### Total pressure losses

_{l}: linear pressure losses (in the tubes)

ΔP

_{f}: pressure losses in pipe fittings (elbows, tees, etc.)

ΔP

_{v}: pressure losses in the control valves

### Linear pressure losses

The linear pressure losses are calculated by the following equations:

_{l}: linear pressure losses [Pa]

ρ: fluid density [Kg/m³]

g: acceleration due to gravity [m/s²]

h

_{f}: head losses [m]

f: friction factor [-]

L: pipe length [m]

D: pipe internal diameter [m]

V: average fluid velocity at the cross section [m/s]

The second equation is widely known as Darcy & Weisbach’s equation. In the previous post, you can find over 10 ways to calculate these losses.

### Pressure losses in pipe fittings

Fitting losses - sometimes in the literature are referred to as local or minor pressure losses - are usually expressed as a function of the velocity head (v

^{2}/2g):

Where:

_{f}: pressure losses in pipe fittings [Pa]

ρ: fluid density [Kg/m³]

ΣK: total resistance coefficient of pipe fittings [-]

V: average fluid velocity at the cross section [m/s]

Each type of fitting has a resistance coefficient that is found experimentally. In most cases, these factors can be found in the literature (see Crane for example). Some typical values are given below:

- Tee, flanged, line flow 0.2
- Tee, flanged, branched flow 1.0
- Elbow, threaded regular 90
^{º}1.5 - Elbow, threaded regular 45
^{º}0.4 - Return bend, threaded 180
^{º}1.5 - Water meter 7.0

### Pressure losses in control valves

The pressure losses in control valves can be expressed by the following equation:

_{v}: pressure losses in the control valve [Pa]

_{water}) [-]

_{v}: control valve flow coefficient [m³/h/Pa, although it is usually expressed in m³/h/bar or in m³/h/KPa]

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