APPLIED PHYSICS

LAB

Technical Report
Experimental Verification of
Pascal's Law Using a Hydraulic Lift

BS-Mechanical Engineering
F-24B

Group Members

Muhammad Rafay Ahmad 005971

Asad Khursheed 005902
Samer Hamad M. Alotaibi 006678

Submitted To: Sir Muhammad Naeem Khan

 Technical Report: Hydraulic Lift for
Applied Physics Laboratory

1. Project Overview
This report outlines the design, construction, and experimental evaluation of a Hy-
draulic Lift, developed to illustrate the principles of Pascal’s Law.
Pascal’s Law states that when a force is applied to a confined fluid, the pressure
generated is transmitted equally and undiminished throughout the fluid. This principle
serves as the foundation for hydraulic systems used in various engineering applications,
such as lifting machinery and industrial tools.
The objective of this project is to create a functional hydraulic lift that demonstrates:

• The transmission of pressure in a confined fluid.

• Force multiplication, where a smaller input force is used to lift a larger load.

• Practical understanding of mechanical advantage in hydraulic systems.

2. Apparatus Description
This section provides a detailed breakdown of the materials and components used in
constructing the hydraulic lift, along with their functional roles.

2.1 Hydraulic System Components

The hydraulic system comprises two pistons of different sizes connected by a sealed pipe
filled with water:

• Small Piston (Effort Piston):

– Diameter: d1 = 0.0381 m
– Cross-sectional Area:
 2
d1
A1 = π = 1.14 × 10−3 m2
2

• Large Piston (Load Piston):

– Diameter: d2 = 0.04064 m

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 – Cross-sectional Area:
 2
d2
A2 = π = 1.30 × 10−3 m2
2

• Connecting Pipe: A sealed hydraulic tube filled with water connects the two
pistons, ensuring a closed hydraulic system for pressure transmission.

• Hydraulic Fluid: Water is used for its incompressibility, cost-effectiveness, and

availability.

2.2 Structural Framework

The framework supports the hydraulic components and provides operational stability.
Key elements include:

• Wooden Stand: Provides support and stability for the hydraulic components.

• Wooden Base: Attached to the large piston, this serves as the platform for sup-
porting the load.

2.3 Control Mechanism

The system’s operation is controlled through a switch and visual feedback:

• Switch System:

– A manually operated switch toggles between two states:

∗ Push right to raise the load.
∗ Push left to lower the load.

• Indicator Lights:

– Green LED: Activates during load lifting.

– Red LED: Activates during load lowering.

2.4 Actuation
The actuation system converts electrical energy into mechanical force. Components in-
clude:

• Electric Motor: The motor powers the compression and release of the small piston
through a screw-nut assembly.

– Shaft Radius: r = 0.003 m

– Stall Torque: τ = 0.0408 N · m
– No-Load Current: IN L = 0.106 A
– Load Current: IL = 0.4 A

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2.5 Sealing and Bonding
• To ensure operational efficiency, all connections are sealed with silicon adhesive.
This prevents leaks and maintains system stability.

3. Experimental Procedure
This section outlines the step-by-step process for setting up and operating the hydraulic
lift.

3.1 Setup
The following steps were undertaken to assemble the hydraulic lift:

1. Assemble the hydraulic lift components, ensuring the pistons and pipe form a sealed
hydraulic circuit.

2. Secure the apparatus on a stable surface to prevent movement during operation.

3. Fill the hydraulic system with water, ensuring no air bubbles are trapped in the
fluid.

3.2 Operation
The hydraulic lift was operated using the following steps:

1. Use the switch to activate the electric motor, which applies a force to the small
piston.

2. Observe the load being raised on the large piston as pressure is transmitted through
the hydraulic fluid.

3. Reverse the switch to release the small piston and lower the load.

3.3 Data Collection

Measurements were recorded as follows:

1. Measure the input force (F1 ) applied to the small piston.

2. Measure the output force (F2 ) exerted by the large piston.

3. Repeat the experiment for three different input forces and record the observations.

4. Observations and Results

The table below summarizes the experimental findings, including the areas of the small
piston (A1 ) and the large piston (A2 ), the output force (F2 ), and the efficiency (E) of the
system.

