Thus a convenient method of expressing the minor losses in flow is by means of a loss coefficient k. Values of the loss coefficient k for typical situations and fittings is found in standard handbooks. The form of Darcy's equation used to calculate minor losses of individual fluid system components is expressed by Equation Minor losses may be expressed in terms of the equivalent length L eq of pipe that would have the same head loss for the same discharge flow rate.
This relationship can be found by setting the two forms of Darcy's equation equal to each other. A fully-open gate valve is in a pipe with a diameter of 10 inches.
What equivalent length of pipe would cause the same head loss as the gate valve? By adding the equivalent lengths of all components to the actual length of pipe in a system we can obtain the L eq value for the entire piping system. Engineering Library.
Pumps Valves. Navy: Fluid Power. This can be expressed by another form of the Darcy equation similar to Equation K is called the resistance coefficient and is defined as the number of velocity heads lost due to the valve or fitting. It is a measure of the following pressure losses in a valve or fitting:. Pipe friction in the inlet and outlet straight portions of the valve or fitting is very small when compared to the other three.
Since friction factor and Reynolds Number are mainly related to pipe friction, K can be considered to be independent of both friction factor and Reynolds Number. Therefore, K is treated as a constant for any given valve or fitting under all flow conditions, including laminar flow. Indeed, experiments showed 1 that for a given valve or fitting type, the tendency is for K to vary only with valve or fitting size.
Note that this is also true for the friction factor in straight clean commercial steel pipe as long as flow conditions are in the fully developed turbulent zone. This only occurs if the fluid flow is in the zone of complete turbulence see the Moody Chart in reference 1 or in any textbook on fluid flow. Equation 4 should now read with D being the diameter of the valve or fitting :. Going back to step four in our five step procedure for calculating the total pressure drop in the pipe, adding the equivalent length to the straight pipe length for use in Equation 1 is fundamentally wrong.
So how should we use equivalent lengths to get the pressure drop contribution of the valve or fitting? The pressure drop for the valves and fittings is then added to the pressure drop for the straight pipe to give the total pipe pressure drop. Another approach would be to use the K values of the individual valves and fittings. The quantity of each type of valve and fitting is multiplied by its respective K value and added together to obtain a total K. This total K is then substituted into the following equation:.
Notice that use of equivalent length and friction factor in the pressure drop equation is eliminated, although both are still required to calculate the values of K 1. As a matter of fact, there is nothing stopping the engineer from converting the straight pipe length into a K value and adding this to the K values for the valves and fittings before using Equation 7.
How significant is the error caused by mismatching friction factors? The answer is, it depends. Below is a real world example showing the difference between the Equivalent Length method as applied by most engineers and the K value method to calculate pressure drop.
Volumetric Flow Rate, gpm:. Viscosity, cp:. Temperature, o F:. Pipe ID, in:. Velocity, fps:. The energy loss in fittings apparatus consists of a series of fittings, a flow control valve, twelve manometers, a differential pressure gauge, and an air-bleed valve Figure 3. The fittings listed below, connected in a series configuration, will be examined for their head loss coefficient K :.
The manometers are tapped into the pipe system one before and one after each fitting, except for the gate valve to measure the pressure head difference caused by each fitting. The pressure difference for the valve is directly measured by the differential pressure gauge. The air-bleed valve facilitates purging the system and adjusting the water level in the manometers to a convenient level, by allowing air to enter them.
Two clamps, which close off the tappings to the mitre, are introduced while experiments are being performed on the gate valve. The flow rate is controlled by the flow control valve [3]. The internal diameter of the pipe and all fittings, except for the enlargement and contraction, is 0. In this equation , , and z are pressure head, velocity head, and potential head, respectively. The total head loss, h L , includes both major and minor losses.
If the diameter through the pipe fitting is kept constant, then. Therefore, if the change in elevation head is neglected, the manometric head difference is the static head difference that is equal to the minor loss through the fitting. The energy loss that occurs in a pipe fitting can also be expressed as a fraction K of the velocity head through the fitting:. Because of the complexity of the flow in many fittings, K is usually determined by experiment [3].
The head loss coefficient K is calculated as the ratio of the manometric head difference between the input and output of the fitting to the velocity head. Due to the change in the pipe cross-sectional area in enlargement and contraction fittings, the velocity difference cannot be neglected. This value will be negative for the contraction since and it will be positive for enlargement because. From Equation 5 , note that will be negative for the enlargement. The pressure difference between before and after the gate valve is measured directly using the pressure gauge.
This can then be converted to an equivalent head loss by using the conversion ratio:. It is not possible to measure head due to all of the fittings simultaneously; therefore, it is necessary to run two separate experiments.
In this part, head losses caused by fittings, except for the gate valve, will be measured; therefore, this valve should be kept fully open throughout Part A. The following steps should be followed for this part:. In this experiment, the head loss across the gate valve will be measured by taking the following steps:.
However the 2K values must be converted to single K values for each fitting type individually. Email Name. Summary Fittings such as elbows, tees, valves and reducers represent a significant component of the pressure loss in most pipe systems.
Definitions : Internal diameter of pipe Inches : Resistance Coefficient : Resistance Coefficient for fitting at : Resistance Coefficient for large fitting at : Reynolds number.
Article Created: October 17, Flow Rate.
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