Concept explainers
A thin plate moves between two parallel, horizontal, stationary flat surfaces at a constant velocity of 5 m/s. The two stationary surfaces are spaced 4 cm apart, and the medium between them is filled with oil whose viscosity is
FIGURE P247
The force required maintain motion at
The force on the plate at
Answer to Problem 87P
The force required maintain motion at
The force on the plate at
Explanation of Solution
Given information:
The moving velocity of the thin plate is
Write the expression for area of the plate.
Here the length of the plate is
Write the expression for shear force acting on the upper side of the plate.
Here, force acting on the upper side of the plate is
Write the expression for shear force acting on the lower side of the plate.
Here, shear force acting on the lower side of the plate is
Write the expression for force required to maintain the motion
Here force required to maintain the motion is
Write the expression for shear force acting on the upper side of the plate.
Here, force acting on the upper side of the plate is
Write the expression for shear force acting on the lower side of the plate.
Write the expression for force required to maintain the motion
Calculation:
Write the height of the plate from upper surface when the plate is between the mid of the surfaces.
Here, height of the plate from upper surface is
Write the height of the plate from bottom surface when the plate is between the mid of the surfaces.
Here, height of the plate from bottom surface is
Write the height of the plate from upper surface.
Here, the height of the plate from upper surface is
Write the height of the plate from bottom surface.
Here, the height of the plate from bottom surface is
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Conclusion:
The force required maintain motion at
The force on the plate at
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Chapter 2 Solutions
Fluid Mechanics: Fundamentals and Applications
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