# How to Calculate Static Pressure in a Duct?

A fan must have enough external static pressure to deliver the required airflow in a duct system. Hence, the static pressure in the duct must be determined. So, how do you calculate static pressure in a duct?

**To calculate the static pressure in a duct, add the pressure loss due to straight ducts, duct fittings such as elbow, reducer and tee, and the pressure loss due to equipment including dampers and grilles. Select a fan that has an external static pressure greater than the static pressure in the duct.**

Static pressure in a duct is calculated differently based on whether it is a straight duct, fitting or a piece of equipment like a damper. So, let’s take a closer look at how the static pressure in a duct is calculated.

## Duct Static Pressure Calculation

Static pressure in a duct is the amount of pressure in the duct when the fan is not running. All fans have a certain amount of static pressure that we often call ESP (external static pressure).

On the flip side, internal static pressure is the strength of the fan needed to overcome its own internal component air resistances and this is taken care of by the fan manufacturer. For us (engineer / technician / homeowner), we just need to select a fan that has an ESP more than the static pressure in the duct.

As a fan moves the air, it creates pressure and this pressure gradually decreases as the air moves further away from the fan. This pressure decrease is due to the air resistance of the internal surface of the duct, duct fittings (elbow, reducer, etc.) and equipment (damper, grille, etc.)

The air resistance due to these duct components is commonly known as pressure loss or pressure drop or static loss or friction loss. Therefore, to calculate the static pressure in a duct, we need to find out the pressure loss due to straight ducts, duct fittings and equipment.

For straight ducts, we can use the Darcy friction loss equation to calculate the pressure loss. For duct fittings, we need to refer to the ASHRAE Duct Fitting Database (DFDB) to find the pressure loss of different duct fittings under different conditions since there are hundreds of them. Finally, the equipment pressure loss is obtained from the manufacturer.

Duct static pressure calculation is a lengthy and complicated process. However, I’ll break it down for you in a step-by-step manner so that you can understand it.

## Duct Static Pressure Formula

From the ASHRAE Handbook of Fundamentals under the Duct Design chapter, friction loss of straight ducts can be calculated using the Darcy friction loss equation. For duct fittings, the loss coefficient must be determined.

### Darcy Friction Loss Equation (Straight Ducts)

The Darcy friction loss equation can be used to **calculate the static pressure of straight ducts and plenum boxes**. It is expressed as follows:

D_{pf} = f(1000/D_{h})(0.5ρV^{2})L

where,

Dpf = Darcy friction loss in terms of total pressure, Pa

f = Friction loss factor

D_{h} = Hydraulic diameter, mm

ρ = Density of air, 1.204 kg/m^{3} at 20°C

V = Velocity, m/s

L = Duct length, m

The Darcy friction loss equation requires inputs that involved several more formulas. At a glance, it seems complicated but I’ll break it down for you.

#### Hydraulic Diameter, D_{h}

From the Darcy friction loss equation, the hydraulic diameter (D_{h}) is calculated using the formula:

D_{h} = 4A/P

where,

D_{h} = Hydraulic diameter, mm

A = Area, mm_{2}

P = Perimeter, mm

The hydraulic diameter requires the area and the perimeter of the duct. For rectangular ducts, the area is simply duct width times duct height and the perimeter is duct width plus duct height times 2.

A_{rectangular} = Width x Height

P_{rectangular} = (Width+Height) x 2

For round ducts, the area is πr_{2} and the perimeter is 2πr.

A_{round} = πr_{2}

P_{round} = 2πr

π = 3.142

After the hydraulic diameter, we also need to calculate the velocity.

#### Velocity, V

The velocity (V) used in the Darcy friction loss equation is calculated using the formula:

V = Q/A

where,

Q = Flow rate, m^{3}/s

A = Area, m^{2}

Hence, the airflow rate and duct size are the two basic pieces of information needed to calculate the static pressure in a duct. But, we’re not done yet.

