What is the pressure increase in the fluid in a syringe when a force of 34.5 N is applied to the circular piston of the syringe, which has a diameter of 10.2 mm?
pressure=force/area
To calculate the pressure increase in the fluid in the syringe, we can use the equation:
Pressure = Force / Area
First, we need to calculate the area of the circular piston. The area of a circle can be calculated using the formula:
Area = π * (radius)^2
Since we have the diameter of the piston, we can calculate the radius by dividing the diameter by 2:
Radius = diameter / 2
Given that the diameter of the piston is 10.2 mm, the radius would be:
Radius = 10.2 mm / 2 = 5.1 mm
Next, we need to convert the radius from millimeters to meters to ensure consistent units. 1 millimeter is equal to 0.001 meter, thus:
Radius = 5.1 mm * 0.001 m/mm = 0.0051 m
Now, we can calculate the area using the radius:
Area = π * (0.0051 m)^2 = 0.00008203 m²
Finally, we can calculate the pressure increase in the fluid by dividing the force applied to the piston by the calculated area:
Pressure = 34.5 N / 0.00008203 m² ≈ 421,000 Pa
Therefore, the pressure increase in the fluid in the syringe when a force of 34.5 N is applied to the circular piston of diameter 10.2 mm is approximately 421,000 Pascal (Pa).