1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Power required to rotate a disc in a fluid

  1. Aug 31, 2015 #1
    1. The problem statement, all variables and given/known data

    This is an optional question given to Fluid mechanic students to work on for leisure.

    P = power
    ρ = fluid density, rho
    ω= angular velocity omega
    μ= dynamic viscosity, mu
    D= diameter

    2. Relevant equations

    Show the that the power required to rotate the disc is given by:

    P/(ρ * ω^3 * D^5) =F[(ρ* D^2 * ω)/μ)]

    3. My attempt at a solution

    The mass flow rate ( upsilon/m-dot) of the fluid flowing over the disc:

    υ = ρAv

    A= area = (Π * D^2)/4

    V = Velocity = (Dω)/2

    ω = 2Πf ?

    The shearing force from the viscous fluid pressure onto the disc:

    F= υv (mass flow rate x velocity)

    F= (Π * D^3 * ω)/8

    Power = rate of fluid doing work onto disc= Force x Fluid velocity

    P = Fv = (Π * D^4 * ω^2)/16

    This is where I am stuck, I don't know how to use dynamic viscosity if a thickness, z, of the disc is not given, therefore a velocity gradient cannot be found. If given an alternative method is:

    Velocity gradient = dv/dz Therefore the shearing stress is (Tau) τ= μ * dv/dz

    Where the inital velocity is zero and z is a constant, replace dv for V in terms of D/2 and dD, differentiate with respect to D to find τ, shear stress.

    F= τA

    Therefore P = Fv.

    Any suggestions? Thanks
  2. jcsd
  3. Aug 31, 2015 #2
    This is a dimensional analysis problem. Try the pi theorem.

  4. Aug 31, 2015 #3
    Thanks for the hint Chet. I will give Pi theorem a try
    Last edited: Aug 31, 2015
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted