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Cylinder Calculations Part 1 (Cap End)

Practice, Practice, Practice!

Cylinder piston surface area is a big deal in hydraulics; it influences the system pressure, the cylinder force and its speed. This puzzle provides several cap-end cylinder calculation challenges for you to sharpen your skills on.

  • For the sake of these calculations round 𝛑 to 3.14.
  • All calculations will refer to the cap end chamber of the cylinder(s).
"Cap end", "bore end", and "blind end" are all popular ways to refer to the non-rod end of a single rod cylinder. All of these terms are correct, but we will stick to "cap end" in this puzzle to keep it simple.

Remember

Cap End Piston Surface Area = Radius x Radius x 𝛑

Forklift

A forklift uses a single 3 in diameter cylinder to raise and lower the forks. When a 1413 lb load is being lifted, what is the pressure at the bottom of the cylinder?

Solution

Hydraulic Press

The hydraulic press uses a single cylinder with a 3.5 in diameter piston. It can apply up to 24 040 lbs of force before the relief valve activates and the press stalls. Approximately what pressure is the relief valve set to?

Solution

Lumber Stacker

A lumber stacking system uses 2 cylinders of the same diameter to lift a completed stack to the conveyor belt above. The system pressure gauge reads 51 psi when the load weighs 1000 lbs.

What is the combined surface area of the cylinder pistons?

What is the diameter of a single piston?

Solution

Shop Lift

The 2 vertical cylinders that power a shop lift each have a diameter of 2.25 in . The empty lift arms weigh 50 lbs in total.

What will the system pressure be (approximately) when lifting a 50 lb weight?

The main relief valve is set to activate at 1600 psi, so system pressure cannot rise beyond that level. Can this lift raise a 10 000 lb weight?

Solution

Solutions

Want to see how we suggest solving these problems? Read on for a detailed walkthrough of each, or skip directly to the end of the lesson.

Forklift Puzzle Solution

Return to Forklift Puzzle

Knowledge

The question tells us that there is a single 3 in diameter cylinder, and that the load is 1413 lb.

To solve this puzzle, we need to recall a couple of formulas.
  • The formula to find the surface area of a circle.

𝛑 × radius2

  • The FPA triangle, solving for pressure.
Force ÷ Pressure = Surface Area

The Math

Step 1

To use the FPA equation, we need the piston surface area. To find that, we need to start by finding the radius from the diameter.

  • Radius = Diameter ÷ 2
  • Radius = 3 ÷ 2
  • Radius = 1.5 in

Step 2

Now that we have the radius, we can use it to find the surface area of the piston.

  • Surface Area = 𝛑 × radius2
  • Surface Area = 3.14 × 1.52
  • Surface Area = 7.069 in2

Step 3

We can now use the surface area in the FPA equation to find the pressure.

  • Pressure = Force ÷ Surface Area
  • Pressure = 1413 ÷ 7.069
  • Pressure = 199.887 psi
    (Rounds to 200 psi)
Return to Forklift Puzzle

Hydraulic Press Puzzle Solution

Return to Hydraulic Press Puzzle

Knowledge

We've been told in the question that the single cylinder has a 3.5 in diameter piston, and that it can apply 24 040 lbs of pressure.

To solve this puzzle, we need to recall a couple of formulas.
  • The formula to find the surface area of a circle.
  • 𝛑 × radius2
  • The FPA triangle, solving for pressure.
  • Force ÷ Surface Area = Pressure

The Math

Step 1

First, we'll need to find the surface area the force is being exerted against. In the case of our press, it's the piston.

Find the radius from the diameter.

  • Radius = Diameter ÷ 2
  • Radius = 3.5 ÷ 2
  • Radius = 1.75 in

Step 2

Use the radius to calculate the surface area.

  • Surface Area = 𝛑 × radius2
  • Surface Area = 3.14 × 1.752
  • Surface Area = 9.616 in2

Step 3

Next, divide the force by that surface area.

