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Homework Help: Hydrostatic pressure law

  1. Jul 12, 2010 #1
    1. The problem statement, all variables and given/known data
    Consider a stationary fluid (u=0) with constant density and take F= (0,0,-g). Find P(z) which satisfies [tex] P=P_a [/tex] on [tex] z=h_0 [/tex], where z is measured positive upwards. What is the pressure on z=0?


    2. Relevant equations

    Euler's equation: [tex] \frac{Du}{Dt}=-\frac{1}{\rho}\nabla P + F [/tex]

    3. The attempt at a solution
    [tex]\frac{1}{\rho}\nabla P = (0,0,-g) [/tex] Gives the answer in the back of the book as:
    then [tex] P = P_a + \rho g(h_0-z); P(0) = P_a + \rho g h_0 [/tex]. How did they get this? Thanks
     
  2. jcsd
  3. Jul 12, 2010 #2

    hunt_mat

    User Avatar
    Homework Helper

    As they say u=0, then as you correctly wrote down:
    [tex]
    \frac{1}{\rho}\nabla P=(0,0,-g)
    [/tex]
    Which means that:
    [tex]
    \frac{\partial P}{\partial x}=0,\quad\frac{\partial P}{\partial y}=0,\frac{\partial P}{\partial z}=-\rho g
    [/tex]
    Which shows that the pressure in independent of both x & y. so you are left to solve:
    [tex]
    \frac{\partial P}{\partial z}=-\rho g
    [/tex]
    Can you solve this? What are the boundary conditions that you need to use?
     
  4. Jul 12, 2010 #3
    Thanks
     
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