Praire dogs live in underground burrows with at least two entrances. They ventilate their burrows by building a mound around one entrance, which is open to a stream of air. A second entrance at ground level is open to almost stagnant air. Use Bernoulli's principle to explain how this construction creates air flow through the burrow.
The sum of all forms of energy in a fluid flowing along an enclosed path (a streamline) is the same at any two points in that path.
is this right?
Air flowing over the mound must accelerate, and Bernoulli's principle will cause the air pressure to be lower there than at the other end of the burrow. This difference in pressures will help ventilate the burrow.
Yes.
Your statement about all forms of energy being constant along a streamline is not necessarily true, and is not Bernoulii's principle. Pressure is not a form of energy, but kinetic energy doe increase when it drops. There can be heat transfer between steamlines while the Bernouli equation remains valid, in incompressible flow.
Yes, you are correct. According to Bernoulli's principle, the sum of all forms of energy in a fluid flowing along an enclosed path (a streamline) is the same at any two points in that path.
In the case of the prairie dog burrow, when air flows over the mound that the prairie dogs construct around one entrance, it must accelerate. This acceleration of the airflow causes a decrease in air pressure, according to Bernoulli's principle.
At the other end of the burrow, where the second entrance is located, the air is not moving as much and is relatively stagnant. Therefore, the air pressure at that end of the burrow is relatively higher compared to the mound where the airflow is accelerated.
This difference in pressures between the two ends of the burrow creates a pressure gradient, which drives the airflow through the burrow. As a result, fresh air from the mound entrance is drawn into the burrow and stale air is pushed out through the ground-level entrance, facilitating ventilation of the underground burrow system.
Yes, you are correct. Bernoulli's principle states that the sum of all forms of energy in a fluid flowing along an enclosed path (a streamline) is constant between any two points in that path. It explains the relationship between pressure, velocity, and height in a flowing fluid.
In the case of the prairie dog burrow, air flows over the mound they built around one entrance. As the air flows over the mound, it accelerates and its velocity increases. According to Bernoulli's principle, an increase in velocity is accompanied by a decrease in pressure. Therefore, the air pressure over the mound is lower than the air pressure at the other end of the burrow.
This pressure difference between the two entrances causes air to flow from the high-pressure area (the entrance with stagnant air) to the low-pressure area (the entrance with the mound and flowing air). This flow of air through the burrow helps to ventilate it, exchanging stagnant air with fresh, oxygen-rich air.
So, the construction of the mound around one entrance of the burrow, by utilizing Bernoulli's principle, creates a pressure difference that facilitates air flow through the burrow.