FLUID MECHANICS LAB

Pascal's Principle Pressure Transmission in Fluids

Hydraulic Press Simulator

SYSTEM READY
↓ PUSH
HYDRAULIC SYSTEM PRESSURE 0.00 kPa
0 kPa 1250 kPa 2500 kPa 3750 kPa 5000 kPa

Hydraulic Parameters

INTERACTIVE CONTROLS
cm²
1 cm²20 cm²
cm²
5 cm²200 cm²
N
0 N500 N
kg
0 kg100 kg
m/s²
1.62 (Moon)9.81 (Earth)24.8 (Jup)

Force Amplification & Area Comparison

AMPLIFICATION: 20.0×
INPUT FORCE 100 N
→
SMALL PISTON 2 cm²
→
FLUID PRESSURE 500 kPa
→
LARGE PISTON 40 cm²
→
OUTPUT FORCE 2000 N
Small Area (A₁) 2 cm²
Large Area (A₂) 40 cm²
HYDRAULIC PRESSURE 500.0 kPa P = F₁ / A₁
AVAILABLE OUTPUT FORCE 2000.0 N F₂ = P × A₂
REQUIRED LIFT FORCE 147.15 N W = m × g
PISTON DISPLACEMENT Δh₁: 25 mm | Δh₂: 1.25 mm A₁·Δh₁ = A₂·Δh₂

Pascal's Principle Verification

REAL-TIME TOLERANCE CHECK
INPUT PRESSURE (P₁) 500.00 kPa F₁ / A₁
=
OUTPUT PRESSURE (P₂) 500.00 kPa F₂ / A₂
PRESSURE DIFFERENCE (ΔP) 0.00 kPa |P₁ - P₂|
✓ PRESSURE TRANSMISSION VERIFIED — PRESSURE TRANSMITTED UNDIMINISHED

Experimental Observation Table

Trial # Small Area (A₁) Large Area (A₂) Input Force (F₁) Pressure (P) Output Force (F₂) Load Mass (m) Amplification Load Lifted?
No recorded observations yet. Click Add Current Reading to log experimental trials.

Guided Laboratory Procedure

1 of 11 Steps
  1. 1
    Select the Small Piston Area (A₁) using the slider or input box (1 – 20 cm²).
  2. 2
    Select the Large Piston Area (A₂) (5 – 200 cm²).
  3. 3
    Set the desired Input Force (F₁) (0 – 500 N).
  4. 4
    Set the Load Mass (m) sitting on the large piston (0 – 100 kg).
  5. 5
    Click and hold Apply Force or drag the small piston handle downwards.
  6. 6
    Observe the animated pressure streamlines propagating through the enclosed fluid chamber.
  7. 7
    Watch the smooth movement of the large piston in response to the transmitted pressure.
  8. 8
    Check the Available Output Force (F₂) generated on the large piston.
  9. 9
    Vary the ratio of piston areas (\(A_2 / A_1\)) to see how force amplification changes proportionally.
  10. 10
    Repeat the experiment for different fluid types or gravity settings.
  11. 11
    Click Add Current Reading to log your measurements in the observation table.

Theory & Mathematical Reference

Pascal's Principle (Law of Pascal): Any change in pressure applied to a completely enclosed, incompressible fluid is transmitted undiminished to every point of the fluid and to the walls of its container.

Hydraulic Pressure
\( P = \frac{F_1}{A_1} = \frac{F_2}{A_2} \)
Pressure is force per unit cross-sectional area.
Output Force Amplification
\( F_2 = F_1 \times \left( \frac{A_2}{A_1} \right) \)
Force is multiplied by the ratio of piston areas.
Work & Displacement Conservation
\( W = F_1 \cdot h_1 = F_2 \cdot h_2 \implies A_1 \cdot h_1 = A_2 \cdot h_2 \)
Volume displaced by small piston equals volume entering large cylinder.