1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Shear stress

  1. Jan 21, 2016 #1
    1. The problem statement, all variables and given/known data
    how to make μ = ρ v as in 8-41 ?


    2. Relevant equations


    3. The attempt at a solution
    since μ = viscocity , it has unit =( kgms^-2)s m^-2 , = kg(m^-1)(s^-1)
    ρ v = (kgm^-3)(ms^-1 ) = kg(m^-2)(s^-1) , the unit for LHS and RHS are not the same , can someone help pls ?
     

    Attached Files:

  2. jcsd
  3. Jan 21, 2016 #2

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    You've mixed up lower case v for velocity with the lower case Greek letter nu (##\nu##), which is used to represent the kinematic viscosity of a fluid.

    The kinematic viscosity is defined ##\nu = \frac{\mu}{\rho}##

    See this article for a discussion of the units:

    https://en.wikipedia.org/wiki/Viscosity
     
  4. Jan 21, 2016 #3
    ok , can you pls explain how the author get the formula of viscous sublayer ? after substitute u= sqrt rt (τ / ρ ) into 8-41 , I have u = ( v / y ) sqrt rt (τ / ρ ) , hwo to get the same form as in 8-42 ?
     

    Attached Files:

  5. Jan 21, 2016 #4

    TSny

    User Avatar
    Homework Helper
    Gold Member

    Note that ##\sqrt{\tau_w/\rho}## is defined to be a fictitious velocity ##u##- (called "friction velocity"). (I'm not sure I got the notation right. It looks like there is a subscript "-" on the ##u## for the fictitious velocity. But it is hard for me to read.) See discussion below equation 8-41.
    ##u##- is not the same as the actual velocity ##u##.
     
    Last edited: Jan 21, 2016
  6. Jan 21, 2016 #5
    u / ##u##- , i haver u [ sqrt rt ( p / т ) ] , how to get the same form as in the 8-42 ?
     
  7. Jan 21, 2016 #6

    TSny

    User Avatar
    Homework Helper
    Gold Member

    Solve ##u##- = ##\sqrt{\tau/\rho}## for ##\tau##. Then sustitute this expression for ##\tau## into equation 8-41. You should then be able to rearrange it to get 8-42.
     
  8. Jan 22, 2016 #7
    hwo to do that ? I have tried , but didn't get the same form ,
     

    Attached Files:

  9. Jan 22, 2016 #8

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Some of your cancellations are wrong. ##\frac x{\sqrt x}## is not ##\frac 1{\sqrt x}##
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Shear stress
  1. Shear Stress (Replies: 0)

  2. Shear stress (Replies: 13)

  3. Shear stress of water (Replies: 3)

Loading...