Pikes Peak near Denver, Colorado, has an elevation of 14,110 ft. Calculate the pressure at this elevation using three different methods. (a) Determine the pressure at this elevation using the standard atmosphere equation. (b) Determine the pressure assuming the air has a constant specific weight of 0.07647 lb/ft3. (c) Determine the pressure if the air is assumed to have a constant temperature of 59 oF.

a) P = 1240 lb/ft^2

b) P = 1040 lb/ft^2

c) P = 1270 lb/ft^2

Explanation:

Given:

- P_a = 2216.2 lb/ft^2

- β = 0.00357 R/ft

- g = 32.174 ft/s^2

- T_a = 518.7 R

- R = 1716 ft-lb / slug-R

- γ = 0.07647 lb/ft^3

- h = 14,110 ft

Find:

(a) Determine the pressure at this elevation using the standard atmosphere equation.

(b) Determine the pressure assuming the air has a constant specific weight of 0.07647 lb/ft3.

(c) Determine the pressure if the air is assumed to have a constant temperature of 59 oF.

Solution:

- The standard atmospheric equation is expressed as:

P = P_a * (1 - βh/T_a) ^ (g / R*β)

(g / R*β) = 32.174 / 1716*0.0035 = 5.252

P = 2116.2 * (1 - 0.0035*14,110/518.7) ^5.252

P = 1240 lb/ft^2

- The air density method which is expressed as:

P = P_a - γ*h

P = 2116.2 - 0.07647*14,110

P = 1040 lb/ft^2

- Using constant temperature ideal gas approximation:

P = P_a * e^ (-g*h / R*T_a)

P = 2116.2 * e^ (-32.174*14110 / 1716*518.7)

P = 1270 lb/ft^2

(a) By applying value into the standard atmospheric equation with density ...

P = (rho) RT

The pressure at standard using values is P = 57447.77 Pa

(b) By using a constant specific weight of 0.7647 lb / ft3 the pressure is

P = 57447.8 Pa

(c) At 59 F Temperature P = 59262.54 Pa