TPRH SW Physics; passage 15, q#1

[Postictal Raiden]

The figure in the passage shows a glass tube with 3 different cross-sectional areas. The cross sectional area gets smaller as water moves from one area of the tube to the other, so A1>A2>A3.

A question asks for the pressure in each area. I thought that Pressure in area 3 would be the greatest and the pressure in area 1 would be the least. The solution shows the opposite; the answer is P1>P2>P3. I don't understand why. Shouldn't pressure and cross-sectional area be inversely related?

---

Members don't see this ad.

 

[Dazzled03]

According to flow rate, as the area gets larger, the velocity will become smaller. Pressure for fluids becomes smaller as velocity increases.

So, the part of the tube with the greatest area will have the slowest velocity and also the greatest pressure.

I remember the correlation between velocity and pressure for fluids by thinking about hurricanes. Hurricanes have very fast winds which causes low air pressure.

 

[Postictal Raiden]

According to flow rate, as the area gets larger, the velocity will become smaller. Pressure for fluids becomes smaller as velocity increases.

So, the part of the tube with the greatest area will have the slowest velocity and also the greatest pressure.

I remember the correlation between velocity and pressure for fluids by thinking about hurricanes. Hurricanes have very fast winds which causes low air pressure.

What I don't understand is why pressure decreases as velocity increases.

Isn't pressure = 1/2 (density) x (velocity)^2?

From the equation above, increasing the velocity will increases the pressure.

 

[circulus vitios]

What I don't understand is why pressure decreases as velocity increases.

Isn't pressure = 1/2 (density) x (velocity)^2?

From the equation above, increasing the velocity will increases the pressure.

Bernoulli's equation:

(z is elevation in this derivation.)

Elevation, density, and g are constant. Velocity increases and the equation must remain constant so the pressure must decrease.