Pressure in Cylinder following Piston engagement

[ldu02167]

Homework Statement

I have been passed the following problem in work - this is a real life question, and not a homework assignment. I'm hoping I have provided enough information for someone to help point me in the right direction - I'm really stuggling and would love any help you could offer!

Hydraulic fluid is pumped into the Press Cylinder (Shown in Blue) forcing the Piston/Ram (shown in Red) down into another Cylinder (Shown in Black) that holds 10kg of a soft plastic. The soft plastic is then extruded through a die at the bottom of the cylinder.

I'm looking to find out the pressure in the black cylinder once the piston has engaged in the cylinder. This will be used to work out a Pressure (likely add 20%) that will cause the system to shut down as it will register as being 20% above the max pressure, and hence 'dangerous'.

- The pressure of the Hydraulic Fluid in the Press is 140Bar/14MPa.
- The Diameter of the Main Piston is 737mm
- The Stroke legnth of the Ram part of the piston is 1111mm
- At full stroke length, the distance (height) between the bottom of black cylinder and face of Ram is 22mm (the majority of the soft plastic has been extruded through the Die to reach this condition)
- The Temperature of the Black Cylinder with the soft plastic is 60 Degrees Celcius (assume no change in Temp.)
- The Diameter of the Ram part of the piston is 267mm
- The I/D of the black cylinder is 268mm


The "Piston" is almost two parts, with a main Piston & a Ram. The Ram is the small 'T' section that engages in the black cylinder and forces the plastic through the die. The large main piston is hollowed out to save weight, rather than being for any sort of performance.

Thanks again for any suggestions/tips/solutions!

 

[rude man]

Assuming an airtight seal between the piston & the black cylinder, pressure will be approximately per pV = nRT.

Equilibrium pressure will be reached when p inside the black cylinder stands off the pressure applied by the piston. The latter will be the applied pressure ph of the hydraulic source, multiplied by the NET area parallel to the piston's motion, plus gravity if the thing is vertical. So we have ph*A_net = p*A_piston - Mg, M = mass of piston.

I see from the picture that, fortunately, there is a lot more area providing downward as opposed to upward motion.

BTW should there not be a space instead of a blue line where the intake enters the blue cylinder? I'm assuming the piston will be completely surrounded by hydraulic fluid. If this is not so then my analysis is inapplicable.