## Sudden Change in Flow Path

Flowing through any system a fluid may pass through different geometries. In the course of flow it may encounter sudden changes in flow direction in form of bends and also sudden changes in flow area. These abrupt changes cause fluid to loose energy. The loss in energy of the fluid is mainly due to flow separation caused by these sudden changes in flow. The contribution to total loss in energy by such changes is smaller as compared to frictional losses. Hence losses attributed to change in flow path are called as minor losses.

## Ways to Estimate Minor Losses

After knowing about minor losses and what their causes are, the more important thing now is to know how to estimate these losses so that they can be incorporated in the energy equation for the ideal flow. Minor losses are estimated in one of the two ways depending upon the cause of loss.

**Loss Coefficient**

One way to estimate minor loss is to consider the loss proportional to the kinetic energy per unit mass of the fluid. The value of loss component is calculated by multiplying the kinetic energy per unit mass to a loss coefficient which is determined experimentally for each situation.

**Equivalent Length**

The other way to find minor losses is by using the same relation which is used to find frictional losses. To find the minor loss due to any object, it is converted an equivalent length of straight pipe. Now the minor loss can calculated using this length in the same relation for the frictional losses.

## Points of Loss

Fluid may loose energy at different points in the course of flow and different methods for estimation of these losses are used.

**Inlets and Exits**

If the inlets to any system of flow are not designed properly and have sharp edges, then it results in head losses. When a fluid enters through inlets with sharp edges, its flow area contracts at the entry point. This increases the fluid speed at entrance. To fill the area, fluid decelerates after entry point. These sudden changes cause abrupt mixing of fluid resulting in some loss in mechanical energy.

Similarly, when a fluid exits to a larger reservoir its kinetic energy is almost completely lost. A part of the kinetic energy can be recovered by providing a diffuser at the exit of the fluid.

**Change in Area of Flow**

Sudden changes in flow area, such as contraction or enlargement, cause separation of flow and turbulence which results in loss in energy of fluid. Loss in such cases is estimated using the loss coefficient with the kinetic energy per unit mass of the flow in the larger section of flow.

These losses can be reduced by installing nozzles or diffusers between the different cross sections. It makes the transition more gradual.

**Bends**

The head loss in a bent pipe is more than a straight pipe of the same length. An equivalent length of straight pipe for the bend can be found which causes same head loss as the bend. This equivalent length is used for calculation of minor losses due to bends.

**Fittings**

Different types of fittings such as valves or joints in any system add to minor losses in the flow. Manufacturing defects increase the loss. Losses due to fittings are also given in terms of the equivalent length. This data is found experimentally and generally provided by the manufacturer.

In the last two articles we have considered the losses part of modification in the Bernoulli Equation. In the next article we will discuss real velocity distribution to modify the velocity term in the energy equation.