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The application of Appropriate Technology

Consider an incompressible fluid (water is almost incompressible) flowing along a pipe, as in Figure 1.

An incompressible fluid flowing along a pipe.

Figure 1

Its volume (V) is given by:

V=A.L

Therefore the volume passing per second (the volumetric flow rate Q) is given by:

Q = V/t = A.L/t

But we can write velocity as distance moved/time (see Equation (1)), so we can replace L/t by v:

Q = A.v

(9)

This is the FLOW EQUATION.

Now consider pipes of different areas A1 and A2 as shown in Figure 2.

Pipes of different areas A1 and A2

Figure 2

The volumetric flow rate (Q) must be the same for both pipes, because we cannot gain or lose any fluid.

Therefore from Equation (8) above:

Q = A_1.v_1 = A_2.v_2

(10)

This is the CONTINUITY EQUATION and it is true for any number of changes in pipe diameter for a single pipe arrangement (a single flow path).