Answer to Question #171664 in Mechanics | Relativity for anonymous

Question

North American prairie dogs live in underground burrows with several exits. They usually build a mount over one of the exits, which causes a draft to pass over the mound. How does this allow for ventilation of the burrow? [Hint: keep it simple – assume that all exits are at the same level and that there are no drafts over the other exits.]

Answer 1

Explanation

• Refer to the sketch attached

• Bernoulli's principle is employed by these animals here in this act.
• When we think the speed of air just above the other exists (one of them shown as A here) be zero & some speed just above the mounting area the hypothetical streamlines of air can be drawn as shown.

• Since the speed of air near other exists is zero the pressure of air can be thought to have a higher value than that just above the mount where the speed of air is considerably higher.

• This can be thought according to the Bernoulli equation (with potential energy part neglected), $\small k= P_A+\frac{1}{2}\rho v_A^2=P_B+\frac{1}{2}\rho v_B^2$

• This results in a generation of a pressure difference across the burrow from A to B which facilitates some airflow through the burrow providing good ventilation to the burrow.

$\qquad\qquad\qquad\small P_a-P_B=\Delta P=\frac{1}{2}\rho v_B^2$