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timurjin [86]
3 years ago
7

where p0 is the atmospheric pressure at sea level and k is a constant. If the atmospheric pressure is 14.7 lb/in.2 at sea level

and 12.6 lb/in.2 at 4,000 ft, find the atmospheric pressure at an altitude of 10,000 ft. (Round your answer to two decimal places.)
Mathematics
1 answer:
balu736 [363]3 years ago
7 0

Answer:

The value of pressure at an altitude of 10000 ft = 10 \frac{lb}{in^{2} }

Step-by-step explanation:

Given data

Atmospheric pressure P_{0} = 14.7 \frac{lb}{in^{2} }

Pressure at 4000 ft = 12.6 \frac{lb}{in^{2} }

If temperature is constant then the atmospheric pressure is varies with the altitude according to law

P (h) = P_{0} e^{- kh} ------ (1)

where k= constant & h = height

12.6 = 14.7 e^{- 4000k}

0.857 = e^{- 4000k}

㏑ 0.857 = - 4000 k

-0.154 = - 4000 k

k = 3.85 × 10^{-5}

Thus the atmospheric pressure at an altitude of 10,000 ft is

P_{10000} = 14.7 × e^{- kh} ----- (2)

Product of k & h is

k h = 3.85 × 10^{-5} × 10000

k h = 0.385

Put his value of k h = 0.385  in equation (2) we get

P_{10000} = 14.7 × e^{-0.385 }

P_{10000} = 10 \frac{lb}{in^{2} }

This is the value of pressure at an altitude of 10000 ft.

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