#### Reynolds Number, Re

The Reynolds number (Re) needed in the friction factor equation is calculated using the formula:

Re = VD_{h}/(1000v)

where,

V = Velocity, m/s

D_{h} = Hydraulic diameter, mm

v = Kinematic viscosity of air, 0.00001516 m^{2}/s at 20°C

The kinematic viscosity of air is determined by the properties of air, just like the density of air. However, both values are based on a set air condition. In the case of duct static pressure calculation, the properties of air are set at 1 atmospheric pressure at 20°C.

#### Friction Loss Factor, f

The friction factor (f) is calculated using the formula:

f’ = 0.11(e/Dh+68/Re)^{0.25}

where,

f’ = Initial friction loss factor

D_{h} = Hydraulic diameter, mm

Re = Reynolds number

e = Duct absolute roughness factor, mm

The friction loss factor is another sub-equation in the Darcy friction loss equation. I use f’ and f to separate the initial and final friction loss factor because it has a rule as follows:

If f’ ≥ 0.018, then f’ = f. Else, f = 0.85f’+0.0028

The duct absolute roughness factor (e) is published by ASHRAE in the ASHRAE Handbook of Fundamentals under the same chapter of Duct Design:

Generally, for galvanized iron (GI) ducts, either round or rectangular, the roughness factor is 0.09 mm. For flexible ducts, the roughness factor is 3.0 mm. Another common type of duct is fiberous glass duct which a roughness factor is 0.9 mm.

With the Darcy friction loss equation and its associated formulas, we can calculate the static pressure of straight ducts and plenum boxes. Next, we’ll look at the formula used to calculate the static pressure of duct fittings.

### Dynamic Pressure and Loss Coefficient (Duct Fittings)

The dynamic pressure formula multiplied by the duct fitting loss coefficient is the pressure loss of the duct fitting. It is expressed as follows:

P_{L} = P_{v}C_{o}

P_{L} = 0.5ρV^{2}C_{o}

where,

P_{L} = Pressure loss, Pa

P_{v} = Dynamic pressure, Pa

ρ = Density of air, 1.204 kg/m^{3} at 20°C

V = Velocity, m/s

C_{o} = Fitting Loss Coefficient

The ASHRAE Handbook of Fundamentals has several pages under the Duct Design chapter that are dedicated to the loss coefficient of various kinds of duct fittings. We need to identify the type of duct fitting in the duct system and use the corresponding loss coefficient to calculate the pressure loss.

## Duct Static Pressure Calculation Example

Now that we’ve gone through all the equations and formulas used to calculate duct static pressure, let’s use an example and I’ll show you how to calculate the static pressure of the duct system.

Below is a diagram showing the duct layout of a simple fresh air system:

From the above diagram, 3 pieces of equipment are marked in bold (fresh air louver, fresh air fan and fresh air grille). The goal is to find out the external static pressure needed for the fresh air fan to deliver 500 CMH at the fresh air grille.

### Equipment Pressure Loss

The pressure loss of the louver and the grille are as follows:

Fresh Air Louver = 50 Pa

Fresh Air Grille = 25 Pa

### Straight Ducts and Plenum Box Pressure Loss

The duct sections marked in blue color are straight ducts and plenum boxes that we can use the Darcy friction loss equation to calculate their pressure losses. Take section 2 (plenum box) as an example, the pressure loss can be calculated as follows:

Flow Rate, Q = 500 CMH = 0.139 m^{3}/s

Area, A = 350 x 350 = 122,500 mm^{2} (0.1225 m^{2})

Perimeter, P = (350+350) x 2 = 1400 mm^{2}

Length = 0.2 m

Hydraulic Diameter, D_{h} = 4A/P = 4(122500)/1400 = 350 mm

Velocity, V = Q/A = 0.139/0.1225 = 1.13 m/s

Reynolds Number, Re = VD_{h}/(1000v) = (1.13×350)/(1000×0.00001516) = 26088

Next is the friction loss factor and the plenum box is made of galvanized iron (GI), the absolute roughness factor (e) is 0.09mm and therefore:

Friction Loss Factor, f’ = 0.11(e/Dh+68/Re)^{0.25}

Friction Loss Factor, f’ = 0.11(0.09/350+68/26088)^{0.25}

Friction Loss Factor, f’ = 0.0254

Since f’ ≥ 0.018, f’ = f and thus, f = 0.0254.

