Question

3. Thin plate is pulled at a constant velocity of $U_0$ through a very narrow gap of height h, as shown in the figure. The upper side of the plate is filled with an oil of viscosity $\mu$, while the lower side of the plate is filled with another oil of viscosity $2\mu$. Assuming that both oils are of Newtonian type, calculate the distance $l$ so that the force required to pull the plate is minimum. The pressure is constant everywhere. (Ans. 0.5858h)

          3. Thin plate is pulled at a constant velocity of $U_0$ through a very narrow gap of height
h, as shown in the figure. The upper side of the plate is filled with an oil of viscosity
$\mu$, while the lower side of the plate is filled with another oil of viscosity $2\mu$. Assuming
that both oils are of Newtonian type, calculate the distance $l$ so that the force required
to pull the plate is minimum. The pressure is constant everywhere. (Ans. 0.5858h)

3. Thin plate is pulled at a constant velocity of U0 through a very narrow gap of height
h, as shown in the figure. The upper side of the plate is filled with an oil of viscosity
μ, while the lower side of the plate is filled with another oil of viscosity 2μ. Assuming
that both oils are of Newtonian type, calculate the distance l so that the force required
to pull the plate is minimum. The pressure is constant everywhere. (Ans. 0.5858h)

Added by Scott H.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Adi S

12/21/2023

Step 1

The shear stress on the upper side (oil of viscosity 1) can be calculated using the formula τ = μ1 * du/dy, where μ1 is the viscosity of oil 1, du/dy is the velocity gradient in the y-direction. Similarly, the shear stress on the lower side (oil of viscosity 2) Show more…

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Bu soruyu çözebilir misin? 3. Thin plate is pulled at a constant velocity of U through a very narrow gap of height h, as shown in the figure. The upper side of the plate is filled with an oil of viscosity 1, while the lower side of the plate is filled with another oil of viscosity 2. Assuming that both oils are of Newtonian type, calculate the distance d so that the force required to pull the plate is minimum. The pressure is constant everywhere. (Ans. 0.5858) Oil of viscosity 1 U/o Oil of viscosity 2 Problem 3