Problem with units

  • Thread starter jdawg
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  • #1
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Homework Statement


The velocity profile between two plates separated by a distance, h=2 {m}, has a flow distribution given by:

1%257D%257B2%255Cmu%257D%255Cfrac%257Bdp%257D%257Bdx%257D%255Cleft%2528y%255E2-hy%255Cright%2529.png


The dynamic viscosity of the fluid is given as 1.5E-1 {Pa s}. The upper wall is moving at velocity u0 of 7 {m/s}. The pressure gradient dp/dx is -0.015 {Pa/m}. Find the shear stress at y=0.8 {m}.

Input your answer to in {N/m2} or {Pa} to four decimal places.

Homework Equations




The Attempt at a Solution


I feel like this problem should be just plug and chug, but my units aren't working out to be in Pa.
u(0.8m)=(7m/s)(0.8m/2m)+(1/(2*(1.5E-1)Pa*s))(-0.015Pa/m)((0.8m)2-1.6m2)
I keep getting 2.85 m/s
 

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  • #2
SteamKing
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Homework Statement


The velocity profile between two plates separated by a distance, h=2 {m}, has a flow distribution given by:

1%257D%257B2%255Cmu%257D%255Cfrac%257Bdp%257D%257Bdx%257D%255Cleft%2528y%255E2-hy%255Cright%2529.png


The dynamic viscosity of the fluid is given as 1.5E-1 {Pa s}. The upper wall is moving at velocity u0 of 7 {m/s}. The pressure gradient dp/dx is -0.015 {Pa/m}. Find the shear stress at y=0.8 {m}.

Input your answer to in {N/m2} or {Pa} to four decimal places.

Homework Equations




The Attempt at a Solution


I feel like this problem should be just plug and chug, but my units aren't working out to be in Pa.
u(0.8m)=(7m/s)(0.8m/2m)+(1/(2*(1.5E-1)Pa*s))(-0.015Pa/m)((0.8m)2-1.6m2)
I keep getting 2.85 m/s
Remember u(y) is the velocity profile of the fluid, not the shear stress, so units of m/s are consistent.

What is the formula for shear stress in a fluid?

https://en.wikipedia.org/wiki/Shear_stress
 
  • #3
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Ohh ok! I guess I should've read the question a little more closely. Did you end up with 0.5344 Pa?
 
  • #4
SteamKing
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Ohh ok! I guess I should've read the question a little more closely. Did you end up with 0.5344 Pa?
I didn't solve the problem. I merely noted that you had confused the formula for the velocity profile with the formula for shear stress.
 
  • #5
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Oh ok, do you think that the value I got is reasonable?
 
  • #6
SteamKing
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Oh ok, do you think that the value I got is reasonable?
I have no idea without solving the problem myself.

Since you have apparently done the work, why don't you post it?
 
  • #7
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τ(y)=μ(u/y)
τ(y)=(1.5E-1 Pa*s)((2.85 m/s)/(0.8m))=0.5344 Pa
 
  • #8
SteamKing
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τ(y)=μ(u/y)
This doesn't seem to be the formula for shear stress in a fluid. What happened to the ∂u/∂y, which is not the same as u/y ?
τ(y)=(1.5E-1 Pa*s)((2.85 m/s)/(0.8m))=0.5344 Pa
Need to use the correct formula here.
 
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