in the book " transport phenomena" (Bird) when obtaining the famous equation of hagen poiseuille

Bird defines a variable that involves the pressure, but when doing an exercise a term magically disappeared, someone could explain to me what happened

(see document)enter image description here

  • $\begingroup$ The equation on the left is for a vertical pipe, and the equation on the right is for a horizontal pipe. In the equation on the left derivation, capital P is defined as $$P=p-\rho g z$$ where p is the pressure. This equation accounts for the weight of the fluid in the pipe. $\endgroup$ – Chet Miller Aug 29 '19 at 1:03

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