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### VARIATION OF AIR DENSITY WITH ALTITUDE

As fluid properties such as pressure and temperature varies non uniformly with the variation of the altitude, in result the density of air also varies nonuniformly. In lower atmosphere with increase in altitude the temperature and pressure of air decreases but as altitude increases the temperature and pressure varies non uniformly and so the density varies with altitude. The variation  of properties follows following Atmospheric model:-

## (ENGLISH UNIT)

H- altitude(ft) ,  T- temperature(℉)  , P - pressure(lbs/sq.ft) , ρ -density(slugs/cu.ft)

## ρ= P/(1718*(T+459.7))

### 1. TROPOSPHERE REGION (H<36152 ft)

T = 59-0.00356H  i.e. Temperature decreases linearly
P = 2116*((T+459.7)/518.6)^ 5.256 i.e. Pressure decreases exponentially

### 2. LOWER STRATOSPHERE REGION (36152<H<82345)

T = -70 i.e. Temperature remains constant
P = 473.1 * e^(1.73-0.000048H) i.e. Pressure decreases exponentially

### 3.UPPER STRATOSPHERE REGION(H>82345)

T= -205.05+0.00164H i.e. Temperature increases linearly
P= 51.97*((T+459.7)/389.98)^(-11.388) i.e. Pressure decreases exponentially

## (SI UNITS)

H- altitude(m) ,  T- temperature(℃)  , P - pressure(Kg/cu.m) , ρ -density(K-Pa)

ρ= P/(0.2869*(T+273.1))

### 1. TROPOSPHERE REGION (H<11000)

T=15.04 - 0.00649H
P= 101.29*((T+273.1)/288.08)^5.256

### 2. LOWER STRATOSPHERE REGION (11000<H<25000)

T= -56.46
P = 22.65*e^(1.73-0.000157H)

### 3.UPPER STRATOSPHERE REGION(H>25000)

T= -131.21 + 0.00299H
P = 2.488* ( (T+273.1)/216.6) ^(-11.388)

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