Water Conveyance Loss and Designing Conveyance System - Practices of Irrigation and On-farm Water Management - page 22

Conservation of Momentum

This says that a moving body cannot gain or loss momentum unless an external
force acts upon it.

1.3.1.2 Theories of Hydraulics and Fluid Flow

Pascal's Law

Pascal's law can be stated as follows: “The intensity of pressure at any point of a
closed conduit is equal in all directions.”
Consider a closed vessel as of Fig. 1.6 . Let the intensity of external pressure on
thevesselliquidbe“ p ”. According to Pascal's law, the intensity of pressure at every
direction of the vessel will be equal and “ p ”. Since water is a noncompressible liquid
(not compressed/reduced in volume due to pressure), it exhibits the unique trait of
transforming pressure to all directions when in a confined space.

Fig. 1.6 Schematic of
pressure distribution in a
closed vessel

p

p

Continuity Equation/Conservation of Mass

If the flow is steady, and the fluid is incompressible, the mass entering a pipe
(Fig. 1.7 ) is equal to the mass leaving.

That is, mass flow entering = mass flow leaving

Or, ρ Q e = ρ Q l

Since the volume flow rate is the product of area and mean velocity, consider that

velocity of flow at entering section V 1

cross-sectional area at entering section

=

= A 1

velocity of flow at leaving section V 2

cross-sectional area at leaving section

=

= A 2

Then, applying the law of conservation of mass, ρ × V 1 × A 1 = ρ × V 2 × A 2

or, A 1 V 1 = A 2 V 2 (1.14)