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Gennadij [26K]
3 years ago
7

The weatherman states that the current temperature is 95 F and the dew point is 74 F. What is the current relative humidity?

Engineering
1 answer:
spayn [35]3 years ago
3 0

Answer:

Current Relative Humidity is 29.623

Given:

Current Temperature, T_{c} = 95 F = 35^{\circ}C

Dew point temperature, T_{d} = 74 F = 23.34^{\circ}C

Solution:

Now, in order to calculate the Relative Humidity, RH, we use the given formula:

T_{d} =100( \frac{\frac{aT_{c}}{b + T}b + lnRH}{a - \frac{aT_{c}}{b + T} + lnRH})

where

a = 17.625

b = 237.7

Now, using the above formula and given values:

23.34 = (237.7\frac{\frac{17.625\times 35}{ 237.7 + 35} + lnRH}{17.625 - \frac{17.625\times 35}{237.7 + 35} + lnRH})

23.34(17.625 - 2.26 + lnRH) = (237.7\times 2.26 + lnRH)

358.62 + 23.34lnRH) = (537.20 + lnRH)

358.62 + 23.34lnRH) = (537.20 + lnRH)

On solving the above eqn, we get:

RH = 29.623

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