This is the most comprehensive set of fan calculation formulas you will ever see

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A fan is a machine used for compressing and transporting gases; from an energy perspective, it is a device that converts the mechanical energy of a prime mover into gas energy. http://p3.pstatp.com/large/66ba0001908ba8ad868a I. Classification and applications of fans: Classified by principle of operation: Turbine fans – fans that compress and transport gases through rotating blades. Positive displacement fan—a machine that compresses and transports gas by changing its volume. http://p9.pstatp.com/large/66b80002a3b0bb8983ba Subtypes are classified according to the direction of air flow: Centrifugal fans – The air flows axially into the fan impeller, where it is compressed under the effect of centrifugal force and then flows mainly in a radial direction. Axial flow fans – The airflow enters the rotating blade channels axially; due to the interaction between the blades and the gas, the gas is compressed and then flows along the axis on a cylindrical surface. Mixed-flow fan — Gas enters the rotating cascade at an angle to the main shaft, flowing approximately along a conical surface. Cross-flow fan — Gas flows across the rotating air ducts, and its pressure is increased by the action of the blades. Classified by production pressure level (calculated in absolute pressure): fans – with an exhaust pressure of less than 112,700 Pa ； Blower—exhaust pressure between 112700 Pa and 343000 Pa ； Compressor—exhaust pressure above 343000 Pa ； The classification of fans into high-pressure and low-pressure types is as follows (under standard conditions): Low-pressure centrifugal fans: Total pressure P ≤ 1000 Pa; Medium-pressure centrifugal fans: Total pressure P = 1000–5000 Pa; High-pressure centrifugal fans: Total pressure P = 5000–30000 Pa. Low-pressure axial flow fans: Total pressure P ≤ 500 Pa; High-pressure axial flow fans: Total pressure P = 500–5000 Pa. The full naming convention for general fans can be found at http://p3.pstatp.com/large/66bc000055fc0b09d1ba. The method for indicating the type and variety of general fans is available at http://p3.pstatp.com/large/66b60002e498e4b6f136. There is also a second method for indicating the type and variety of fans. II. Units used in fan calculations: Pressure: For centrifugal fans, pressure refers to the increase in pressure (relative to atmospheric pressure), that is, the increase in pressure of the gas inside the fan or the difference in pressure between the inlet and outlet of the fan. It is divided into static pressure, dynamic pressure, and total pressure. The performance parameter refers to the total pressure (equal to the difference between the total pressure at the fan’s outlet and inlet), and its units commonly include Pa, KPa, mmHg, mH2O, mmH2O, etc. Flow rate: The volume of gas that passes through the fan per unit of time, also known as air volume. It is commonly denoted by Q, with the common units being m3/s, m3/min, and m3/h (seconds, minutes, hours). (Sometimes \"mass flow rate\" is also used, which refers to the mass of gas that passes through the fan per unit of time. In such cases, it is necessary to take into account the density of the gas at the fan’s inlet; this density is closely influenced by the gas composition, local atmospheric pressure, gas temperature, and inlet pressure. Conversions are required in order to obtain the conventional \"gas flow rate\".) Rotational speed: The rotation speed of the fan rotor. It is often denoted by n, and its unit is r/min (where r represents rotational speed and min represents minutes). Power: The power required to drive the fan. It is often denoted by N, with the unit being Kw. III. Common parameters and technical requirements for fans: General exhaust fans: total pressure P=…Pa, flow rate Q=…m3/h, altitude (local atmospheric pressure), drive method, medium to be transported (air may not need to be specified), impeller rotation direction, inlet and outlet angles (viewed from the motor side), operating temperature T=…℃ (normal temperature may not need to be specified), motor model……, etc. High-temperature fans and other special fans: total pressure P=…Pa, flow rate Q=…m3/h, density of inlet gas Kg/m3, drive method, medium to be transported (air can be omitted), impeller rotation direction, inlet and outlet angles (viewed from the motor side), operating temperature T=.....℃, maximum instantaneous temperature T=…℃, density of inlet gas □Kg/m3, local atmospheric pressure (or local altitude), dust concentration, fan control valve, motor model, inlet and outlet expansion joints, integral base, hydraulic coupling (or frequency converter, liquid resistance starter), light oil station, slow-speed operation device, actuator, starting cabinet, control cabinet…. etc. Common calculation formulas for fans: 1. Shaft power: http://p3.pstatp.com/large/66b70002c9f798a911d7. Note regarding the calculation of shaft power: 0.8 represents the fan efficiency, which is a variable; 0.98 represents the mechanical efficiency, also a variable (for fans with direct drive, this value is 1) ； The rotational connection of the coupling is 0.98 ； The belt-driven fan is 0.95 ； 2. Fan total pressure: (not corrected under standard conditions) http://p1.pstatp.com/large/66bb0000575e05566740. The formula for calculating fan total pressure is as follows: P1 = total pressure under operating conditions (Pa), P2 = design standard pressure (or total pressure specified in the table, in Pa), B = local atmospheric pressure (mmHg), T2 = temperature of the medium under operating conditions, in °C; T1 = design temperature specified in the table or without correction, in °C. 760 mmHg represents the atmospheric pressure at an altitude of 0 m and at a temperature of 20 °C. 2.1 Converting altitude to local atmospheric pressure: (760 mmHg) – (altitude ÷ 12.75) = local atmospheric pressure (mmHg). Note: No correction is necessary for altitudes below 300 m. 1 mmH2O = 9.8073 Pa; 1 mmHg = 13.5951 mmH2O; 760 mmHg = 10332.3117 mmH2O. No correction is required for fan flow rates between 0 and 1000 meters above sea level ； Add 2% flow at altitudes of 1000–1500M ； Add 3% to the flow rate at altitudes of 1500–2500 meters ； Add 5% to the flow rate at altitudes above 2500m. Specific speed: nshttp://p1.pstatp.com/large/66b60002e499c24774cd Specific speed. Note: ρ is the density of the gas (Kg/m3); formula: P1 = P2 × 1.2/ρ, ρ = 1.2 × (273 + T2)/(273 + 20) ； 20℃=1.2, 50℃=1.089, 80℃=0.996, 100℃=0.943, 150℃=0.813, 200℃=0.743, 250℃=0.672, 280℃=0.636, 300℃=0.614, 350℃=0.564. Pressure coefficient: http://p3.pstatp.com/large/66b80002a3b451307c11. Pressure coefficient ψ = pressure coefficient; P = total pressure (Pa); ρ = gas density (Kg/m3); U = circumferential velocity at the outer edge of the impeller (m/s). Maximum torque of the fan: 550 × motor power ÷ speed = …. Nm (this applies to large motors, or those required by the user). Dynamic load coefficient of the fan: 0.5 at 2900 revolutions per minute, 0.25 at 1450 revolutions per minute, 0.175 at 960 revolutions per minute, and 0.0875 at 580 revolutions per minute. Torque of the control valve: Tmix = (2–2.5) × 10⁻⁶ × Q³/2 × P = …. N.m