Question

A single-acting hydraulic press has a plunger diameter of 55 mm, a stroke length of 106 mm and a ram diameter of 144 mm.
2.1.1
Calculate the volume of liquid per stroke.
2.1.2
Calculate the force exerted by the ram if a force of 75 N is applied on the plunger

Answer 1

To solve the problems, we will need to calculate the volumes and forces using the relationships in hydraulic systems.

### 2.1.1 Calculate the Volume of Liquid per Stroke

The volume of liquid displaced per stroke in a hydraulic press can be calculated using the volume formula for a cylinder:

\[
V = A \cdot h
\]

where:
- \( V \) is the volume
- \( A \) is the cross-sectional area of the cylinder
- \( h \) is the height (or stroke length)

First, we need to calculate the cross-sectional area of the plunger and then use the stroke length.

**Step 1: Calculate the area of the plunger**

The area \( A \) can be calculated as:
\[
A = \pi \left( \frac{d}{2} \right)^2
\]

where \( d \) is the diameter.

For the plunger:
\( d_{plunger} = 55 \, \text{mm} = 0.055 \, \text{m} \)

\[
A_{plunger} = \pi \left( \frac{0.055}{2} \right)^2 = \pi \left( 0.0275 \right)^2 \approx 0.002375 \, \text{m}^2
\]

**Step 2: Calculate the volume per stroke**

Height (stroke length) \( h = 106 \, \text{mm} = 0.106 \, \text{m} \)

\[
V = A_{plunger} \cdot h = 0.002375 \, \text{m}^2 \cdot 0.106 \, \text{m} \approx 0.00025125 \, \text{m}^3
\]

So, the volume of liquid per stroke is approximately:
\[
\text{Volume} \approx 0.000251 \, \text{m}^3 \, (or \, 251 \, cm^3)
\]

### 2.1.2 Calculate the Force Exerted by the Ram

The force exerted by the ram can be calculated using Pascal's principle, which states that the pressure applied to a confined fluid is transmitted undiminished in all directions.

**Step 1: Calculate the force exerted on the plunger**

Given the force applied on the plunger \( F_{plunger} = 75 \, \text{N} \).

**Step 2: Calculate the pressure in the system**

Pressure \( P \) generated by the plunger is given by:
\[
P = \frac{F_{plunger}}{A_{plunger}}
\]

Calculate the pressure:
\[
P = \frac{75 \, \text{N}}{0.002375 \, \text{m}^2} \approx 31578.95 \, \text{Pa}
\]

**Step 3: Calculate the area of the ram**

Now we will calculate the area of the ram:
\[
A_{ram} = \pi \left( \frac{d_{ram}}{2} \right)^2
\]

for the ram:
\( d_{ram} = 144 \, \text{mm} = 0.144 \, \text{m} \)

\[
A_{ram} = \pi \left( \frac{0.144}{2} \right)^2 = \pi \left( 0.072 \right)^2 \approx 0.0162585 \, \text{m}^2
\]

**Step 4: Calculate the force exerted by the ram**

Using the pressure calculated previously:
\[
F_{ram} = P \cdot A_{ram}
\]
\[
F_{ram} = 31578.95 \, \text{Pa} \cdot 0.0162585 \, \text{m}^2 \approx 512.13 \, \text{N}
\]

So, the force exerted by the ram is approximately:
\[
\text{Force exerted by the ram} \approx 512.13 \, \text{N}
\]

### Summary
- Volume of liquid per stroke: \( \approx 251 \, cm^3 \)
- Force exerted by the ram: \( \approx 512.13 \, N \)