numerical on calculation of dynamic viscocity | Summary and Q&A

TL;DR

Learn how to calculate the viscosity of oil on an inclined plate using a specific formula.

Key Insights

• 🏋️ The viscous resistance to motion on an inclined surface can be calculated using the component of the weight of the object along the slope.
• 🫡 The equation for viscous resistance is τ = μ(dV/dy)A, where τ is the viscous resistance, μ is the viscosity, dV/dy is the rate of change of velocity with respect to the gap, and A is the area of the object.
• 🪡 The given measurements and velocity need to be converted to the appropriate units for the calculation.

Transcript

Read and summarize the transcript of this video on Glasp Reader (beta).

Questions & Answers

Q: How does the viscous resistance to motion in this scenario relate to the weight of the plate?

The viscous resistance is equal to the component of the plate's weight along the sloping surface. This means that the force responsible for the motion of the plate during the inclined plane is the component of the weight along the inclined surface.

Q: What equation is used to calculate the viscous resistance?

The equation used to calculate the viscous resistance is τ = μ(dV/dy)A, where τ is the viscous resistance, μ is the viscosity of the oil, dV/dy is the rate of change of velocity with respect to the gap between the surfaces, and A is the area of the plate.

Q: How do you convert the given measurements and velocity into the appropriate units for the calculation?

The given velocity in meters per second and the gap measurement in millimeters need to be converted to the appropriate units for the calculation. This can be done by multiplying the velocity by 10^-3 to convert it to meters per second and leaving the gap measurement as is since it is already in millimeters.

Q: What is the final value of the viscosity of the oil?

By substituting the given values into the equation and solving, the viscosity of the oil is determined to be 0.1 kgf·s/m^2.

Summary & Key Takeaways

• A rectangular plate with specific measurements and weight glides down a 30-degree incline surface at a uniform velocity of 2 meters per second.

• The gap between the plate and inclined surface is filled with oil, and the goal is to determine the viscosity of the oil using a constant 2mm gap.

• The viscous resistance to the motion is equal to a component of the plate's weight along the sloping surface, and the equation for determining the resistance is provided.