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 Input Force (F1 ) [N] A1 [m2 ] A2 [m2 ] Output Force (F2 ) [N] Efficiency (%)
−3
13.6 1.14 × 10 1.30 × 10−3 4.00 25.81
−3 −3
13.6 1.14 × 10 1.30 × 10 8.00 51.61
−3 −3
13.6 1.14 × 10 1.30 × 10 10.00 64.52

• The areas of the pistons (A1 , A2 ) remain constant, determined by their geometries.
• The efficiency (E) is calculated as:
Actual Output Force (F2 )
E(%) = × 100
Theoretical Output Force (15.5 N)

5. Analysis and Discussion

This section analyzes the system’s performance and explains key theoretical and experi-
mental findings.

5.1 Force Transmission

Using Pascal’s Law, the relationship between the input force (F1 ) and the output force
(F2 ) is given by:
F1 F2
=
A1 A2
Rearranging:
F1 × A2
F2 =
A1
Substituting values (F1 = 13.6 N, A1 = 1.14 × 10−3 m2 , A2 = 1.30 × 10−3 m2 ):
13.6 × 1.30 × 10−3
F2 = = 15.5 N
1.14 × 10−3
This calculated output force matches the theoretical prediction for the maximum system
capacity under ideal conditions. However, the observed values (F2 = 4.00 N, 8.00 N, 10.00 N)
are lower, reflecting practical inefficiencies.

5.2 Mechanical Advantage (MA)

Mechanical advantage (M A) is a measure of how effectively a machine amplifies an input
force. In an ideal hydraulic system, M A is calculated as:
A2 1.30 × 10−3
MA (ideal) = = = 1.14
A1 1.14 × 10−3
This theoretical value assumes no losses and reflects the system’s capacity to amplify the
input force based purely on piston geometry.
Experimentally, M A is calculated as:
F2
MA =
F1
For the given conditions:

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 • When F2 = 4.00 N, MA = 4.00
13.6
= 0.29

• When F2 = 8.00 N, MA = 8.00

13.6
= 0.59

• When F2 = 10.00 N, MA = 10.00

13.6
= 0.74

Mechanical advantage quantifies the system’s ability to amplify an input force. A

higher M A indicates greater amplification, enabling smaller efforts to perform tasks re-
quiring larger forces. The theoretical M A = 1.14 remained constant, while experimental
M A varied due to practical inefficiencies.

5.3 System Efficiency (E)

The efficiency (E) measures how closely the observed output force matches the theoretical
output force (F2 = 15.5 N):

Actual Output Force (F2 )

E(%) = × 100
Theoretical Output Force

• For F2 = 4.00 N, E = 4.00

15.5
× 100 = 25.81%

• For F2 = 8.00 N, E = 8.00

15.5
× 100 = 51.61%

• For F2 = 10.00 N, E = 10.00

15.5
× 100 = 64.52%

The efficiency increases with higher output forces, reflecting reduced losses at larger loads.
Practical inefficiencies such as friction, fluid resistance, and imperfect sealing contribute
to these deviations.

6. Precautions
To ensure consistent results and prevent errors, the following precautions were observed
during the experiment:

• Ensure no air bubbles are present in the hydraulic fluid to maintain uniform pressure
transmission.

• Avoid overloading the system beyond its designed capacity to prevent damage to
the pistons or motor.

• Verify that the motor operates within its specified current range (0.106 A to 0.4 A)
to avoid overheating or failure.

• Use silicon adhesive to securely seal all connections and prevent leaks in the hy-
draulic circuit.

• Regularly check for wear and tear in the mechanical and electrical components to
maintain system performance.

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7. Conclusion
This project successfully validates the principles of Pascal’s Law by demonstrating the
force amplification capabilities of a hydraulic system. According to Pascal’s Law, any
pressure applied to a confined fluid is transmitted equally and undiminished through-
out the fluid. In this experiment, the small piston applied a constant input force (F1 =
13.6 N), which created pressure in the hydraulic fluid. This pressure was transmitted uni-
formly to the larger piston, resulting in amplified output forces (F2 = 4.00 N, 8.00 N, 10.00 N)
depending on the load conditions.
While the theoretical mechanical advantage (M A = 1.14) is constant, practical M A
values varied (0.29, 0.59, 0.74), reflecting inefficiencies in the system. Efficiency calcu-
lations (25.81% to 64.52%) further highlight these losses. Despite these deviations, the
experiment validates Pascal’s Law, demonstrating the reliable transmission of pressure
and force amplification in hydraulic systems.
This experiment serves as a valuable educational tool for understanding hydraulic
mechanics and their applications in real-world systems such as hydraulic lifts, automotive
braking systems, and industrial machinery.