Prairie dogs are burrowing rodents. They do not suffocate in their burrows becau

Question

Prairie dogs are burrowing rodents. They do not suffocate in their burrows because the effect of air speed on pressure creates sufficient air circulation. The animals maintain a difference in the shapes of two entrances to the burrow (see picture), and because of this difference, the air (p = 1.29 kg/m^3) blows past the openings at different speeds, as the drawing indicates. Assuming that the openings are at the same vertical level, find the difference in air pressure between the openings and indicate which way the air circulates.Express the pressure difference between the openings at a percentage of atmospheric pressure.

Va=8.5 m/s (to the right) & Vb=1.1 m/s (to the right)

Explanation / Answer

Velocity at opening 'a' = Va =8.5 m/s (to the right)

Velocity at opening 'b' = Vb =1.1 m/s (to the right)

Density of air = p = 1.29 kg/m^3

Using Bernoullie's theorem,

Pa+(1/2)pVa^2 = Pb+(1/2)pVb^2

Pb - Pa = (1/2)pVa^2 - (1/2)pVb^2

Pb - Pa = (1/2)p [ Va^2 - Vb^2 ]

Pb - Pa = (1/2)*1.29 [ 8.5^2 - 1.1^2 ]

Pb - Pa = 0.645 [ 72.25 - 1.21 ]

Pb - Pa = 0.645 [ 71.04 ]

Pb - Pa = 45.821 pascal
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