Page 72 - ebook fluid mechanics_finalize

FLUID MECHANICS

vp = fluid mean velocity through P-P

QR = discharge through cross-section R-R

AR = cross-sectional area through R-R

vR = fluid mean velocity through R-R

Q =Q
P
R

Discharge at section P = Discharge at section R

QP = QR

AP vP = AR vR

Application

We can apply the principle of continuity to pipes with cross sections that have

changes along their length. Consider the diagram at Figure 4.3 below, of a pipe

with a contraction.

Section 1 Section 2

Figure 4.3 Pipe
pOPrinciple

A liquid is flowing from left to right and the pipe is narrowing in the same direction.

By the continuity principle, the discharge must be the same at each section. The
mass going into the pipe is equal to the mass going out of the pipe.

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