Liquid flow & velocity & area

[acidandroid]

Homework Statement

Assume a liquid is flowing through a pipe of cross-sectional area A at pressure P and velocity v. If, at some point, the area decreases, then;

-velocity increase, pressure remains same
-velocity increases, pressure decreases
-velocity increases, pressure increases

correct answer is Velocity increases, and pressure P decreases.

Homework Equations

-p1v1A1=p2v2A2
-Pressure=Force/Area

The Attempt at a Solution

-I understand that velocity increases because p(density)v(velocity)A(area).
But I don't understand why pressure would decrease.
I used Pressure=Force/Area, thus if area decreases, pressure must increase.

 

[JaredJames]

Flow is always from high pressure to low pressure.

If pressure was constant, there would be no flow.
If pressure increased, the flow would be in the opposite direction.

Think of it like constricting the end of a hosepipe:
The pressure inside the hose is less than the outside of the house. Thus water flows out the end. These pressure values never change.
When you squeeze the end, as the area decreases the flow velocity increases. The force of the water coming out the end becomes greater.
Area decreases (causing flow velocity to increase), force increases, net effect is that pressure remains constant.

Jared

 

[cjl]

The reason the pressure decreases is because of the velocity increase. The exact pressure decrease is found using the Bernoulli equation:

$$P + 1/2 \rho v^2 = constant$$

If V increases, then P must decrease.

Oh, and Jared, that's not necessarily true. Flow can go from a lower pressure region to a higher pressure region if in the process it slows down. This can also be seen from the equation above - if V decreases, P will increase.

(Note that this equation assumes no energy is added to or removed from the flow)

 

[JaredJames]

A lecturer of mine gave this exact problem and I simply gave his answer.

Do you have an example of something flowing from low to high pressure?

 

[rwisz]

Can someone explain this concept?

As the area decreases, the same amount of liquid is now flowing through a smaller space. This causes an increase in velocity, as the liquid needs to move faster to maintain the same flow rate. However, since the amount of liquid and the force pushing it through the pipe remain the same, the pressure must decrease in order to maintain a constant flow rate. This is because the force is spread out over a smaller area, resulting in a decrease in pressure. This can be seen in the equation p1v1A1 = p2v2A2, where a decrease in A2 (the smaller area) results in a decrease in p2 (the pressure).