Читать книгу Hydraulic Fluid Power - Andrea Vacca - Страница 60

For the regions of fully developed flow, it is possible to analytically demonstrate that for laminar flow conditions:

(3.28)

Figure 3.11 Example of analysis of major and minor losses in a pipe flow.

The velocity value v represents the average velocity over the section. From considerations based on dimensional analysis, it is possible to derive the Darcy‐Weisbach equation, which has validity for both laminar and turbulent flow conditions:

(3.29)

where the friction factor f is a function of the Reynolds number and the relative roughness of the pipe:

(3.30)

Figure 3.12 shows the results from the pioneering work performed by Moody [15] on the determination of the friction factor. The Moody's diagram is nowadays the most used chart for determining the major head losses in pipe flows. Analytical expressions for f can also be found in basic fluid mechanics textbooks. A widely adopted one is the Colebrook's formula:

(3.31)

From Eq. (3.28), it is possible to conclude that the loss term h_major in laminar conditions is proportional to the average fluid velocity (v) because of the presence of the Reynolds number, Re, at the denominator of the expression. However, under conditions of complete turbulence, where the friction factor f is constant, the loss term follows a quadratic relation with v.

The major loss term h_major is proportional to the average fluid velocity, v, in laminar conditions, and to v² in complete turbulent conditions.