Singular head losses

Borda s model gives three general principles for the sizing of singular head 

The dimensionless parameter g is the singular head drop coefficient. It mainly 

1 Unfortunately, this book in Russian by I.E. Idel cik has apparently not been translated into English. 

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The study shows that the additive has more influence on friction losses than on singular head losses. 

For the solution of this problem, gravity will not be considered. The flnid is water. For simplicity, it is assumed that the ehannels are rectilinear in geometry, as shown in the Figure 2.VII.1, and wall friotion is neglected. The grid induees a singular head loss in the flow, written as EH = KpU 2. K= 3 will be used for the numerical applications. 

Passing through the valve (between I and J) generates a sudden head loss, called a singular head loss. As the cross-sections are identical at the inlet and outlet of the valve, the variation is the same for the head and the pressure. 

The notion of a singular head loss, already encountered in the case of a sudden expansion (Borda s model). A head loss corresponds to a loss of energy. The differences between cross-sectional expansions and contractions, already considered in section 2.6, are again discussed in section 4.4. We retain here the basic idea that a substantial expansion in the cross-section of a pipe, in the direction of the flow, results in a head loss, whereas energy can be conserved in a cross-sectional contraction. 

The singular head loss produced in a hydraulic circuit by various elements (valves, bends, obstacles, etc.) is regnlated by kinetic energy. Any singular head loss is therefore quantified in the form ... 

Singular head losses depend on the direction of the flow. 

We can recall, in summary, that singular head losses oecur in areas where the cross-section available to the flow is enlarged, while energy is conserved in zones where the cross-section is restricted. ... 

Write the head loss versus flow rate relationship for the whole circuit. Head variations other than the regular head loss in the pipe, the singular head loss at the valve, and the head increase produced by the pump will be neglected. 

Controlling the flow rate in each secondaiy pipe is achieved by adjusting a plate which partially blocks the cross-section of the secondaiy pipe (Figure IV.2). For secondaiy pipe n, express the singular head loss coeffident, Q, as a function of the blocked cross-section S of the pipe and the unblocked cross-section So of the pipe. 

In a circuit, pressure reaches a minimum level at the inlet of each pump, which mandates preventative action against cavitation. Let us consider the example of Figure 5.3 that shows a pump moving a liquid from a lower basin to an upper basin. The head increase pghtot between point A, which is located at the surface of the lower basin, and point D, which is located at the surface of the upper basin, is provided by the pump, which also has to compensate for the regular head losses in the pipes and the singular head losses (at the outlet into the upper basin, for example). Denoting by tot the total head losses in the circuit, we therefore write ... 

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