At a certain point in an oil the shear stress is 0.2 N/m2 and the velocity gradient is 0.21 s-1 . If the mass density of the oil is 950 kg/ m3 find the kinematic viscosity
Question
At a certain point in an oil the shear stress is 0.2 N/m2 and the velocity gradient is 0.21 s-1 . If the mass density of the oil is 950 kg/ m3 find the kinematic viscosity
Solution
The kinematic viscosity (v) can be calculated using the formula:
v = μ/ρ
where: μ is the dynamic viscosity, and ρ is the mass density.
The dynamic viscosity (μ) can be calculated from the shear stress (τ) and the velocity gradient (du/dy) using the formula:
μ = τ / (du/dy)
Given: τ = 0.2 N/m² du/dy = 0.21 s⁻¹ ρ = 950 kg/m³
First, calculate the dynamic viscosity:
μ = τ / (du/dy) = 0.2 N/m² / 0.21 s⁻¹ = 0.9524 Ns/m²
Then, calculate the kinematic viscosity:
v = μ/ρ = 0.9524 Ns/m² / 950 kg/m³ = 0.0010025 m²/s
So, the kinematic viscosity of the oil is approximately 0.0010025 m²/s.
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