# Calculating speed, forces and pressures when extending a cylinder

So I have the following circuit:

And the first question is, if DV1 is pushed all the way to the right, what speed will the clamp cylinder attain and as it extends what will be the pressure at P1.

Similarly Once the clamp cylinder has become fully extended, if the button on DV2 is pressed, what will be the speed of the piston of the lift cylinder and the pressure at P1?

The specifications are as such:

• Clamp cylinder -> Bore = 20 mm diameter, rod of 15mm diameter and a stroke of 1m.
• Lift Cylinder -> Bore = 200mm diameter, rod = 15mm diameter, stroke = 1m
• Clamp cylinder has a resistive force of 2.5kN that opposes motion
• Lift Cylinder moves a mass of 50kg and no resistive forces
• The relief valve is set to 20 MPa
• Pressure valve, PV2 is set to 10MPa
• Pump -> 5mL/rev and 1440 RPM
• no pressure losses in line or components or internal leakage

So my thoughts are;

The pump is pumping at 5 *1440 = 7200mL/minute.

I'm going to just ignore PV1 as it's just a pressure relief valve, so it will just limit the system to whatever it is set to (20MPa).

I think we can ignore PV2 and everything beyond for the first question too. Or since this flow goes back to tank, I think it may mean that the system can't be more than 10MPa?

Now I think we calculate the Area of the head of the cylinder which is A = (0.2/2)^2 * pi = 0.0314 m^2.

So from here I think we can just put it into the formula Vext = Qp / A.

So 7.2*10^-3 / 3.14*10^-2 = 0.2293 m/s

Is this correct, or do I have to subtract some flow that would go to the other parts of the system (towards flow 2 and PV2).

Then the pressure at head should be P = F/A. This is my main problem, as 2.5*10^3/0.0314 = 80MPa which is way higher than any of the possible answer choices. Not to mention higher than what PV1 is set for.

So where have I gone wrong and how can I solve these problems?

So when DV1 is pushed to the right the flow will be acting on the head of the cylinder so we work out the head Area:

A = PI * r^2


As you said however you used the radius of the lift clamp not the clamp cylinder so it should be 0.02 (20mm) divided by 2 squared times pi.

This will give A = 0.000314 m^2.

The next step is, as you said, using the formula:

v = q/A


However your units are a bit messed up. If your q is in L/s (q = 5 * 10^-3 * 1440/60 = 0.12) then you need to convert it to m^3 by multiplying it by 10^-3 and then dividing it by the area:

v = 0.12 L/s * 10^-3 / 0.000314 m^2
v = 0.382 m/s


Now the pressure will be:

P = F/A
P = 2500/0.000314
P = 7.9 * 10^6 Pa =~ 8 MPa


Since this is less than the 10 for the sequence valve we won't have to go back and adjust the flow.

As to your second question, since the lift cylinder is fully extended the flow cannot go to the clamp cylinder anymore so all of it goes to the lift cylinder so the process is the same:

v = q/A
v = 0.12 * 10^-3 / 0.0314
v = 0.00382 m/s =~ 4 mm/s


and same for pressure (with a slight difference)

P = F/A
P = 50 * 9.8 / 0.0314
P = 15.6 kPa


Since P here is 15.6 kPa, which is less than the 10 MPa of the sequence valve, the pressure at P1 will be 10 MPa.