A large platé moves with speed vo over a static that of a parabola, with the oil at the plates ha the moving plate from the oil? If a linear profi I For a parabolic profile, v= ay. When y = %3D %3D
A large platé moves with speed vo over a static that of a parabola, with the oil at the plates ha the moving plate from the oil? If a linear profi I For a parabolic profile, v= ay. When y = %3D %3D
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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1.23 Please help explain the solution and what theories used thanks!
![A large plate moves with speed vo over a stationary plate on a layer of oil (see Fig. 1-5). If the velocity profile is
that of a parabola, with the oil at the plates having the same velocity as the plates, what is the shear stress on
the moving plate from the oil? If a linear profile is assumed, what is the shear stress on the upper plate?
I For a parabolic profile, v= ay. When y = d, v = vo. Hence, vž = ad, a = våld. Therefore,
%3D
v (v/d)(y) (v)(y/d)
v = v,Vyld du/dy [(vo)(1/Va)(})(y-J
T = u (dv/dy) = µ[(v)(1/Va)(})(y]
For y = d, T u((v)(1/Va)()(d)= uvo/(2d). For a linear profile, du/dy = vold, T= u(v/d).
%3D
Assumed profile
Vo
Oil
layer
Fig. 1-5](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7bcbc0fa-bf79-4a04-9af0-c90cc99d167f%2F74b9d667-6397-429f-b181-2db9f1c0ba31%2Fb88cii9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A large plate moves with speed vo over a stationary plate on a layer of oil (see Fig. 1-5). If the velocity profile is
that of a parabola, with the oil at the plates having the same velocity as the plates, what is the shear stress on
the moving plate from the oil? If a linear profile is assumed, what is the shear stress on the upper plate?
I For a parabolic profile, v= ay. When y = d, v = vo. Hence, vž = ad, a = våld. Therefore,
%3D
v (v/d)(y) (v)(y/d)
v = v,Vyld du/dy [(vo)(1/Va)(})(y-J
T = u (dv/dy) = µ[(v)(1/Va)(})(y]
For y = d, T u((v)(1/Va)()(d)= uvo/(2d). For a linear profile, du/dy = vold, T= u(v/d).
%3D
Assumed profile
Vo
Oil
layer
Fig. 1-5
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