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: Applying Bernoulli's equation to magnetohydrodynamic flow

  1. May 16, 2010 #1
    1. The problem statement, all variables and given/known data
    A static electrically conducting fluid, in the presence of electric and magnetic fields, experiences a Lorentz force. Determine the fluid pressure at point (1,2,1) when the pressure [tex]p_{0}[/tex] at origin (0,0,0) is under the effect of gravity and the electric and magnetic field are given by:

    i) [tex]E = 2\hat{i}, B = 4\hat{k}[/tex]
    ii) [tex]E = \hat{i}+3\hat{j}-\hat{k}, B = 2\hat{i}+\hat{j}+4\hat{k}[/tex]


    2. Relevant equations
    Lorentz force:
    [tex]F_{L}[/tex]=[tex]E \times B[/tex]

    Bernoulli's equation:
    [tex]\frac{p}{\rho} + \frac{u \cdot u}{2} + gz = constant[/tex]

    3. The attempt at a solution
    i)
    Modify Bernoulli's equation to account for Lorentz's force:
    [tex]\frac{p}{\rho} + \frac{u \cdot u}{2} + gz + F_{L} = constant[/tex]
    Divide by g to find the heads
    [tex]\frac{p}{\rho g} + \frac{u \cdot u}{2 g} + z + \frac{F_{L}}{g} = constant[/tex]

    Apply modified Bernoulli's equation to the two points.
    [tex]\frac{p_{0}}{\rho g} + \frac{u \cdot u}{2 g} + z_{0} + \frac{F_{L}}{g} = \frac{p_{x}}{\rho g} + \frac{u \cdot u}{2 g} + z_{x} + \frac{F_{L}}{g}[/tex]
    [tex]\frac{p_{0}}{\rho g} + z_{0} = \frac{p_{x}}{\rho g} + z_{x}[/tex]
    [tex]\frac{p_{x}}{\rho g} = \frac{p_{0}}{\rho g} + z_{0} - z_{x}[/tex]
    [tex]p_{x} = p_{0} + (z_{0} - z_{x})\rho g[/tex]
    [tex]p_{x} = p_{0} - \rho g[/tex] as [tex](z_{0} - z_{x}) = 0 - 1[/tex]

    I'm pretty much stuck from here, I don't think I modified Bernoulli's equation properly because I don't end up using the Lorentz force in my calculation of the pressure at point (1,2,1).
     
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted