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Hydraulics & Pascal's Law Lab

Investigate how pressure is transmitted through confined fluids. Build hydraulic presses and lifts, calculate force multiplication, and explore how depth affects fluid pressure.

Guided Experiment: Force Multiplication

How does changing the ratio of piston areas affect the output force? If you double the area ratio, what happens to the mechanical advantage?

Write your hypothesis in the Lab Report panel, then click Next.

Hydraulic System Diagram

F₁ = 100 NF₂ = 10023.8 NP = 200497.5 PaEqual pressure transmittedA₁ = 4.9876 cm²A₂ = 499.9475 cm²MA = 100.2382
Input ForceOutput ForceHydraulic Fluid

Controls

Input Piston (small)
4.99
Output Piston (large)
499.95
Force and Distance

Hydraulic Press Results

F2=F1×A2A1F_2 = F_1 \times \frac{A_2}{A_1}
Area RatioA2/A1A_2 / A_1
100.2382
System PressureP=F1/A1P = F_1 / A_1
200497.5 Pa
Output ForceF2F_2
10023.8 N
Mechanical AdvantageMA=A2/A1MA = A_2 / A_1
100.2382
Input Distanced1d_1
10 cm
Output Distanced2=d1timesA1/A2d_2 = d_1 \\times A_1/A_2
0.09976 cm
Work InputWtextin=F1d1W_{\\text{in}} = F_1 d_1
10 J
Work OutputWtextout=F2d2W_{\\text{out}} = F_2 d_2
10 J
Efficiency
100 %

Data Table

(0 rows)
#TrialA₁ (cm²)A₂ (cm²)F_in (N)P (Pa)F_out (N)MAd₁/d₂
0 / 500
0 / 500
0 / 500

Reference Guide

Pascal's Law

Pressure applied to a confined fluid is transmitted undiminished in every direction throughout the fluid and to the walls of the container.

P=FA  ⟹  F2=F1×A2A1P = \frac{F}{A} \implies F_2 = F_1 \times \frac{A_2}{A_1}

This principle, discovered by Blaise Pascal in 1653, is the foundation of all hydraulic machinery.

Hydraulic Press

A hydraulic press uses two connected cylinders with different piston areas. The mechanical advantage equals the ratio of piston areas.

MA=A2A1,d1A1=d2A2MA = \frac{A_2}{A_1}, \quad d_1 A_1 = d_2 A_2

While force is multiplied, distance is divided by the same factor. Energy is conserved (Work in = Work out in an ideal system).

Pressure at Depth

The pressure in a static fluid increases linearly with depth. It depends only on fluid density, gravitational acceleration, and the height of the fluid column above the point.

P=ρgh,Pabs=Patm+ρghP = \rho g h, \quad P_{\text{abs}} = P_{\text{atm}} + \rho g h

At 10 meters of water depth, gauge pressure is approximately 1 atmosphere (98,100 Pa).

Hydraulic Systems

Real hydraulic systems include car brakes, construction equipment, aircraft controls, and industrial presses. They lose some energy to friction, heat, and fluid compressibility.

η=WoutWin=F2 d2F1 d1\eta = \frac{W_{\text{out}}}{W_{\text{in}}} = \frac{F_2 \, d_2}{F_1 \, d_1}

Typical hydraulic system efficiencies range from 80% to 98% depending on the design and operating conditions.