Knowing what you now know about hydraulic systems and how to make one, try 
these experiments yourself.

1. Remove the plungers completely to measure the diameters of the 10 ml syringe plunger and the 20 ml syringe plunger. Remember that the diameter is the length from one side of a circle to the other passing through the center.

2. Use these measurements to calculate the cross-sectional area of the inside of each syringe. If you need help with this, use the online calculator at https://www.omnicalculator.com/math/area-of-a-circle. What is the ratio between the cross-sectional area of each syringe? Or, what is
    

   \[
   \frac{A_{\text{input}}}{A_{\text{output}}} = \frac{A_{10\,\text{ml}}}{A_{20\,\text{ml}}}
   \]

   In other words, if the cross-sectional area of the 10 ml syringe is 679 mm² and the cross-sectional area of the 20 ml syringe is 1207 mm², then the ratio would be

   \[
   \frac{A_{10\,\text{ml}}}{A_{20\,\text{ml}}} = \frac{679\,\text{mm}^2}{1207\,\text{mm}^2} = 0.56 
   \]

3. Make a simple hydraulic system with a 10 ml and 20 ml syringe. Make sure that the 10 ml syringe and tube is full of water before connecting the 20 ml syringe and that the 20 ml plunger is pushed all the way in.
4. If you move the 10 ml plunger 2 cm (0.8 in) how far does the 20 ml plunger move? How does the ratio of these distances relate to the ratio of the syringes’ cross-sectional areas? In the example above where the ratio of the cross-sectional areas was 0.56, we would find that the 20 ml plunger would move. \[
   \frac{d_{\text{input}}}{d_{\text{output}}} = \frac{d_{10\,\text{ml}}}{d_{20\,\text{ml}}}
   \]
    
5. Use what you know about the ratio of the cross-sectional areas of your syringes to calculate what force would be applied to the 20 ml plunger if a force of 15 N is applied to the 10 ml plunger. In the example above where the ratio of the cross-sectional areas was 0.56, we would find that the force applied to the 20 ml syringe would be \[
   \begin{align*} \frac{\text{Cross-sectional area}_{10\,\text{ml}}}{\text{Cross-sectional area}_{20\,\text{ml}}} &= \frac{\text{Force}_{10\,\text{ml}}}{\text{Force}_{20\,\text{ml}}} \\ \therefore \text{Force}_{20\,\text{ml}} &= \frac{F_{10\,\text{ml}}}{\text{ratio of cross-sectional areas}} \\ &= \frac{15\,\text{N}}{0.56} \\ &= 26.79\,\text{N} \end{align*} \]
    

6. Now, use a t-piece hose connector to connect two 20 ml syringes (the output) to a single 10 ml syringe (the input) as shown below. As usual, make sure that the 10 ml syringe and all the tubes are full of water before connecting the 20 ml syringes and that the 20 ml plungers are pushed all the way in.

   
7. Calculate is the ratio of the cross-sectional area of the 10 ml syringe (the input) to both 20 ml syringes (the output)? In other words, what is \[
    \frac{A_{\text{input}}}{A_{\text{output}}} = \frac{A_{10\,\text{ml}}}{A_{20\,\text{ml}} + A_{20\,\text{ml}}} \]
    
8. How do you think the addition of another 20 ml syringe to the output will affect the distance travelled by the 20 ml plungers for each unit distance travelled by the 10 ml plunger?
9. Move the 10 ml a distance of 2 cm (0.8 in). How far do the 20 ml plungers move now? How does this compare to the case were there was only one 20 ml syringe connected? Why do you think this is the case?
10. Use what you know about the ratio of the cross-sectional areas of the input (10 ml) syringe and the output (20 ml syringes) to calculate what force will be applied by the output (the two 20 ml plungers combined) if a force of 15 N is applied to the input 10 ml plunger.

11. Add another t-piece to your setup so that you can connect three 20 ml syringes (the output) to one 10 ml syringe (the input).

    
12. Calculate the ratio of the cross-sectional areas. \[
    \frac{A_{\text{input}}}{A_{\text{output}}} = \frac{A_{10\,\text{ml}}}{A_{20\,\text{ml}} + A_{20\,\text{ml}} + A_{20\,\text{ml}}} \]
     
13. Experiment with how the increase in the output cross-sectional area (the three 20 ml syringes) affects the distance travelled by the 20 ml plungers for each unit distance travelled by the input 10 ml plunger.
14. If a force of 15 N is applied to the input 10 ml plunger, what force would you expect to be applied to the output (the three 20 ml plungers combined).
15. If you have one, add a 50 ml syringe into the mix. First, connect it to a 10 ml syringe and then use the t-pieces to add some 20 ml syringes. What combination will give you the maximum output force? Why is this?
16. Take some time to construct your own hydraulic lift or press. There are many resources available on the internet for you to refer to. How great a mass do you think you could lift with your system?