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In a liquid, the force required to maintain the flow of layers is 5N, velocity gradient in du/dx, area of contact is 20m2. Then what is the value of viscosity?
- a)6.25 dz/du
- b)0.15 dz/du
- c)0.2 dz/du
- d)0.25 dz/du
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
In a liquid, the force required to maintain the flow of layers is 5N, ...
Given:
Force required to maintain the flow of layers (F) = 5N
Velocity gradient (du/dx) = ?
Area of contact (A) = 20m²
Viscosity (η) is a measure of a fluid's resistance to flow. It is defined as the ratio of the shear stress (τ) to the velocity gradient (du/dx):
η = τ / (du/dx)
Shear stress (τ) can be calculated using the force (F) and the area of contact (A):
τ = F / A
Therefore, substituting the values:
τ = 5N / 20m²
τ = 0.25 N/m²
Now, substituting the value of shear stress (τ) into the equation for viscosity:
η = 0.25 N/m² / (du/dx)
Hence, the value of viscosity (η) is 0.25 dz/du (option D).
Force required to maintain the flow of layers (F) = 5N
Velocity gradient (du/dx) = ?
Area of contact (A) = 20m²
Viscosity (η) is a measure of a fluid's resistance to flow. It is defined as the ratio of the shear stress (τ) to the velocity gradient (du/dx):
η = τ / (du/dx)
Shear stress (τ) can be calculated using the force (F) and the area of contact (A):
τ = F / A
Therefore, substituting the values:
τ = 5N / 20m²
τ = 0.25 N/m²
Now, substituting the value of shear stress (τ) into the equation for viscosity:
η = 0.25 N/m² / (du/dx)
Hence, the value of viscosity (η) is 0.25 dz/du (option D).
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In a liquid, the force required to maintain the flow of layers is 5N, ...
The formula of force required to maintain the flow of layers is given by the formula F = ηAdu/dz, where η is the coefficient of viscosity, A is the area of contact and du/dz is the velocity gradient. So by substituting we get an answer as 0.25dz/du.
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