The following data refers to a single-acting hydraulic press: Force exerted on the ram piston Force exerted on the plunger Diameter of the plunger Stroke length of the plunger Calculate the following: The diameter of the ram piston

1. The hydraulic press operates under Pascal’s law. Hence, the pressure in the system is the same at all points: \[ P=\frac{F_{\text{ram}}}{A_{\text{ram}}}=\frac{F_{\text{plunger}}}{A_{\text{plunger}}}. \] 2. Rearranging the above, \[ \frac{F_{\text{ram}}}{F_{\text{plunger}}}=\frac{A_{\text{ram}}}{A_{\text{plunger}}}. \] 3. The area \( A \) for a circular piston of diameter \( D \) is given by: \[ A=\frac{\pi D^2}{4}. \] Thus, \[ \frac{A_{\text{ram}}}{A_{\text{plunger}}}=\frac{\frac{\pi D_{\text{ram}}^2}{4}}{\frac{\pi D_{\text{plunger}}^2}{4}}=\frac{D_{\text{ram}}^2}{D_{\text{plunger}}^2}. \] 4. Equating the two expressions, \[ \frac{F_{\text{ram}}}{F_{\text{plunger}}}=\frac{D_{\text{ram}}^2}{D_{\text{plunger}}^2}. \] 5. Solving for the diameter of the ram piston \( D_{\text{ram}} \), \[ D_{\text{ram}}^2 = \frac{F_{\text{ram}}}{F_{\text{plunger}}} \cdot D_{\text{plunger}}^2. \] Taking the square root, \[ D_{\text{ram}} = D_{\text{plunger}}\,\sqrt{\frac{F_{\text{ram}}}{F_{\text{plunger}}}}. \] Thus, the diameter of the ram piston is \[ D_{\text{ram}} = D_{\text{plunger}}\, \sqrt{\frac{F_{\text{ram}}}{F_{\text{plunger}}}}. \]