Problem Statement
A piston is moving through a cylinder at a speed of 5.7 m/s. The film of oil separating the piston from the cylinder has a viscosity of 0.95 NS/m². Calculate the force required to maintain this motion.
Given Data
- Speed of piston (v) = 5.7 m/s
- Viscosity of oil (μ) = 0.95 NS/m²
- Diameter of piston (D) = 124.7 mm = 0.1247 m
- Length of piston (L) = 75 mm = 0.075 m
- Oil film thickness (dr) = 0.15 mm = 0.00015 m
Solution
1. Calculate Surface Area of Piston
A = π × D × L
A = π × 0.1247 × 0.075 = 0.0294 m²
2. Calculate Velocity Gradient
dv/dy = 5.7/0.00015 = 38,000 s⁻¹
3. Calculate Shear Stress
τ = μ × (dv/dy)
τ = 0.95 × 38,000 = 36,100 N/m²
4. Calculate Total Force
F = τ × A
F = 36,100 × 0.0294 = 1,060.7 N
Required Force = 1,060.7 N
Key Points
- The force is directly proportional to the oil’s viscosity
- Thinner oil film (smaller gap) requires more force
- Force increases with piston surface area and speed
