Understanding Pressure and Force in Hydraulic Systems

[phy1210]

Pressure is defined as the force acting per unit area.

If we take a hydraulic system of a car, the pressure that will be acting on both piston will be the same. If we apply a small force on the pedal, it will result in a bigger force on the brakes.

Here is a multiple choice question that is troubling me:
There are 2 identical stone tiles. One is vertical (Small surface area acting on the ground) and the other is horizontal (Large surface area acting on the ground).

Through the above definition, I would say the pressure is the same while the forces are different. But the answer was that the pressure was different and the forces are the same. Could you explain the answer?

Thanks in advance!

 

[tiny-tim]

welcome to pf!

hi phy1210! welcome to pf!

There are 2 identical stone tiles. One is vertical (Small surface area acting on the ground) and the other is horizontal (Large surface area acting on the ground).

Through the above definition, I would say the pressure is the same while the forces are different.

hint: what are the forces on each of the tiles?

 

[phy1210]

Thanks tiny-tim!

I forgot to mention that they are identical tiles. We can deduce that they have the same forces. But how can the pressure be different then?

They have the same pressure acting per unit area, isn't?

 

[tiny-tim]

We can deduce that they have the same forces.

yes: the forces are the weights, so they are the same

But how can the pressure be different then?

physics is equations …

so what is the equation for pressure? ​

 

[phy1210]

Pressure=Force/Area

If the force is the same and area is smaller, the pressure will be higher and vice versa.

I understand this part!

Lets take a water bottle. Pressure on the wall of the bottle and on the cap is the same despite different surface areas?

 

[tiny-tim]

Lets take a water bottle. Pressure on the wall of the bottle and on the cap is the same despite different surface areas?

pressure (+ ρgh) is the same everywhere in a stationary liquid

 

[phy1210]

Pfff... I am not being able to convey what I don't understand!

If there was no water in the bottle. Air molecules would collide at the same rate everywhere inside the bottle.

If we take the cap:
Area is small
Force is the same
Hence, Pressure is high

If we take the base of the bottle:
Area is bigger
Force is the same
Hence, Pressure is low

But as pressure is defines as force per unit area

These 2 regions will have the same force per unit area and hence they will have the same pressure.

 

[Nugatory]

If we take the cap:
Area is small
Force is the same
Hence, Pressure is high

If we take the base of the bottle:
Area is bigger
Force is the same
Hence, Pressure is low

But as pressure is defines as force per unit area

These 2 regions will have the same force per unit area and hence they will have the same pressure.

Think about the sail of a sailboat. The pressure on the sail comes from air molecules hitting the sail, just as the pressure in the bottle comes from air molecules hitting the inside of the bottle. The pressure is the same (the air molecules are hitting just as hard) on a big sail as a little sail, but a big sail generates more force and can drive a bigger boat.

So it should be:

If we take the cap:
Area is small
Pressure is the same
Hence, Force is lower

If we take the base of the bottle (same wind, bigger sail):
Area is bigger
Pressure is the same
Hence, Force is higher

 

[phy1210]

I think I got it now.

Thanks for your help, tiny-tim and nugatory.