Questions: Two hydraulic cylinders are connected at their piston ends (cap ends rather than rod ends) by a single pipe. Cylinder A has a 2-in diameter and cylinder B has a 4-in diameter. A 500-lb retraction force is applied to the piston rod of cylinder A. Determine the a. Pressure in cylinder A b. Pressure in cylinder B c. Pressure in the connecting pipe d. Output force of cylinder B

Solution Steps

The area \( A \) of a circle is given by the formula: \[ A = \pi \left(\frac{d}{2}\right)^2 \] For cylinder A with a diameter of 2 inches: \[ A_A = \pi \left(\frac{2}{2}\right)^2 = \pi \times 1^2 = \pi \, \text{in}^2 \]

Pressure \( P \) is defined as force \( F \) divided by area \( A \): \[ P = \frac{F}{A} \] For cylinder A with a retraction force of 500 lb: \[ P_A = \frac{500}{\pi} \, \text{psi} \]

For cylinder B with a diameter of 4 inches: \[ A_B = \pi \left(\frac{4}{2}\right)^2 = \pi \times 2^2 = 4\pi \, \text{in}^2 \]

Since the cylinders are connected by a single pipe, the pressure in cylinder B is the same as in cylinder A: \[ P_B = P_A = \frac{500}{\pi} \, \text{psi} \]

The pressure in the connecting pipe is the same as the pressure in both cylinders: \[ P_{\text{pipe}} = P_A = \frac{500}{\pi} \, \text{psi} \]

The output force \( F_B \) of cylinder B is given by: \[ F_B = P_B \times A_B \] Substituting the known values: \[ F_B = \left(\frac{500}{\pi}\right) \times 4\pi = 2000 \, \text{lb} \]

Final Answer