  • Pressure = Force ÷ Surface Area
  • Pressure = 24 040 ÷ 9.616
  • Pressure = 2500 psi
Return to Hydraulic Press Puzzle

Lumber Stacker Puzzle Solution

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Knowledge

We've been told in the question that there are 2 cylinders, and that the system registers 51 psi when lifting a load of 1000 lbs.

To solve this puzzle, we need to recall a couple of formulas.
  • The formula to find the surface area of a circle.
𝛑 × radius2

Permutation to find the radius

  • The FPA triangle, solving for pressure.
Force ÷ Pressure = Surface Area

The Math - Question 1

Step 1

To find the combined surface area of the cylinder pistons, we'll need to use the FPA equation.

  • Surface Area = Force ÷ Pressure
  • Surface Area = 1000 ÷ 51
  • Surface Area = 19.608 in2

The Math - Question 2

Step 1

In the last question we calculated the total surface area for both pistons. Let's start by dividing it in half, to get the surface area for a single piston.

  • SA1 = SAtotal ÷ 2
  • SA1 = 19.608 ÷ 2
  • SA1 = 9.804 in2

Step 2

We'll need to re-arrange the 𝛑r2 equation to get the radius, and then the diameter.

  • Radius = √(Surface Area ÷ 𝛑)
  • Radius = √(9.804 ÷ 3.14)
  • Radius = 1.767 in

Step 3

Now that we have the radius, we can use it to calculate the diameter.

  • Diameter = Radius × 2
  • Diameter = 1.767 × 2
  • Diameter = 3.534 in
    (Rounds to 3.5 in)
Return to Lumber Stacker Puzzle

Shop Lift Puzzle Solution

Return to Shop Lift Puzzle

Knowledge

We've been told in the question that there are 2 cylinders, each with a diameter of 2.25 in, and that the empty lift arms weight 50 lbs total.

To solve this puzzle, we need to recall a couple of formulas.
  • The formula to find the surface area of a circle.
𝛑 × radius2

Since we're working with 2 matched cylinders, the surface area will be doubled.

(𝛑 × radius2) x 2
  • The FPA triangle, solving for pressure.

Force ÷ Surface Area = Pressure

The Math - Question 1

Step 1

First, we'll need to find the surface area the force is being exerted against. In the case of our press, it's the piston.

Find the radius from the diameter.

  • Radius = Diameter ÷ 2
  • Radius = 2.25 ÷ 2
  • Radius = 1.125 in

Step 2

Use the radius to calculate the surface area.

  • Surface Area = 𝛑 × radius2
  • Surface Area = 3.14 × 1.125 in2
  • Surface Area of a single cylinder = 3.974 sq. in

Double the surface area to include both pistons.

  • SAtotal = SA1 + SA2
  • SAtotal = 3.974 + 3.974
  • SAtotal = 7.948 in2

Step 3

We know that the empty arms weigh 50 lbs, and that they are lifting a 50 lb weight. Added together, we are working with a force of 100 lbs.

Divide the force by the total surface area to get the system pressure.

  • Pressure = Force ÷ Surface Area
  • Pressure = 100 ÷ 7.948
  • Pressure = 12.582
    (Rounds to 13 psi)

The Math - Question 2

We need to determine whether lifting 10 050 lbs (the 10 000 lbs weight and the 50 lbs added by the arms) will induce a system pressure near or over 1600 psi.

Step 1

Recall that we've already calculated the total surface area: 7.948 in2, so all that's left to do is to solve for pressure.

  • Pressure = Force ÷ Surface Area
  • Pressure = 10 050 ÷ 7.948
  • Pressure = 1264.469 psi

1264 psi is less than 1600 psi, so this system should be able to lift the 10 000 lb weight.

Return to Shop Lift Puzzle

Great Work!

You've solved all of the cap-end puzzles. Are you ready to go on to some rod-end puzzles?

We hope you enjoyed Cylinder Calculations Part 1 (Cap End)

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