Machinery's Handbook, 31st Edition
NOZZLES 2821 reduction level. Exhaust cleaners may be required in some cases where contaminants are present. The proper cleaning system will depend on the contaminant type and level, flow rate, pressure, and construction. Nozzles.— These devices include a restriction through which a gas passes from a region of higher pressure to a region of lower pressure, typically atmospheric. Nozzles are used to accelerate and direct a gas to perform some function. Analysis of nozzles is greatly simplified if one assumes that there is zero heat transfer during discharge, or the discharge is adiabatic. Real nozzles are not adiabatic, but this assumption is generally safe to make. Flow rate of gas through a nozzle is calculated using the following equation: m · ρ v n A n = where A n is the cross sectional area of the nozzle, v n is velocity through the nozzle, and m · is the mass flow rate. In the following equations, v n and p n are nozzle outlet velocity and exit pressure ( p n = atmospheric normally), v t and p t are source (tank) velocity and pressure, g is specific weight, and k is the adiabatic exponent given in Table 39. Pressures are absolute. Table 39. Adiabatic Gas Exponent and Critical Pressure Ratio Gas k Critical Pressure Ratio Gas k Critical Pressure Ratio Air 1.4 0.528 Nitrogen 1.41 0.527 Ammonia 1.32 0.542 Oxygen 1.4 0.528 Carbon Dioxide 1.3 0.546 Propane 1.15 0.574 Flow rate through a converging nozzle reaches a maximum at a critical pressure ratio. At this ratio, the nozzle velocity is equal to the speed of sound for that gas at those condi- tions. For subsonic flow, an increase in nozzle cross sectional area causes flow velocity to decrease. For supersonic flow, an increase in nozzle area causes flow velocity to increase. To calculate the critical pressure ratio use the following equation: p ' n p t --- c 2 k +1 ------ k k – 1 ---------- = If a converging nozzle’s pressure ratio ( p n / p t ) is greater than the critical pressure ratio, use the following equation to calculate flow. W A n = where W is the weight flow rate. If a converging nozzle is not operating above the critical pressure ratio, then velocity is equal to sonic velocity and the following equations are used: Pressure at the nozzle throat is equal to the critical pressure: p t γ t 2 gk k +1 ---------- 2 k +1 ------ 2 k – 1 ----------
k k +1 -----------
2 k +1 ------
p ' n = =
p n
p t
k +1 2 k – 1 ( ) ------------------
2 k +1 ------
m ·
n kp i ρ i
=
A
where subscript i indicates inlet conditions, m · is the mass flow in kg/s, A is nozzle area in m 2 , and p is pressure in Pa.
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