## Monday, March 31, 2014

### Proving Pascal’s Principle With Syringe Hydraulics

The Syringe Hydraulics Arm project on my website has been one of the most popular project articles. Lately I have been working on building a simulator to demonstrate Pascal’s Principle of fluids using syringes and plastic tubing.

“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

1. 2. 3. 