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The frictional resistance in feet is found from the equation ;

h= ( K ) ( V

where ; K : resistance coefficient which depends on design and size of valve or fitting, V : average velocity in pipe of corresponding diameter ( ft / s ) and g : acceleration of gravity ( = 32.17 ft / s

Table given below indicates the wide variation in published values of K.

A comparison of the " Darcy - Weisbach " equation and the above equation suggests that K = f ( L / D ) to produce the same head loss in a straight pipe as in the valve or fitting. The ratio ( L / D ) or " equivalent length in pipe diameters " of straight pipe may then be used as another method to estimate valve and fitting losses. Tests have shown that while K decreases with size of different lines of valves and fittings, ( L / D ) is almost constant. In the zone of complete turbulence, as shown in figure below, K for a given size and ( L / D ) for all sizes of valves and fittings are constant. In the transition zone K increases as does the friction factor f with decreasing.

" Reynolds " number Re while L / D remains approximately constant. Table given below lists suggested values of L / D for various valves and fittings.

Multiplying L / D by the inside diameter of pipe corresponding to the schdule number shown in table given below gives the equivalent length of straight pipe.

When using the equivalent length method, the friction head loss is determined by employing the " Darcy - Weisbach " equation. This method therefore takes into consideration the viscosity of the liquid, which in turn determines the " Reynolds " number and the friction factor.

The loss of head through valves, particularly control valves, is sometimes expressed in terms of the " flow coefficient, C

lb / in

The following examples illustrate the use of the " resistance coefficient, K " and the " equivalent length in pipe diameters, L / D " methods for estimating losses in valves and fittings.

* ID = 2.067 in

* EPSILON / D = 0.00087

* NU = 0.0009 ft

* V = ( 60 / 2.067

* ( V ) ( D" ) = ( 5.73 ) ( 2.067 ) = 11.8 ft / sec . in

* Re = 1 x 10

* f = 0.032

h

* ID = 1.610 in

* EPSILON / D = 0.0011

* NU = 0.00009 ft

* V = ( 60 / 1.610

* ( V ) ( D" ) = ( 9.44 ) ( 1.610 ) = 15.2 ft / sec . in

* Re = 1.5 x 10

* f = 0.030

h

* 2 - in bellmouth, K = 0.05

h

* 2 - in LR, 90

h

* 2 - in gate valve, K = 0.16 +- 25 %

h

* 1 1/2 - in gate valve, K = 0.19 +- 25 %

h

* 1 1/2 - in swing - check valve, K = 2.4 +- 30 %

h

TOTAL h

TOTAL variation = +- ( 0.202 + 0.021 + 0.066 + 1.0 ) = +- 1.29 ft

* 2 - in LR, 90

L

* 2 - in gate valve, L / D = 13

L

* 1 1/2 - in gate valve, L / D = 13

L

* 1 1/2 swing - check valve, L / D = 135

L

Using f from example given above, total valve and fitting losses are ;

Total valve and fitting losses from example given above ;

TOTAL h

The loss of head for a sudden increase in diameter with velocity changing from V

The value of K is also approximately equal to unity if a pipe discharges into a relatively large reservoir. This indicates that all the kinetic energy V

The diffuser converts some of the kinetic energy into pressure. Values for the coefficient used with the above equations for calculating head loss are shown in the figure. The optimum total angle appears to be 7.5

Figure shown below gives values of the resistance coefficient to be used for sudden reducers.

Figure given below may be used to determine the resistance coefficient for 90

Figure shown below gives resistance coefficients for less than 90

These two figures are not recommended for elbows with R / D below 1.

Table shown below gives values of resistance coefficients for miter bends.

Figures given below illustrate two typical rectangular to round reducing suction elbows. Elbows of this configuration are sometimes used under dry pit vertical volute pumps. These elbows are formed in concrete and are designed to require a minimum height, thus permitting a higher pump setting with reduced excavation. Figure (first) shows a long - radius elbow and figure (second) shows a short - radius elbow. The resulting velocity distribution into the impeller eye and the loss of head are shown for these selected two designs.

Orifices, nozzles, and venturi meters are used to measure rate of flow. These metering devices, however, introduce additional loss of head into the pumping system. Each of these meters is designed to create a pressure differential through the primary element. The magnitude of the pressure differential depends on the velocity and the density of the liquid and the design of the element. The primary element restricts the area of flow, increases the velocity, and decreases the pressure. An expanding section following the primary element provides pressure head recovery and determines the meter efficiency. The pressure differential between inlet and throat taps measures rate of flow ; the pressure differential between inlet and outlet taps measures the meter head loss (an outlet tap is not usually provided). The meters offering the least resistance to flow are in the following decreasing order ; venturi, nozzle, and orifice. Figures given below illustrate these different meter designs.

When meters are designed and pressure taps are located as recommended, figures given below may be used to estimate the overall pressure loss. The loss of pressure is expressed as a percentage of the differential pressure measured at the appropriate taps and values are given for various size meters.