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

1. Problem Description

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

2. Solution Steps

First, we need to convert the given units to SI units.

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

Pressure: $P = 20 \text{ bar} = 20 \times 10^5 \text{ Pa}$ (Pascals)

The area of the piston is given by the formula for the area of a circle:

$A = \pi r^2$

where $r$ is the radius of the piston. Since $d = 2r$, we have $r = d/2$. So, $r = 0.8 \text{ m} / 2 = 0.4 \text{ m}$.

Thus, the area is:

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

The force exerted on the piston is given by the product of pressure and area:

$F = P \times A$

$F = (20 \times 10^5 \text{ Pa}) \times (0.16\pi \text{ m}^2) = 3.2 \pi \times 10^5 \text{ N}$

$F \approx 3.2 \times 3.14159 \times 10^5 \text{ N} \approx 10.053 \times 10^5 \text{ N} = 1005308.84 \text{ N} \approx 1.005 \times 10^6 \text{ N}$

3. Final Answer

The force exerted on the piston is approximately $1.005 \times 10^6 \text{ N}$.