Question

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.)

Answer 1

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.