Fundamental Fluid Static Equations in Scalar Form

Considering gravity as the only external body force acting on the fluid element, Eq. (3.13) can be expressed in its scalar components with respect to a cartesian coordinate system (see Fig. 3.3) as

(in x direction)                           (3.13a)	Xz: the external body force per unit mass in the positive direction of z (vertically upward), equals to the negative value of g (the acceleration due to gravity).
(in y direction)                          (3.13b)
( in z direction)           (3.13c)

From Eqs (3.13a)-(3.13c), it can be concluded that the pressure p is a function of z only.

Thus, Eq. (3.13c) can be re-written as,

(3.14)