B038:Minor Losses in pipe flow

Introduction

It is often necessary to determine the head loss, hL, that occurs in a pipe flow so that the energy equation can be used in the analysis of pipe flow problems. The overall head loss for the pipe system consists of the head loss due to viscous effects in the straight pipes, termed the major loss and denoted hL-major. The head loss in various pipe components, termed the minor loss and denoted hL-minor. That is:

                         h_L=h_L-major+h_L-minor

The head loss designations of “major” and “minor” do not necessarily reflect the relative importance of each type of loss. For a pipe system that contains many components and a relatively short length of pipe, the minor loss may actually be larger than the major loss.

For any type of system there are additional so-called minor losses due to

Losses due to inlet and outlet.
Sudden expansion and contraction.
Bends, elbows, tees, and other fittings.
Valves, open or partially closed.
Gradual expansion and contraction.

These components interrupt the smooth flow of the fluid and cause additional losses because of the flow separation and mixing they induce. In a typical system with long pipes, these losses are minor compared to the total head loss in the pipes (the major losses) and are called minor losses. The losses may not be so minor; for example, a partially closed valve can cause a greater pressure drop than a very long pipe. The losses are commonly measured experimentally and correlated with the pipe flow parameter. The data, especially for valves, are somewhat dependent on the particular manufacturer’s design. The measured minor loss is usually given as a ratio of the head loss h_m=∆p/ (ρg) through the device to the velocity head V²/(2g) of the associated piping system: Loss coefficient

                                k = h_m/V²   2g

Inlet loss

Inlet loss in pipe flow completely depends on the geometry or alignment of the pipe. For different alignments, the loss coefficient changes its value. Now,

Taking the example of a tank and a pipe and changing the position and geometry of the pipe, we will note the value of loss coefficient.

In the first case, the pipe connected to the tank is slightly inside the tank and this alignment disturbs the flow. In this case, the value of loss coefficient KL=0.8.
In the second case, the pipe is attached to the tank through the wall of the tank, but the corners are pointed. In this case, the value of loss coefficient KL=0.5.
In the third case, the alignment is the same as in case two, but this time the corners are rounded, which smooths the flow. The value of loss coefficient KL=0.2.
In the fourth case, pipe alignment is the same as in case two and three, but the geometry is different. In this case, the corners of the pipe are more curved. The value of loss coefficient KL=0.02.

From the above experiment, we can conclude that as the alignment and geometry of the pipe changes, the value of loss coefficient also changes. The smoother the path of the flow, the lesser the value of loss coefficient KL
The loss again depends on the ratio of the pipe diameters and the angle of enlargement.

Exit loss

An outlet loss differs from the inlet loss; exit loss does not depend on the alignment or the geometry of the pipe. Again, we take the example of a pipe and tank and change the geometry of the pipe with respect to the tank and record the value of loss coefficient KL.

In the first case, the pipe ends inside the tank, which also leads to flow separation. In this case, the value of loss coefficient KL= 1.0.
In the second case, the pipe discharges the liquid at the wall of the container, but the corners of the pipe are sharp. The value of the loss coefficient Kl=1.0.
In the third case, the pipe discharges the liquid at the wall of the container, but this time the corners of the pipe are slightly rounded. The value of the loss coefficient Kl=1.0.
In the fourth case, again the pipe discharges the liquid at the wall of the container, but this time the corners of the pipe are well rounded. But the value of the loss coefficient Kl is still =1.0.

From the above discussion, one can conclude that in outlet loss, the coefficient is completely independent of the geometry and alignment of the pipe.^{[original research?]}

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B038:Minor Losses in pipe flow

Introduction

Inlet loss

Exit loss

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