*“Pascal's Principle states that when there is an increase in pressure at any point in a confined fluid, there is an equal increase at every other point in the container*.”

What exactly does this mean in practice? For the simulator I used a large syringe that has a piston cross section diameter of 34 mm and small syringe with cross section diameter of 13 mm. Like other mechanical systems there is a mechanical advantage where distance moved and force tradeoff. When the smaller piston is pushed with a force, that force is distributed equally across the larger piston cross section causing a greater net force. For the fluid to be spread across the larger cross section more fluid volume must be moved from the smaller cylinder.

For my first experiment I worked from the other direction and pushed the large cylinder a short distance of 8 mm which extended the small cylinder a much longer distance of around 45 mm until it could not move any farther. I calculated this also which was off somewhat from my observations which can happen when there are inaccuracies in the measured values.

Cylinder at Start Position |

Large Cylinder Moved 8 mm Small Cylinder Moved 45 mm |

For calculations we need the formula for the area of a circle :

Area of Circle = π x radius²

Large Piston cross section area = 3.14 x (34/2)² =

**907 sq mm**

Small Piston cross section area = 3.14 x (13/2)² =

**133 sq mm**

Moving the large piston 8 mm will displace amount fluid = cross section x length of movement

Fluid Displaced = 907 sq mm x 8 mm =

**7256 cu mm**

The movement of the small cylinder should be the fluid displaced / cross section area of small cylinder.

7256 / 133 =

**54 mm**movement of small cylinder

Actual movement was recorded at

**45 mm**or 4.5 centimeters

I have not checked the amount of force generated but did check the amount required just to move the opposite cylinder. Moving the small cylinder with the large cylinder took a large amount of force, 1250 grams or around 12 newtons. This is like pushing down on the short end of a lever. Pushing the small cylinder took very little force.

Large Force Needed to Move Small Cylinder Pushing Large Cylinder |

Small Amount of Force to Move Pushing Small Cylinder |

Bill Kuhl

I tested this again and had close to 60 mm of extension on small cylinder closer to calculated.

ReplyDeleteYes, I should think that the descrepancies between the calculated distance and the measured distance is primarily due to small inacuracies in measurement over such a short distance.

ReplyDelete