Problem Statement
The diameters of the fixed ram and fixed cylinder of an intensifier are 100 mm and 250 mm respectively. If the pressure of the water supplied to the fixed cylinder is 25 N/cm², find the pressure of the water flowing through the fixed ram.
Given Data & Constants
- Diameter of fixed ram, \(d = 100 \, \text{mm} = 0.1 \, \text{m}\)
- Diameter of fixed cylinder, \(D = 250 \, \text{mm} = 0.25 \, \text{m}\)
- Supply pressure to cylinder, \(P_1 = 25 \, \text{N/cm}^2\)
Solution
1. Calculate the Area of the Cylinder (A) and Ram (a)
2. Calculate the Downward Force on the Cylinder (F)
First, convert the supply pressure to standard units (N/m²).
3. Calculate the Intensified Pressure in the Ram (\(P_2\))
The force exerted on the cylinder is transmitted to the water inside the ram. This force, acting on the smaller area of the ram, creates a higher pressure.
Converting this back to N/cm² for comparison:
The pressure of the water flowing through the fixed ram is \(156.25 \, \text{N/cm}^2\).
Explanation of a Hydraulic Intensifier
A hydraulic intensifier is a device used to increase the pressure of a fluid, essentially acting as a hydraulic transformer. It works on the same fundamental principle as a hydraulic press (Pascal's Law), but in a slightly different configuration.
Low-pressure fluid acts on a large-area piston (the fixed cylinder in this case). This generates a large force. This entire force is then applied to a smaller, connected piston (the fixed ram). Because the force is concentrated onto a much smaller area, the resulting pressure is "intensified". The ratio of the pressures is equal to the ratio of the areas (\(P_2/P_1 = A/a\)). In this problem, the area ratio is 6.25, so the pressure is intensified by a factor of 6.25.
