the ratio of the inlet pistol force and outlet pistol force is 2:7.calculate the diameter of the inlet pistol if the radius of pistol one is 15cm
To calculate the diameter of the inlet pistol, we first need to find the ratio of the areas of the inlet and outlet pistons. Since the force is directly proportional to the area of the piston, we can use the ratio of forces to find the ratio of areas.
Given that the ratio of the inlet piston force to the outlet piston force is 2:7, we can set up the following equation:
Area of inlet piston / Area of outlet piston = 2/7
Now, let's substitute the formula for the area of a circle into the equation:
(π * r₁²) / (π * r₂²) = 2/7
Here, r₁ is the radius of the inlet piston (15 cm) and r₂ is the radius of the outlet piston.
We can simplify the equation by canceling out the π:
(r₁²) / (r₂²) = 2/7
Now, let's solve for the radius of the outlet piston (r₂):
r₂² = (7/2) * r₁²
r₂ = sqrt((7/2) * r₁²)
r₂ ≈ sqrt((7/2) * (15 cm)²)
r₂ ≈ sqrt((7/2) * 225 cm²)
r₂ ≈ sqrt(787.5 cm²)
r₂ ≈ 28.04 cm
Finally, we can calculate the diameter of the inlet piston by doubling its radius:
Diameter of inlet piston = 2 * radius of inlet piston
Diameter of inlet piston = 2 * 15 cm
Diameter of inlet pistol = 30 cm
Therefore, the diameter of the inlet piston is approximately 30 cm.