# Pressure loss

The pressure loss , also known as the pressure drop , is the pressure difference that occurs due to wall friction and dissipation in pipes , fittings , fittings , etc. ${\ displaystyle \ Delta p_ {v}}$

The pressure loss due to wall friction in the straight pipe is determined by the pipe friction coefficient . With a laminar flow it depends on the Reynolds number ; in the case of a turbulent flow, however, the roughness of the surface is particularly important . ${\ displaystyle \ lambda}$

For elements that are built into a pipeline ( valves , orifices , flow connections, flow divisions, etc.), a pressure loss coefficient is used in technology , which can be found in tables . It can depend on the volume flow , geometry, Reynolds number , etc. ${\ displaystyle \ zeta}$

## calculation

The calculation of the pressure loss has to be done as a compressible or an incompressible flow depending on the medium .

Very detailed algorithms exist, for example, for sections and small networks for self-programming as well as an applicable computer program for liquid, gas and vapor flow.

### Incompressible flow

The empirical equation . For pressure losses in flow through pipelines, including moldings (e.g., sheets. Reductions and fittings) under the condition of a constant density is by Darcy-Weisbach : ${\ displaystyle \ rho}$

${\ displaystyle \ Delta p_ {v12} = {\ frac {\ rho \ cdot u ^ {2}} {2}} \ left (\ lambda \ cdot {\ frac {l} {d}} + \ sum \ zeta _ {i} \ right)}$

With

• Pressure loss (derived SI unitPa )${\ displaystyle \ Delta p_ {v}}$
• mean flow velocity (SI unit: m / s)${\ displaystyle u}$
• Pipe friction coefficient ( dimensionless )${\ displaystyle \ lambda}$
• Length of the pipeline (SI unit: m)${\ displaystyle l}$
• Inner diameter of the pipeline (SI unit: m)${\ displaystyle d}$
• Pressure loss coefficient (dimensionless).${\ displaystyle \ zeta}$

This is a pressure loss approach of the extended Bernoulli energy equation . The initially frictionless ( ideal ) Bernoulli energy equation (in differential pressure form) is expanded to include the pressure loss term : ${\ displaystyle \ Delta p_ {v12}}$

${\ displaystyle p_ {1} + {\ frac {\ rho} {2}} \ cdot u_ {1} ^ {2} + \ rho \ cdot g \ cdot h_ {1} = p_ {2} + {\ frac {\ rho} {2}} \ cdot u_ {2} ^ {2} + \ rho \ cdot g \ cdot h_ {2} + \ Delta p_ {v12}}$

rearranged follows:

${\ displaystyle \ Leftrightarrow \ Delta p_ {v12} = p_ {1} -p_ {2} + {\ frac {\ rho} {2}} \ cdot (u_ {1} ^ {2} -u_ {2} ^ {2}) + \ rho \ cdot g \ cdot (h_ {1} -h_ {2}).}$

With

• Gravitational acceleration (SI unit: m / s 2 )${\ displaystyle g}$
• geodetic height relative to a selected reference point (SI unit: m).${\ displaystyle h}$

Pressure losses generally increase the static component of the pressure change, the other two components can not be influenced by pressure losses: ${\ displaystyle p_ {1} -p_ {2}}$

• the change in kinetic pressure is only a function of the changing cross-section or the changing speed${\ displaystyle {\ frac {\ rho} {2}} \ cdot (u_ {1} ^ {2} -u_ {2} ^ {2})}$
• the geodetic pressure change is only a function of the location.${\ displaystyle \ rho \ cdot g \ cdot (h_ {1} -h_ {2})}$

#### Non-consideration of the geodetic heights

In systems with closed streams (e.g. hot water heating ), the altitude is generally removed from consideration, since the fluid moves upwards and downwards by the same height difference. This only applies under the condition of constant density along the stream filament. This fact enables the function of a gravity heating , where the liquid flows in a circle only because of the density and height differences.

Even in systems with open streams (e.g. drinking water systems), the geodetic pressure difference is pragmatically removed from consideration, since it can also be balanced retrospectively along the stream, assuming constant density and pure dependence on the altitude. This simplifies the calculation process considerably.

#### Dissipation

Pressure losses always correspond to energy losses. According to the extended Bernoulli equation, the pressure losses from the potential pressure energy in the fluid and on the pipe wall are converted (dissipated) into frictional heat and sound energy ; however, the share of sound energy is very small and therefore technically negligible. The extended energy equation assumes that the energy is transferred out of the system beyond the system boundary of the pipe wall and is therefore not available to the fluid.

In fact, the pressure energy dissipates as frictional heat in the fluid and leads to an increase in the fluid temperature. Due to the low dissipation energy per unit of time, this warming is hardly measurable with incompressible fluids (e.g. water), so that the model assumption of constant density is technically always guaranteed.

## Residual pressure loss

The term residual pressure loss is often used in filtration technology.

When cleanable surface filters are operated, a filter cake is formed which essentially takes over the cleaning performance, but ensures an increase in the pressure loss and therefore has to be cleaned at regular intervals. The difference between the static pressures before and after the filter medium, determined immediately after cleaning, is called the residual pressure loss . It increases continuously over the life of a surface filter.