Air is drawn into a wind tunnel used for testing automobiles

Air is drawn into a wind tunnel used for testing automobiles as shown in Fig. P3.46. Determine the manometer reading, h, when the velocity in the test section is 97 km/h. Note that there is a 2.5 cm column of oil on the water in the manometer, Determine the difference between the stagnation pressure on the front of the automobile and the pressure in the test section.

Solution

97 km/h = 26.94 m/s

a)

Patm = P + 1/2*rho_air*V^2

Also, P + rho_water*g*h = Patm + rho_oil*g*0.025

Combining both,

Patm - 1/2*rho_air*V^2 = Patm + rho_oil*g*0.025 - rho_water*g*h

- 1/2*rho_air*V^2 = rho_oil*g*0.025 - rho_water*g*h

rho_water*g*h = rho_oil*g*0.025 + 1/2*rho_air*V^2

h = (rho_oil/rho_water)*0.025 + 1/2*(rho_air/rho_water)*V^2 /g

= 0.9*0.025 + 1/2 * (1.2/1000) *26.94^2 / 9.81

= 0.0668 m = 6.68 cm

b)

Stagnation pressure = Ambient Pressure = Pamb

Pamb - P = 1/2*rho_air*V^2

= 1/2 * 1.2* 26.94^2

= 435.45 Pa