Pressure in a hydraulic system:
Hydraulic systems operate according to the laws of hydrostatics. Pascal’s Law states: “The pressure in a compressed fluid at rest propagates uniformly in all directions in a closed system”.
The following animation shows the principle of a hydraulic system with two pistons, lines with a pressure gauge, and oil (colored blue).
The left piston is pushed downwards with a certain force (F1). As a result of the displacement of the fluid in the left piston, the right piston is pushed upwards with the force (F2). The diameters of both cylinders are the same. In this paragraph we will calculate the pressures and forces in two hydraulic systems.
To calculate the force F2, we must first determine the weight (kg) and the acceleration due to gravity (m/s²). The weight of the fictitious BMW is 1000 kg. We round the gravitational acceleration to 10. With this data we fill in the formula to calculate the required force:
With the following formula you can calculate the pressure indicated by the manometer:
Where:
- p = pressure in Pa (Pascal)
- F = force in N (Newton)
- A = area in m²
We fill in the formula to calculate the fluid pressure under both pistons.
A mnemonic:
- 1 kPa (kilopascal) = 1,000 Pa;
- 1 MPa (megapascal) = 1,000,000 Pa;
- 1 bar = 100,000 Pa = 100,000 N/cm².
A pressure of 10,000,000 Pa is therefore equal to 100 bar.
In the following animation, the diameter of the right piston has been increased tenfold. We calculate the pressure under the right piston using the area (A2) of 100 cm².
The fluid pressure in the entire system is the same. We substitute the pressure into the following formulas:
The formulas show that the 1000 kg car can be lifted with a force (F1) of 100 kg on the left piston. The distance travelled by the left piston is proportionally ten times greater than that of the right piston.
By filling in the following equation, we can demonstrate that the pressure is the same throughout the system:
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