Two equations..which to use?

[BoneMental]

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I'm talking about the continuity equation and Bernoulli's equation.

For example, let's say you have a pipe with a diameter of 5cm at point A and a diameter of 10cm at point B. Water flows through the pipe.

-----------A-------------------------B-----------

To find the velocities at each point, do you use the continuity equation? Or do you use Bernoulli's equation? Can you use both?

What are the cases when you use Bernoulli and the continuity equation, respectively? They both seem similar...

 

[justhanging]

I'm talking about the continuity equation and Bernoulli's equation.

For example, let's say you have a pipe with a diameter of 5cm at point A and a diameter of 10cm at point B. Water flows through the pipe.

-----------A-------------------------B-----------

To find the velocities at each point, do you use the continuity equation? Or do you use Bernoulli's equation? Can you use both?

What are the cases when you use Bernoulli and the continuity equation, respectively? They both seem similar...

You can always use both depending on what they gave you. I don't think you can solve for velocities at A or B because you haven't given enough info. though you can solve for the ratio of velocities at A and B. If they gave you pressure then use bernolis but if they gave you area or diameter use the continuity. Bernolis is a conservation of energy formula while the continuity formula basically just says that the amount of fluid going out of A will be the same as going in B.

 

[BoneMental]

Alright, thanks dude!

 

[kupa]

Also note that fluid velocity is different depending on the position with respect to the diameter due to shear stress. It makes a lot of difference whether the points are at the center of the fluid motion or on the edge.

 

[RogueUnicorn]

Also note that fluid velocity is different depending on the position with respect to the diameter due to shear stress. It makes a lot of difference whether the points are at the center of the fluid motion or on the edge.

way out of scope for the mcat, unless it's a concept introduced in a passage

 

[kupa]

way out of scope for the mcat, unless it's a concept introduced in a passage

Exactly. What I tried to imply was that a question like the one introduced by the OP would not be on an MCAT, because as I said, the velocity of a fluid varies greatly along the diameter of the pipe.

 

[RogueUnicorn]

Exactly. What I tried to imply was that a question like the one introduced by the OP would not be on an MCAT, because as I said, the velocity of a fluid varies greatly along the diameter of the pipe.

no mon frer, in my humble opinion OP's question is a classic way to test fluid dynamics on the mcat, using the Av'=A'v' equation

 

[kupa]

no mon frer, in my humble opinion OP's question is a classic way to test fluid dynamics on the mcat, using the Av'=A'v' equation

The v you are using in that equation is the average velocity of the liquid.
For a fluid motion at any single point in time, there is one Vmax and one Vavg, but infinitely many velocities.

 

[RogueUnicorn]

The v you are using in that equation is the average velocity of the liquid.
For a fluid motion at any single point in time, there is one Vmax and one Vavg, but infinitely many velocities.

yes. but i am having a hard time understanding your point?

 

[Rabolisk]

I'm going to have to agree with bleargh here. This seems like a very typical question, both on the MCAT and in your first year physics class.

 

[michaelfranklin]

I agree. You should know how the Continuity Equation and Bernouilli's Equation may interact. Here's a good example of how you might need to use both to answer a question.

Suppose that a stream of fluid flows steadily through a horizontal pipe of varying cross-sectional diameter. Neglecting viscosity, where is the fluid pressure greatest?
A) At the intake point
B) At the point of maximum diameter
C) At the point of minimum diameter
D) At the point of maximum change in diameter.

From Bernouilli’s Equation, where P + ρgh + ½ ρv^2 = K, absolute pressure P will be the greatest where ρgh and ½ ρv2 is the smallest. Since you assume that h is the same for all points, Bernouilli's becomes P + ½ ρv^2 = K. So you want to look for a point that has the lowest fluid velocity. From the Continuity Equation, where Q = Av and Q is constant in this case, you know that fluid velocity will be smallest at a point where cross-sectional area is the greatest. The answer is B