Question
A flat plate 0.3times 0.5m slide on oil with viscosity of 80 Poise as shown in the figure Force of 1000N is applied on the plate. Calculate velocity of this plate if oil film thickness is 8 mu m.
Solution
4.1
(247 Votes)
Andrew
Master · Tutor for 5 years
Answer
Here's how to calculate the velocity of the plate:**1. Understand the concept**The plate is moving due to the applied force overcoming the viscous resistance of the oil film. This is governed by Newton's law of viscosity, which states that shear stress is proportional to the velocity gradient.**2. Formula**Newton's law of viscosity is expressed as:τ = μ * (du/dy)Where:* τ is the shear stress* μ is the dynamic viscosity* du/dy is the velocity gradient (change in velocity with respect to the change in distance perpendicular to the flow)Since the force applied is distributed over the area of the plate, the shear stress is:τ = Force / Area**3. Unit Conversions*** Viscosity: 80 Poise = 8 Pa·s (1 Poise = 0.1 Pa·s)* Film thickness: 8 μm = 8 x 10⁻⁶ m* Area: 0.3 m * 0.5 m = 0.15 m²**4. Calculation*** Shear stress (τ): τ = 1000 N / 0.15 m² = 6666.67 Pa* Velocity gradient (du/dy): Since the velocity changes from the plate's velocity (which we'll call 'v') to zero at the stationary surface over the film thickness, the velocity gradient is v / (8 x 10⁻⁶ m).* Applying Newton's law of viscosity:6666.67 Pa = 8 Pa·s * (v / (8 x 10⁻⁶ m))**5. Solve for velocity (v)**v = (6666.67 Pa * 8 x 10⁻⁶ m) / 8 Pa·sv = 6.67 x 10⁻³ m/s**Answer:**The velocity of the plate is 6.67 x 10⁻³ m/s, or 6.67 mm/s.