Learn how pressure applied to an enclosed fluid is transmitted uniformly in all directions, how hydraulic systems act as force multipliers, and how this principle powers hydraulic jacks and brakes.
See how a small input force on a narrow piston produces a much larger output force on a wide piston through uniform pressure transmission.
Pressure applied at the small input piston is transmitted uniformly through the enclosed hydraulic fluid. The larger output piston area produces a proportionally larger output force.
Since pressure is transmitted uniformly throughout the enclosed fluid:
Pascal's principle for hydraulic systems
Multiplying factor \(= \dfrac{A_2}{A_1}\)
When \(A_2 > A_1\), the output force \(F_2\) is greater than the input force \(F_1\). A small input force can therefore lift a heavy load.
Pascal's principle states that the pressure applied on an enclosed fluid is transmitted uniformly in all directions in the fluid.
When a Pascal's piston filled with water is pushed, water spurts out with equal speed from every hole. This shows that pressure produced on the water surface is transmitted uniformly throughout the water in all directions.
A hydraulic system uses a liquid to transmit pressure. Because \(P_1 = P_2\), we get \(\frac{F_1}{A_1} = \frac{F_2}{A_2}\). The output force is \(F_2 = \frac{A_2}{A_1} \times F_1\).
Pressure is force per unit area, \(P = \frac{F}{A}\). Keeping the same pressure across a larger output piston area produces a proportionally larger output force. The multiplying factor is \(\frac{A_2}{A_1}\).
Worked Example 1
Multiplying factor \(= \frac{A_2}{A_1} = \frac{50}{10} = 5\).
Output force \(F_2 = 5 \times 12\ \mathrm{N} = 60\ \mathrm{N}\).
Worked Example 2
\(\frac{840}{A_2} = \frac{60}{0.80}\), so \(A_2 = \frac{840 \times 0.80}{60} = 11.2\ \mathrm{cm^2}\).
Answer in your mind, then press “Check Answer”.
What does Pascal's principle state?
In a hydraulic system, an input force of \(4.0\ \mathrm{N}\) acts on a piston with surface area \(0.50\ \mathrm{cm^2}\). Calculate the output force produced on a piston with surface area \(6.4\ \mathrm{cm^2}\).
A small syringe has a piston diameter of \(1.5\ \mathrm{cm}\). To multiply force from \(6\ \mathrm{N}\) to \(72\ \mathrm{N}\), what must be the diameter of the large syringe piston?
Force is transmitted equally throughout an enclosed liquid.
Pressure is transmitted equally, not force. The output force increases proportionally with the surface area of the output piston.
Pascal's principle works in open containers or gases that leak easily.
Pascal's principle strictly applies to an enclosed fluid where fluid cannot escape and the volume remains confined.
Objective: Check your understanding of Pascal's principle, hydraulic force multiplication, and hydraulic system components.
1 Which of the following statements correctly expresses Pascal's principle?
2 In a hydraulic press, an input force of \(15\ \mathrm{N}\) is applied to a piston of cross-sectional area \(3\ \mathrm{cm^2}\). What is the output force exerted on a larger piston with an area of \(30\ \mathrm{cm^2}\)?
3 Pascal's principle states that the pressure applied on an fluid is transmitted uniformly in all directions in the fluid.
4 The multiplying factor of a hydraulic system with an input piston area \(A_1\) and an output piston area \(A_2\) is given by the ratio .
Match each component of a hydraulic system or device to its correct function or description. If using a phone, tap the answer first, then tap the matching box.
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