Fluid Dynamics Help (Force with a dynamic viscosity)

[Colt 45 J]

Problem Statement
A 50cm by 30cm by 20cm block weighing 150N is to be moved at a constant velocity of .8 m/s on an inclined surface with a friction coefficient of 0.27. (a) Determine the force f that needs to be applied in the horizontal direction. (b) if a .4mm thick oil film with a dynamic viscosity of .012Pa*s is applied between the block and inclined surface, determine the percent reduction in the required force.

Given: P=150N V=.8m/s a=0, mu(v)=.012Pa*s mu(f)=.27

Find: F(a), F(b), %r

Diagram:
http://img18.imageshack.us/img18/7915/fluids275.png The attempt at a solution

I solved the F(a) to be 40.5N using statics equations (since there is no acceleration F=ma=0)

When using the equations presented in my text I get:
F=mu(v)*A*V/l
F=.012*(.5*.2)*.8/.0004
F=2.4
F(b)=2.4/cos(20*)
F(b)=2.554N

Thus the percentage would be a ~94% reduction in force, which sounds highly unrealistic and leads me to think I did something wrong...

Some Help?

Thanks, Colt 45 J

 

[nvn]

Colt 45 J: Your answer currently looks correct. The oil reduces the required force by a large amount. By the way, please note the following international standard for writing units. Secondly, please do not post wide images directly to the forum page. Just post a text link to wide images. Or crop the image.

1. Always leave a space between a numeric value and its following unit symbol. E.g., 50 cm, not 50cm.
   
   
2. Numbers less than 1 must always have a zero before the decimal point. E.g., 0.5, not .5. See the international standard for writing units (ISO 31-0).

 

[Colt 45 J]

I was considering, would I end up using the shear force (calculated using the force already found). The result from doing that is about a 37% reduction, which seems much more realistic.

(V=F/A)

For the future I'll be sure to crop and use the ISO standards.

 

[nvn]

Colt 45 J: I think the force already found (F = 2.40 N) is already the shear force. Therefore, you would not divide it by A.

 

[DeeNos]

Dear Colt 45 J,

Thank you for reaching out for assistance with your fluid dynamics problem. After reviewing your attempted solution, I can confirm that your calculations and approach are correct. The large reduction in force may seem unrealistic, but it is actually a result of the low dynamic viscosity of the oil film. Dynamic viscosity is a measure of a fluid's resistance to flow, and in this case, the low value of 0.012Pa*s indicates that the oil film is quite slippery and will significantly reduce the friction between the block and the inclined surface.

In practical applications, it is common to use lubricants with low dynamic viscosity to reduce friction and improve the efficiency of movement. The high reduction in force in this problem simply reflects the effectiveness of the oil film in reducing friction.

I hope this helps to clarify your solution and understanding of the problem. Keep up the good work in your studies of fluid dynamics!

Best,
[Your name]