Equal Pressure in Efflux: Understanding Fluid Dynamics in a Tank

[suffian]

Consider a large tank open to the air with a small opening near its bottom. Consider water flowing out of this tank through the opening. Why must the pressure near the surface and near the bottom be equal to atmopheric pressure?

As fluid elements travel down the tank, they will be accelerating. Therefore I don't see how one could apply the rule of thumb that the pressure between two interfaces should be equal.

 

[suffian]

i think i got the idea. the pressure at the surface isn't equal to atmospheric pressure. But it doesn't matter because it is the pressure of the air that is pertinent in bernoulli's equation since the eq uses the pressure applied at the front and rear of the flow tube by its surroundings (which need not be another fluid element).

right?

 

[M98Ranger]

The concept of equal pressure in efflux is based on the principle of conservation of energy and the laws of fluid dynamics. In this scenario, as the water flows out of the tank through the small opening at the bottom, it experiences a decrease in height and velocity. This decrease in height results in a decrease in potential energy, which is converted into kinetic energy. As a result, the water exiting the tank will have a higher velocity compared to the water at the surface of the tank.

According to Bernoulli's equation, an increase in velocity of a fluid element results in a decrease in pressure. This means that the water at the bottom of the tank will have a lower pressure compared to the water at the surface. However, in order for the water to flow out of the tank smoothly and continuously, the pressure at the bottom must be equal to atmospheric pressure. This is because if the pressure at the bottom is lower than atmospheric pressure, air will rush into the tank, disrupting the flow of water. On the other hand, if the pressure at the bottom is higher than atmospheric pressure, the water will not be able to flow out of the tank at all.

Therefore, in order for the water to flow out of the tank smoothly and continuously, the pressure near the surface and near the bottom must be equal to atmospheric pressure. This ensures that there are no disruptions in the flow and that the water can flow out at a constant rate. This concept of equal pressure in efflux is crucial in understanding fluid dynamics in tanks and other systems where fluids are in motion.