The problem asks to calculate the force applied to the piston of a diesel engine. The diameter of the piston is given as $d = 800 \text{ mm}$, and the pressure during combustion is $P = 20 \text{ bar}$.

1. Problem Description

The problem asks to calculate the force applied to the piston of a diesel engine. The diameter of the piston is given as $d = 800 \text{ mm}$, and the pressure during combustion is $P = 20 \text{ bar}$.

2. Solution Steps

First, we need to convert the units to a consistent system.

The diameter is given in millimeters, so let's convert it to meters:

$d = 800 \text{ mm} = 0.8 \text{ m}$

Then, we calculate the radius $r$ from the diameter $d$:

$r = \frac{d}{2} = \frac{0.8}{2} = 0.4 \text{ m}$

Next, we need to convert the pressure from bar to Pascals (Pa):

$1 \text{ bar} = 10^5 \text{ Pa}$

So, $20 \text{ bar} = 20 \times 10^5 \text{ Pa} = 2 \times 10^6 \text{ Pa}$

Now, we can calculate the area of the piston:

$A = \pi r^2 = \pi (0.4)^2 = \pi (0.16) \approx 0.50265 \text{ m}^2$

The force $F$ applied to the piston is given by the formula:

$F = P \times A$

Where $P$ is the pressure and $A$ is the area.

So, $F = (2 \times 10^6 \text{ Pa}) \times (0.16 \pi \text{ m}^2) = (2 \times 10^6) \times 0.50265 \approx 1005309.65 \text{ N}$

$F \approx 1.005 \times 10^6 \text{ N}$

3. Final Answer

The force applied to the piston is approximately $1005309.65 \text{ N}$, or $1.005 \times 10^6 \text{ N}$.