Now, put everything into the Darcy friction loss equation:

D_{pf} = f(1000/D_{h})(0.5ρV^{2})L

D_{pf} = (0.0254)(1000/350)(0.5)(1.204)(1.13^{2})(0.2)**D _{pf} = 0.01 Pa**

Using the same calculation process, the pressure loss in other straight duct sections can be determined. The below table shows the calculation result:

Duct Section | Pressure Loss |
---|---|

2 | 0.01 Pa |

4 | 1.47 Pa |

6 | 0.49 Pa |

9 | 0.25 Pa |

11 | 2.46 Pa |

13 | 0.72 Pa |

Total | 5.40 Pa |

### Duct Fitting Pressure Loss

From the earlier diagram, duct fittings are marked in red color. To find the loss coefficient, we need to identify the duct fitting type. Take section 5 (90° elbow) as an example, its loss coefficient can be determined as follows:

**Duct Section 5:** 90° Elbow**ASHRAE Fitting Code:** CR3-1 | Elbow, Smooth Radius, Without Vanes

Assume that the radius (r) is 250 mm, then r/W = 1.0 which means the C_{p} value is 0.23. Since it is a 90° elbow, the angle factor (K) is 1.00. Therefore, the loss coefficient (C_{o}) of this duct elbow is 0.23.

If the same duct elbow only has 45°, applying the angle factor of 0.60 will result in a loss coefficient (C_{o}) of 0.138.

The loss coefficient table shown above is extracted from the 2009 ASHRAE Handbook of Fundamentals. However, it is incomplete. The complete version needs to be purchased from ASHRAE. The mobile app version is very handy but it comes with a cost.

With the loss coefficient, the pressure loss of the 90° elbow can be calculated as follows:

Velocity, V = Q/A = 0.139/0.05 = 2.78 m/s

Pressure Loss, P_{L} = 0.5ρV^{2}C_{o}

Pressure Loss, P_{L} = (0.5)(1.204)(2.78^{2})(0.23)**Pressure Loss, P _{L} = 1.07 Pa**

Following the same process, the pressure loss in other duct fittings can be determined. The below table shows the result:

Duct Section | Description | Fitting Code | Loss Coefficient | Pressure Loss |
---|---|---|---|---|

3 | Reducer | SR4-2 | 0.06 | 0.28 Pa |

5 | 90° Elbow | CR3-1 | 0.23 | 1.07 Pa |

7 | Square to Round Connector (Fan Inlet) | SD4-2 | 0.06 | 1.73 Pa |

8 | Round to Square Connector (Fan Outlet) | SR4-3 | 3.30 | 15.33 Pa |

10 | 90° Elbow | CR3-1 | 0.23 | 1.07 Pa |

12 | Flexible Duct Collar | SR5-12 | 1.13 | 5.45 Pa |

14 | Round to Square Connector (Diffuser) | SR4-3 | 41.75 | 3.75 Pa |

Total | 28.68 Pa |

### Total Static Pressure

Now, let’s summarize what we have and what we’ve calculated so far:

- Equipment Pressure Loss: 75 Pa
- Straight Duct Pressure Loss: 5.40 Pa
- Duct Fitting Pressure Loss: 28.68 Pa

For straight ducts and duct fittings that undergo a complex calculation and selection process, a 15% safety factor can be given. Hence, the total static pressure can be calculated as follows:

Total Static Pressure = Equipment + Straight Duct + Duct Fitting

Total Static Pressure = 75 Pa + (5.4 x 1.15) + (28.68 x 1.15)**Total Static Pressure = 114 Pa**

Since the duct system has a static pressure of 114 Pa, the fresh air fan needs to be able to deliver 500 CMH of airflow at 114 Pa.

## Duct Static Pressure Excel Calculator

Calculating the static pressure in a duct is a very lengthy process. But, if we’re able to create an Excel calculator for duct static pressure calculation, we can speed up the process dramatically. However, the selection of the duct fitting loss coefficient is most likely to remain manual.

If you want to shorten your calculation time and increase your productivity at work, check out the Design Engineer Starter Pack. It contains 11 Excel calculators specifically for HVAC applications and one of them is a duct static pressure calculator.

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