
 
  • #14
That's what I had in the OP; Sal gives the equation Pin=Pout, but in the Bernoulli equation P is not necessarily constant.
 
  • #15
That's because, despite Chestermiller confusingly trying to assert otherwise, it is a principle of fluid statics, and thus is only meant to be applied to unmoving fluids.
 
  • #16
Chestermiller said:
This is not correct. Certainly, in the standardTorricelli problem, the inlet and outlet pressures are atmospheric.

Sure, problems exist where the pressure at two points is identical despite fluid moving, but the principle in question is a principle of fluid statics, and does not apply in general unless the fluid is not moving.
 
  • #17
cjl said:
Sure, problems exist where the pressure at two points is identical despite fluid moving, but the principle in question is a principle of fluid statics, and does not apply in general unless the fluid is not moving.
The Bernoulli equation does not only apply to fluid statics.
 
  • #18
Chestermiller said:
The Bernoulli equation does not only apply to fluid statics.

Of course not. Pascal's principle is the principle at question here though, and it only applies to statics. Bernoulli only really is meaningful with fluid dynamics, hence the apparent contradiction between the two.
 
  • #19
I looked over the Khan video, and, as far as I can tell, the analysis (although poorly presented) is essentially consistant with the Bernoulli equation. Which part don't you feel is consistent with Bernoulli?

Applying Bernoulli, $$P_1 + \rho g z_1=P_2 + \rho g z_2$$where ##P_1=F_1/A_1## and ##P_2=F_2/A_2##

Now, geometrically, $$z_2-z_1=D_2+D_1$$

So $$P_1=P_2+\rho g (D_1+D_2)$$

Now, if ##D_1## is differentially small, then so is ##D_2##, and the Bernoulli equation approaches:

$$P_1\approx P_2$$

Now do you see why I think the presentation in the Khan video was poor.
 
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  • #20
Chestermiller said:
Now do you see why I think the presentation in the Khan video was poor.
Very much so. So, Pascal's principle is just for static situations where there is no difference in height. Would it also apply when the system is in a non-static equilibrium, still with no difference in height?

Thank you very much.
 
  • #21
No, that's when you would use Bernoulli (for non-static cases that are still at a steady state and where you can ignore viscosity), or delve into increasingly complex fluid dynamics equations depending on what assumptions you make.
 
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  • #22
Isaac0427 said:
Very much so. So, Pascal's principle is just for static situations where there is no difference in height. Would it also apply when the system is in a non-static equilibrium, still with no difference in height?

Thank you very much.
Pascal's law (often incorrectly stated) refers to conditions at a single point in a fluid, not to multiple locations, or to locations throughout the fluid. It applies whether of not the fluid is flowing. It says that the pressure at a point acts equally in all directions at the point. In fluid mechanics parlance, fluid pressure is "isotropic."
 
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  • #23
Okay, thank you. I understand this now.
 

What is Pascal's Principle?

Pascal's Principle, also known as the principle of transmission of fluid-pressure, states that a change in pressure applied to an enclosed fluid is transmitted equally to every part of the fluid and the walls of the container.

What is Bernoulli's Principle?

Bernoulli's Principle states that as the speed of a fluid increases, its pressure decreases. This principle is based on the conservation of energy and is commonly observed in the flow of fluids such as air or water.

What is the main difference between Pascal's Principle and Bernoulli's Principle?

The main difference between Pascal's Principle and Bernoulli's Principle is that Pascal's Principle focuses on the transmission of pressure in an enclosed fluid, while Bernoulli's Principle focuses on the relationship between the speed and pressure of a fluid in motion.

How are Pascal's Principle and Bernoulli's Principle related?

Pascal's Principle and Bernoulli's Principle are both based on the properties of fluids and how they behave under different conditions. They are related in that they both demonstrate the effects of pressure on fluids, but they approach this concept from different angles.

What are some real-life applications of Pascal's Principle and Bernoulli's Principle?

Pascal's Principle is used in many hydraulic systems, such as car brakes and heavy machinery, to multiply force and create powerful movements. Bernoulli's Principle is used in applications such as airplane wings, where the shape of the wing creates a difference in air pressure that allows for lift and flight.

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