Clarification w/ Fluids: Greater Area --> Lower Velocity --> Higher Pressure?

[onedirection]

Can someone clarify if that relationship is true

I know the first part is true because Av is constant so if Greater area exists the velocity should decrease

but how about the second part

I can't think of the logic as to why it's true off the top of my head because P = F/A and if area increased, pressure should decrease

This is for laminar flow/ideal fluid flow

---

Members don't see this ad.

 

[tasteslikejeef]

.

 

[SpaceBuff12]

The total pressure along a streamline is constant. An increase in velocity results in a increase in dynamic pressure, but a decrease in static pressure. Conversely, a lower velocity will have a lower dynamic pressure, but a higher static pressure.

 

[discowisco]

I have a question regarding pressure in liquids as well.

Say you have flasks of different shapes but same height and hold the same amount of liquid, and you wanted to know the pressure relationship between them, would the pressure be the same in all of them?

I know total Pressure is = Patm + pgh or something so will the Patm be different for all of the flasks depending on how much area of the openinga is exposed to the atm?

 

[DrBTS]

As long as there is an infinitesimally small opening, the pressure of the atmosphere will equilibriate. The Pressure at some depth would be Ptotal = Pgauge(at that depth) + Patm. The pressure applied within a fluid is uniformly perpendicular to the surface (unlike pressure strain in solids and from my limited understanding of fluid dynamics, we take these pressure values in their scalar quantities for the MCAT.

As for the equation: P = F/A , F = mg, p= m/v so we plug in F = (pv)g for the mass, and then P = (pvg)/A for the force into the pressure eq. Taking this one step further for depth in a container we can say that volume, v = Ad and plugging this v into the pressure eq Area cancels out to give you : P = pgd

 

[jtran7]

I have a question regarding pressure in liquids as well.

Say you have flasks of different shapes but same height and hold the same amount of liquid, and you wanted to know the pressure relationship between them, would the pressure be the same in all of them?

I know total Pressure is = Patm + pgh or something so will the Patm be different for all of the flasks depending on how much area of the openinga is exposed to the atm?

If the flasks are "open" the Patm will be the same for both no matter what, because the pressure above the fluid will become equal to the atmospheric pressure. The total Pressure however, changes depending on the P gauge which is equal to roe x g x h (the height of a point below the water surface). So if you have Flask A which is filled with water 5 meters high and Flask B filled with water 10 meters high, the Total Pressure at the bottom of flask B would be greater than in flask A (a result of the difference in Pgauge not of Patm).

In the situation you presented yes the P total will be the same. You do not need to worry about the volume of the fluid in each flask as long as the height of the fluid is equal the Pgauge at the bottom of each flask would be the same. And as stated earlier Patm does not vary between the flask therefore they will have equal Patm and equal Pgauge resulting in the equal PTotal.