The diameter of the ram of a mass-loaded accumulator is 400 mm , the nass of the ram is 800 kg . An additional weight of 15 rings, each with a veight of 7 kN , is placed on the ram. Calculate the pressure in the ccumulator.

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To calculate the pressure in the accumulator, we can follow these steps:

1. **Extract known conditions:**
   - Diameter of the ram, $$ d = 400 \, \text{mm} = 0.4 \, \text{m} $$
   - Mass of the ram, $$ m_{\text{ram}} = 800 \, \text{kg} $$
   - Weight of each ring, $$ W_{\text{ring}} = 7 \, \text{kN} = 7000 \, \text{N} $$
   - Number of rings, $$ n = 15 $$

2. **Calculate the total weight on the ram:**
   - The total weight of the rings is given by:
     $$
     W_{\text{total}} = n \times W_{\text{ring}} = 15 \times 7000 \, \text{N}
     $$
   - The weight of the ram can be calculated using the formula:
     $$
     W_{\text{ram}} = m_{\text{ram}} \times g
     $$
     where $$ g $$ (acceleration due to gravity) is approximately $$ 9.81 \, \text{m/s}^2 $$.

3. **Calculate the total weight acting on the ram:**
   $$
   W_{\text{total}} = W_{\text{ram}} + W_{\text{total}}
   $$

4. **Calculate the area of the ram:**
   - The area $$ A $$ of the ram can be calculated using the formula for the area of a circle:
     $$
     A = \pi \left( \frac{d}{2} \right)^2
     $$

5. **Calculate the pressure in the accumulator:**
   - Pressure $$ P $$ is given by the formula:
     $$
     P = \frac{F}{A}
     $$
   where $$ F $$ is the total force (weight) acting on the ram.

Now, let's perform the calculations step by step.

### Step 1: Calculate the total weight of the rings
$$
W_{\text{total}} = 15 \times 7000 = 105000 \, \text{N}
$$

### Step 2: Calculate the weight of the ram
$$
W_{\text{ram}} = 800 \times 9.81 = 7848 \, \text{N}
$$

### Step 3: Calculate the total weight acting on the ram
$$
W_{\text{total}} = 7848 + 105000 = 112848 \, \text{N}
$$

### Step 4: Calculate the area of the ram
$$
A = \pi \left( \frac{0.4}{2} \right)^2 = \pi \left( 0.2 \right)^2 = \pi \times 0.04 \approx 0.12566 \, \text{m}^2
$$

### Step 5: Calculate the pressure in the accumulator
$$
P = \frac{112848}{0.12566} \approx 897,000 \, \text{Pa} \text{ or } 897 \, \text{kPa}
$$

Thus, the pressure in the accumulator is approximately $$ 897 \, \text{kPa} $$.
The pressure in the accumulator is approximately 897 kPa.

The diameter of the ram of a mass-loaded accumulator is 400 mm , the nass of the ram is 800 kg . An additional weight of 15 rings, each with a veight of 7 kN , is placed on the ram. Calculate the pressure in the ccumulator.

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