What is the total force on a 4" piston with a cylinder pressure of 100 psig?

What is the total force on a 4" piston with a cylinder pressure of 100 psig?

• A. 1000 lbs
• B. 1256.64 lbs
• C. 1500 lbs
• D. 2000 lbs

Answer: (B)

To determine the total force exerted by a piston, you can use the equation: \[ \text{Force} = \text{Pressure} \times \text{Area} \] In this case, the pressure given is 100 psig (pounds per square inch gauge), and you need to calculate the area of the piston first. For a circular piston, the area \( A \) can be calculated using the formula: \[ A = \pi \times \left(\frac{D}{2}\right)^2 \] where \( D \) is the diameter of the piston. Given that the diameter of the piston is 4 inches, the radius \( r \) is: \[ r = \frac{4}{2} = 2 \text{ inches} \] Now, substituting the radius into the area formula: \[ A = \pi \times (2)^2 = \pi \times 4 \approx 12.5664 \text{ square inches} \] Next, you multiply this area by the pressure to determine the total force: \[ \text{Force} = 100 \text{ psig} \times 12.5664 \text{ in}^2

To determine the total force exerted by a piston, you can use the equation:

[ \text{Force} = \text{Pressure} \times \text{Area} ]

In this case, the pressure given is 100 psig (pounds per square inch gauge), and you need to calculate the area of the piston first.

For a circular piston, the area ( A ) can be calculated using the formula:

[ A = \pi \times \left(\frac{D}{2}\right)^2 ]

where ( D ) is the diameter of the piston. Given that the diameter of the piston is 4 inches, the radius ( r ) is:

[ r = \frac{4}{2} = 2 \text{ inches} ]

Now, substituting the radius into the area formula:

[ A = \pi \times (2)^2 = \pi \times 4 \approx 12.5664 \text{ square inches} ]

Next, you multiply this area by the pressure to determine the total force:

[ \text{Force} = 100 \text{ psig} \times 12.5664 \text{ in}^2