Fluid Characteristics and Pressure

[kkentm]

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Here's the question:

A decrease in which of the following fluid characteristics would increase the pressure at any given point in a moving ideal fluid?

A. temperature
B. density
C. cross-sectional area of the pipe
D. velocity

I know why D is correct but why is C wrong? im basing my answer of this question off of P = F/A. If someone could explain this that would be great, thanks!

 

[PingPongPro]

Q(flow) = Cross sectional Area x Velocity

If you increase area, velocity must go down in order to maintain Q.

If you look at bernoulli's equation Pressure1 + 1/2 density xvelocity^2 + densityxgh . If you increase velocity (2nd term) the Pressure1 must decrease.

 

[englishtablet]

the formula you are looking at is not apt here

look at it this way

A1V1= A2V2 ( that is the flow rate must be constant) so if you decrease the area at , for instance, A2, then you are increasing the velocity in order to maintain the flow rate.
So we know that when the velocity is increased, pressure decreases ( contrary to our intuition)

I like to think it this way:- ( that is EKs way)

Reason being that the pressure is created by random translation motion of the fluid. So if the energy is used in increasing the uniform translation motion( kinetic energy->increase velocity) we will not be able to utilize that energy to create random translation motion in turn the pressure.


Hence the choice D

 

[whiteshadodw]

still water runs deep.

essentially, the more pressure, the lower the velocity.

ping pong pro is right on. this is one of those topics that becomes EXTREMELY easy with a lot of practice. it just becomes something you have memorized because of how many times you've seen it.

 

[plzNOCarribbean]

still water runs deep.

essentially, the more pressure, the lower the velocity.

ping pong pro is right on. this is one of those topics that becomes EXTREMELY easy with a lot of practice. it just becomes something you have memorized because of how many times you've seen it.

I remember reading this and studying it the first time through when I took the MCAT. fluids was one of the hardest for me. The bolded statement just seems so counter-intuitive to me.

I always imagine a garden hose, and that if you squeeze it (decrease A), the pressure inside the hose increases(since P=F/A) and the velocity INCREASES, but apparently this is not the case. never really quite understood why or made the connection with the Bernoulli equation.

I think its because since the flow RATE has to be constant throughout the pipe, ie it has to be the same at any two points along the pipe. flow rate, f=Av, so if we increase area, the velocity decreases to maintain the same flow rate throughout the pipe. The same flow rate does not mean that the pressure in two different part of the pipe with different cross sectional areas are the same. The point at which Area is larger, velocity is smaller and thus the pressure is greatest at that point.

http://00.educdn.com/files/static/mcgrawhillprof/9780071626613/FLUID_DYNAMICS_02.GIFDoes

If you look at the diagram above, the pressure should be greatest at point A, and the flow rate f should be the same in A as in B.

^im pretty sure thats correct but if someone could look over it and double check or validate it that be great. Good luck OP

 

[plzNOCarribbean]

^could someone please validate my statement. Is it correct or am I wrong?

the flow rate must be constant at every point in the tube, BUT the pressure is NOT if the area of the pipe changes at different regions.

Its incorrect to assume that since A decreases, P increases based on the equation P=F/A. This does NOT hold true for fluids. as A decreases, V increases which means P DECREASES

so I think its correct to ALWAYS assume the greatest pressure in the pipe at the point with the largest area (and smallest velocity)

 

[infid3l]

^could someone please validate my statement. Is it correct or am I wrong?

the flow rate must be constant at every point in the tube, BUT the pressure is NOT if the area of the pipe changes at different regions.

Its incorrect to assume that since A decreases, P increases based on the equation P=F/A. This does NOT hold true for fluids. as A decreases, V increases which means P DECREASES

so I think its correct to ALWAYS assume the greatest pressure in the pipe at the point with the largest area (and smallest velocity)

As PingPongPro said, this question needs to be solved keeping in mind the bernoulli's equation assuming potential energy is constant. THe other two components of equation represent kinetic energy (0.5 x density x v^2). As area decreases velocity increases ( flow rate is constant). Bernoullis equation represent conservation of energy so the increase in velocity needs to be balanced out by a decrease in pressure.

 

[muhali3]

Continuity equation (A1V1=A2V2) and Bernoulli's equation go hand-in-hand. If area of a vessel increases (vasodilation), the velocity will decrease.

If the velocity decreases, then the KE term in Bernoulli's equation will decrease, and the P term will increase proportionally.