Find Viscosity of Fluid on an Inclined Plane

[Perodamh]

Homework Statement

A plate having an area of 0.6m^2 is sliding down the inclined plane at 30 degrees to the horizontal with a velocity 0.36 ms^-1. There is a cushion of fluid 1.8mm thick between the plate and plane. Find the viscosity of the fluid if the weight of the plate is 280N.

Homework Equations

viscosity = shear stress/velocity gradient

The Attempt at a Solution

shear stress = 280N / 0.6m^2 = 466.7 N/m^-2
converting 1.8mm to m gives 1.8 * 10^-3m
du = 0.36ms^-1
I'm not sure about how to go about dy, is the 1.8mm the length of the hypothenuse since its an inclined plane? If so does that mean dy becomes 1.8 * 10^-3m * cos 30. I'm sort of confused because it says 1.8mm thick, doesn't really tell if its the length of the hypotenuse. Thanks

 

[Aswin Sasikumar 1729]

Homework Statement

A plate having an area of 0.6m^2 is sliding down the inclined plane at 30 degrees to the horizontal with a velocity 0.36 ms^-1. There is a cushion of fluid 1.8mm thick between the plate and plane. Find the viscosity of the fluid if the weight of the plate is 280N.[/B]

Homework Equations

View attachment 215646
viscosity = shear stress/velocity gradient

The Attempt at a Solution

shear stress = 280N / 0.6m^2 = 466.7 N/m^-2
converting 1.8mm to m gives 1.8 * 10^-3m
du = 0.36ms^-1
I'm not sure about how to go about dy, is the 1.8mm the length of the hypothenuse since its an inclined plane? If so does that mean dy becomes 1.8 * 10^-3m * cos 30. I'm sort of confused because it says 1.8mm thick, doesn't really tell if its the length of the hypotenuse. Thanks

Hi friend,
The answer of your doubt is very simple and the doubt regarding "why that inclination is given?" is also good.
The inclination doesn't have any effect on the thickness because thickness is the perpendicular distance between the two surfaces.The effect of the inclination will reflected while calculating the shear force . When you take force devided by area , you have to consider the weight component along the surface.So shear strees will be,
shear stress = 280 x sin(30) / 0.6 Nm^-2
Take dy =1.8 x 10^-3 m
You will get your answer.I hope this will help.

 

[Perodamh]

Hi friend,
The answer of your doubt is very simple and the doubt regarding "why that inclination is given?" is also good.
The inclination doesn't have any effect on the thickness because thickness is the perpendicular distance between the two surfaces.The effect of the inclination will reflected while calculating the shear force . When you take force devided by area , you have to consider the weight component along the surface.So shear strees will be,
shear stress = 280 x sin(30) / 0.6 Nm^-2
Take dy =1.8 x 10^-3 m
You will get your answer.I hope this will help.

Thanks, i'd give it a try