Consider an airplane flying with a velocity of 40 m/s in conditions identical to those at an altitude of 5 km in the standard atmosphere. at a point on the wing, the airflow velocity is 70 m/s. calculate the pressure at this point. assume inviscid, incompressible flow and the u. s. standard atmosphere is the relevant atmospheric model.

pressure = 52804.85 Pa

Explanation:

given data

velocity v1 = 40 m/s

altitude distance d =  5 km

velocity v2 = 70 m/s

solution

we will apply here Bernoullis equation that is

P1 + 0.5 × ρ × v1² = P2 + 0.5 × ρ × v2²   1

here P1 and P2 is pressure at point 1 ans 2  and ρ is density of water and V1 and V2 is velocity at point 1 and 2

so at 5 km we get here P1 and ρ from table

P1 = 54019.91 Pa

and ρ is = 0.7364 kg/m³

so from equation 1 we get 54019.91 + 0.5 × 0.7364 × 40² = P2 + 0.5 × 0.7364 × 70²

solve it we get

P2 = 52804.85 Pa