Concept explainers
Oil of viscosity
The top plate is stationary, but the bottom plate is moving at velocity
(a)
Velocity profiles between the plates and the distance where velocity is zero.
Answer to Problem 132P
The below figure shows the velocity profile.
The velocity is zero from bottom at the height of
Explanation of Solution
Given information:
Dynamic viscosity is
The velocities will be zero at the boundaries of the plate due to no slip condition.
Write the expression for the velocity.
Here, the pressure gradient is
Calculation:
Substitute
The below figure shows the velocity profile.
Figure-(1)
Conclusion:
The velocity is zero from bottom at the height of
(b)
The force required for moving the middle plate at constant speed.
Answer to Problem 132P
The force required for moving the middle plate at constant speed is
Explanation of Solution
Write the expression for the force required.
Here, shear stress is
Write the expression for the shear stress.
Here, shear stress is
Substitute
Write the expression for the force required between first and second plate.
Here, velocity gradient between plate one and two is
Write the expression for the force required between the second and third plate.
Here, velocity gradient between plate two and three is
Write the expression for the total force.
Here, total force is
Write the expression for velocity gradient between plate one and two.
Here, steady velocity of plate two is
Write the expression for velocity gradient between plate two and three.
Here, steady velocity of plate two is
Substitute
Calculation:
Substitute
Conclusion:
The force required for moving the middle plate at constant speed is
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Chapter 2 Solutions
Fluid Mechanics: Fundamentals and Applications
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