a question related to Bernoulli's equation.!!!

[peacefulheart]

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The diagram below shows a cross-sectional view of a
cylindrical pipe of varying diameter. ( Point A is in a greater cross-sectional area compared with point B)

If an ideal fluid isflowing through the pipe, all of the
following statements are true EXCEPT:
A. The cross-sectional area is greater at point A than at
point B.
B. The pressure is lower at point B than at point A.
C. The volume flow rate is greater at point A than at
point B.
D. The flow speed is greater at point B than at point A.

1. I have no problem with answer C.

2. For the choice B, using Bernoulli's equation, P+ pgh+ 1/2mv^2=K. Since the flow speed of point A is less than at point B by continuity equation Q=AV, the pressure is lower at point B than point A. What about pgh. are they same at both points?

3. thanks a lot .

 

[Captain Sisko]

The diagram below shows a cross-sectional view of a
cylindrical pipe of varying diameter. ( Point A is in a greater cross-sectional area compared with point B)

If an ideal fluid isflowing through the pipe, all of the
following statements are true EXCEPT:
A. The cross-sectional area is greater at point A than at
point B.
B. The pressure is lower at point B than at point A.
C. The volume flow rate is greater at point A than at
point B.
D. The flow speed is greater at point B than at point A.

1. I have no problem with answer C.

2. For the choice B, using Bernoulli's equation, P+ pgh+ 1/2mv^2=K. Since the flow speed of point A is less than at point B by continuity equation Q=AV, the pressure is lower at point B than point A. What about pgh. are they same at both points?

3. thanks a lot .

If it's a horizontal pipe then the rho g h term cancels out (h is constant)

 

[peacefulheart]

If it's a horizontal pipe then the rho g h term cancels out (h is constant)

1. Thanks for the explanation.

2. It is horizontal pipe with varying diameter. h is measured from bottom to top since gravitational potential energy is involved. So, rho gh can not be cancelled out.

3. thanks .

 

[Captain Sisko]

1. Thanks for the explanation.

2. It is horizontal pipe with varying diameter. h is measured from bottom to top since gravitational potential energy is involved. So, rho gh can not be cancelled out.

3. thanks .

Ok so are the centers of the pipe level with each other? If they are, and the fluid completely fills it at both locations you can cancel the h term. If they are not, and the pipe is actually slanted, then no, you cannot ignore the pressure head term.

 

[peacefulheart]

Ok so are the centers of the pipe level with each other? If they are, and the fluid completely fills it at both locations you can cancel the h term. If they are not, and the pipe is actually slanted, then no, you cannot ignore the pressure head term.

1. Thanks for the explanation.

2. The centers of the pipe are level with each other and the two points are at the center line. But they have different h(from bottom to the top) since point A is in a area with greater diameter .

thanks

 

[milski]

1. Thanks for the explanation.

2. The centers of the pipe are level with each other and the two points are at the center line. But they have different h(from bottom to the top) since point A is in a area with greater diameter .

thanks

If you're talking about the exact points in the center of the pipes and they are lined up, you can ignore the height - in that case deltaH is 0 anyway.

If you want to be picky, the pressure at the higher side of the pipe is slightly lower than the pressure at the lower side. Unless the problem is asking specifically about that difference, you can safely ignore it.

 

[peacefulheart]

If you're talking about the exact points in the center of the pipes and they are lined up, you can ignore the height - in that case deltaH is 0 anyway.

If you want to be picky, the pressure at the higher side of the pipe is slightly lower than the pressure at the lower side. Unless the problem is asking specifically about that difference, you can safely ignore it.

1. Thanks for the explanation.

2. What do you mean by delta H is 0. I do not understand. Point A and point B has different delta h since they are in different cross-section area with different diameter.

3. The question really makes me confused. Everybody keeps saying the h is the same but how .

thanks

 

[milski]

1. Thanks for the explanation.

2. What do you mean by delta H is 0. I do not understand. Point A and point B has different delta h since they are in different cross-section area with different diameter.

3. The question really makes me confused. Everybody keeps saying the h is the same but how .

thanks

If the centers of the pipes are lined up, the centers are at the same height.

You are technically correct but the difference which is concerning you so much is negligible for most realistic setups.

 

[peacefulheart]

If the centers of the pipes are lined up, the centers are at the same height.

You are technically correct but the difference which is concerning you so much is negligible for most realistic setups.

thanks a lot