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Main points are:Basic Equation, Derivation, Pressure Variation, Incompressible Fluid, Fluid Statics, Force Balance, Fluid Elemental Volume, Equation in Scalar Form, Hydrostatic Pressure, Static Pressure Gradient
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2- Now, let us calculate pressure – gradient in a static fluid. Identify all forces: pressure forces, and external body force which is gravity in the present case.Consider a differential fluid elemental volume,.
Force Balance (in vector form ) (pressure force + gravitational force) = 0
or,
or, (form previous lecture)
or, This is the basic (vector) equation for fluid statics. The equation in the scalar form: : x direction
: y direction
: z direction
Where,
If gravity acts in the negative z-direction
or
where
Engineering calculations based on the fluid static equation
Integrating,
(Fig. 4b) Therefore, pressure decreases lineally with altitude, or increases with depth in the fluid
(Fig. 4c) or,
(Fig. 4d) ( , where is the depth of the fluid measured from the top )
