To find the new gauge pressure at the bottom of the water after increasing the air pressure, we need to understand how pressure works in a fluid system. Gauge pressure is the pressure relative to atmospheric pressure, and it can be calculated by considering both the pressure exerted by the water column and any additional pressure from the air above it.
Understanding the Initial Conditions
Initially, the gauge pressure at the bottom of the water is given as 2500 Pa. This gauge pressure already accounts for the atmospheric pressure, which is typically around 101325 Pa, but since we are dealing with gauge pressure, we focus only on the pressure exerted by the water column.
Calculating the New Conditions
When additional air is pumped into the container, the pressure of the air above the water increases by 1500 Pa. This increase in air pressure directly adds to the gauge pressure at the bottom of the water.
Step-by-Step Calculation
- Initial Gauge Pressure: 2500 Pa
- Increase in Air Pressure: 1500 Pa
- New Gauge Pressure: 2500 Pa + 1500 Pa = 4000 Pa
Thus, the new gauge pressure at the bottom of the water after pumping in additional air is 4000 Pa. This means that the total pressure exerted at that point has increased due to the added air pressure, which is a direct result of the additional force being applied by the air molecules above the water.
Visualizing the Concept
Think of it like this: imagine you have a balloon filled with water. The pressure at the bottom of the balloon is determined by the weight of the water above it. Now, if you were to blow more air into the balloon, you would be increasing the pressure inside the balloon. This added pressure pushes down on the water, increasing the pressure at the bottom of the balloon as well.
Final Thoughts
In summary, when you increase the air pressure above the water, it directly contributes to the gauge pressure at the bottom of the water. In this case, the final gauge pressure is 4000 Pa, which reflects the combined effects of the initial water pressure and the additional air pressure. Understanding these principles is crucial in fields like fluid mechanics and engineering, where pressure dynamics play a significant role in system design and analysis.
