## Head Loss – Pressure Loss

In the practical analysis of piping systems the quantity of most importance is the **pressure loss due to viscous effects** along the length of the system, as well as **additional pressure losses** arising from other **technological equipments** like, valves, elbows, piping entrances, fittings and tees.

At first, an **extended Bernoulli’s equation** must be introduced. This equation permits account of viscosity to be included in an empirical way and quantify this with a physical parameter known as **the head loss**.

**The head loss **(or the pressure loss) represents the reduction in the total head or pressure (sum of elevation head, velocity head and pressure head) of the fluid as it flows through a hydraulic system. **The head loss** also represents the energy used in overcoming friction caused by the walls of the pipe and other technological equipments. The head loss is unavoidable in real moving fluids. It is present because of the friction between adjacent fluid particles as they move relative to one another (especially in turbulent flow).

The head loss that occurs in pipes is dependent on the **flow velocity, pipe diameter **and **length**, and a **friction factor** based on the roughness of the pipe and the **Reynolds number** of the flow. Although the **head loss represents a loss of energy**, it **does not represent a loss of total energy** of the fluid. The total energy of the fluid conserves as a consequence of the **law of conservation of energy**. In reality, the head loss due to friction results in an equivalent **increase in the internal energy** (increase in temperature) of the fluid.

Most methods for evaluating head loss due to friction are based almost exclusively on **experimental evidence**. This will be discussed in following sections.

## Classification of Head Loss

**The head loss** of a pipe, tube or duct system, is the same as that produced in a straight pipe or duct whose length is equal to the pipes of the original systems plus the sum of the equivalent lengths of all the components in the system.

As can be seen, the head loss of piping system is divided into two main categories, “**major losses**” associated with energy loss per length of pipe, and “**minor losses**” associated with bends, fittings, valves, etc.

**Major Head Loss**– due to friction in pipes and ducts.**Minor Head Loss**– due to components as valves, fittings, bends and tees.

The head loss can be then expressed as:

** h_{loss} = Σ h_{major_losses} + Σ h_{minor_losses}**

## Summary:

**Head loss**or**pressure loss**are the reduction in the**total head**(sum of potential head, velocity head, and pressure head) of a fluid caused by the**friction**present in the fluid’s motion.**Head loss and pressure loss**represent the same phenomenon –**frictional losses**in pipe and losses in hydraulic components, but they are expressed in**different units**.- Head loss of hydraulic system is divided into
**two main categories**:**Major Head Loss**– due to friction in straight pipes**Minor Head Loss**– due to components as valves, bends…

**Darcy’s equation**can be used to calculate**major losses**.- A
**special form of Darcy’s equation**can be used to calculate**minor losses**. - The
**friction factor**for fluid flow can be determined using a**Moody chart**.

## Why the head loss is very important?

As can be seen from the picture, the head loss is forms **key characteristic** of any hydraulic system. In systems, in which some certain flowrate must be maintained (e.g. to provide sufficient cooling or heat transfer from a reactor core), **the equilibrium** of the** head loss** and the **head added** by a pump determines the flowrate through the system.

## Major Head Loss – Frictional Loss

See also: Major Head Loss – Frictional Losses

**Major losses**, which are associated with **frictional energy loss** per length of pipe depends on the **flow velocity, pipe length, pipe diameter, and a friction factor** based on the roughness of the pipe, and whether the flow is laminar or turbulent (i.e. the Reynolds number of the flow).

Although the **head loss represents a loss of energy**, it **does not represent a loss of total energy** of the fluid. The total energy of the fluid conserves as a consequence of the **law of conservation of energy**. In reality, the head loss due to friction results in an equivalent **increase in the internal energy** (increase in temperature) of the fluid.

By observation, the **major head loss is roughly proportional to the square of the flow rate** in most engineering flows (fully developed, turbulent pipe flow).

The most common equation used to calculate major head losses in a tube or duct is the **Darcy–Weisbach equation** (head loss form).

where:

- Δh = the head loss due to friction (m)
*f*= the Darcy friction factor (unitless)_{D}- L = the pipe length (m)
- D = the hydraulic diameter of the pipe D (m)
- g = the gravitational constant (m/s
^{2}) - V = the mean flow velocity V (m/s)

**Darcy-Weisbach equation**provides insight into factors affecting the head loss in a pipeline.

- Consider that the
**length of the pipe**or channel is**doubled**, the resulting**frictional head loss will double**. - At constant flow rate and pipe length, the
**head loss is inversely proportional to the 4th power of diameter**(for laminar flow), and thus reducing the pipe diameter by half increases the head loss by a factor of 16. This is a very significant increase in head loss, and shows why larger diameter pipes lead to much smaller pumping power requirements. - Since the head loss is roughly proportional to the square of the flow rate, then if the
**flow rate is doubled**, the**head loss increases by a factor of four**. - The
**head loss is reduced by half**(for laminar flow) when the**viscosity of the fluid is reduced by half**.

With the exception of the **Darcy friction factor**, each of these terms (the flow velocity, the hydraulic diameter, the length of a pipe) can be easily measured. The Darcy friction factor takes the fluid properties of density and viscosity into account, along with the **pipe roughness**. This factor may be evaluated by the use of various empirical relations, or it may be read from published charts (e.g. **Moody chart**).

## Minor Head Loss – Local Pressure Loss

See also: Minor Head Loss – Local Pressure Loss

In industry any pipe system contains **different technological elements** as **bends**, **fittings**, **valves** or **heated channels**. These additional components add to the overall head loss of the system. Such losses are generally termed **minor losses, although they often account for a major portion of the head loss**. For relatively short pipe systems, with a relatively large number of bends and fittings, minor losses can easily exceed major losses (especially with a partially closed valve that can cause a **greater pressure loss** than a long pipe, in fact when a valve is closed or nearly closed, the minor loss is infinite).

The minor losses are commonly measured **experimentally**. The data, especially for valves, are somewhat dependent upon the particular manufacturer’s design.

Generally, most of methods that are used in industry, define a **coefficient K** as a value for certain technological component.

Like pipe friction, the **minor losses are roughly proportional to the square of the flow rate** and therefore they can be easy integrated into the **Darcy-Weisbach equation**. K is the sum of all of the loss coefficients in the length of pipe, each contributing to the overall head loss.

The following methods are of practical importance in local pressure loss calculations:

**Equivalent Length Method****K-Method – Resistance Coefficient Method****2K-Method****3K-Method**

See also: Minor Head Loss – Local Pressure Loss

## Head Loss of Two-phase Fluid Flow

See also: Two-phase Pressure Drop

In contrast to single-phase pressure drops, calculation and prediction of two-phase pressure drops is much more sophisticated problem and leading methods differ significantly. Experimental data indicates that the **frictional pressure drop in the two-phase flow** (e.g. in a boiling channel) is **substantially higher** than that for a single-phase flow with the same length and mass flow rate. Explanations for this include an apparent increased surface roughness due to bubble formation on the heated surface and increased flow velocities.

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