Understanding Pascal's, Bernoulli's, Hagen-Poiseulle equations

[ana111790]

This is more of a general question rather than a specific problem. I just want to verify that my understanding of these principles is correct:

As far as I know all three are used to calculate pressure difference.

• Pascal's is used for fluid not in motion, like the typical manometer set-up.
  
  $$\Delta$$P = $$\rho$$g$$\Delta$$h
  P₂-P₁ = $$\rho$$g h₂-h₁ Is this the correct form? I have seen the equation written as
  $$\Delta$$P = - $$\rho$$g$$\Delta$$h (with the minus) is that just a reference choice?​
• Bernoulli's is used for a fluid in motion, with the assumptions that it is inviscous, isothermal, incompressible, steady-state and there's no shaft work.
  
  y₂ + v₂²/2g + P₂/($$\rho$$g) = y₁ + v₁²/2g + P₁/($$\rho$$g)​
• Hagen-Poiseulle is used for a fluid in motion, if the fluid is Newtonian, incompressible, continuous, fully developed, laminar, steady-state and with negligible hydrostatic effects.
  
  P₁-P₂= 128$$\mu$$LQ/($$\pi$$d⁴)
  Is the P₁-P₂ just a matter of reference also? (meaning can it be written as P₂-P₁​

Are these correct? Bernoulli's and Hagen-Poiseulle's are derived from energy conservation and Newton's law of viscosity, whereas Pascal's is derived from summation of the forces on a fluid element, so are there any assumptions to be made when using Pascal's?
Is the slip condition only valid for viscous fluid flow? Is the viscous flow the only case when the velocity profile of the flow is parabolic?

Thank you very much.

 

[jbsteele]

Yes, your understanding of the principles is correct. Pascal's Law is derived from the summation of forces on a fluid element and does not require any assumptions. The slip condition is only valid for viscous fluid flow, and the velocity profile for viscous flow is parabolic.