Bernoulli's Equation - conceptual question

[AOT11]

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Suppose that a stream of fluid flows steadily through a horizontal pipe of varying cross-sectional diameter. Neglecting viscosity, where is the fluid pressure the greatest?

Answer: At the point of maximum diameter (because of Bernoulli's equation)

I thought it would be the point of minimum diameter because I assumed pgh would be small (because I thought h would be small since it's minimum diameter), which would make P big. Why am I wrong? (this is from AAMC 4R)

 

[milski]

Please, post in the title that it is an AAMC question.

ρgh Bernoulli's equation is to take care of non-horizontal pipes, where one end of the pipe is higher than the other. In that case some energy is lost/gained when the fluid is transported up/down. For horizontal pipes h is constant and you can ignore that member of the equation.

 

[ingramw1202]

Suppose that a stream of fluid flows steadily through a horizontal pipe of varying cross-sectional diameter. Neglecting viscosity, where is the fluid pressure the greatest?

Answer: At the point of maximum diameter (because of Bernoulli's equation)

I thought it would be the point of minimum diameter because I assumed pgh would be small (because I thought h would be small since it's minimum diameter), which would make P big. Why am I wrong? (this is from AAMC 4R)

Bernoulli's equation seems counter intuitive but think of it like this. Pressure is force per unit area. And it is measured by the force that the fluid exerts on the walls of the pipe. If the cross sectional diameter is large, then there is more fluid in that section of the pipe than in an area where the cross sectional diameter is small. This means that the there are more frequent collisions between the molecules of the liquid and the walls of the container ( not only are there more molecules of liquid in the area of the pipe with greater cross sectional area, there is also more wall of pipe to interact with). When cross sectional area decreases, the amount of fluid in the pipe decreases, as well as the area with which the fluid can actually interact. Hence pressure goes down. As cross sectional area decreases, velocity increases.
Scenario:
Pipe is fat then pipe is skinny.
So the pressure in the fat area is greater than the pressure in the skinny area. This pressure difference causes the liquid moving through the skinny area to accelerate forward, thus increasing velocity. This is the reason why rockets have funnels on the bottom that have the big side opening downward. Greater pressure underneath causes the rocket to accelerate upwards.