# 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.

Solution

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.

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.

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

### 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.

• 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

#### 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)

## Hydraulic Press Puzzle Solution

### 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.
• 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

#### 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

## Lumber Stacker Puzzle Solution

### 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.

• 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)

#### 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)

## Shop Lift Puzzle Solution

### 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.

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

• 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

#### 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.

# Great Work!

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