Calculating Weight Flow Rate: A Physics Problem

Hey guys! Let's dive into a classic physics problem. We're going to break down how to calculate the weight flow rate of water filling a tank. This is a common type of problem you might encounter in a physics class, and it's super important for understanding concepts like fluid dynamics and how things like flow rate work in the real world. So, grab your notebooks and let's get started!

The Problem Setup and Given Information

Alright, let's look at the scenario. (Brunetti, 2008) presented us with a problem: A tap fills a tank with a capacity of 6,000 liters in 1 hour and 40 minutes. We're also given the density of water (ρ = 1000 kg/m³) and the acceleration due to gravity (g = 10 m/s²). Our mission, should we choose to accept it, is to determine the weight flow rate in Newtons per second (N/s). This problem provides a great opportunity to apply our understanding of fluid mechanics and unit conversions, which are fundamental concepts in physics.

First, let's break down the information we've got. The tank's capacity is 6,000 liters, which tells us the volume it can hold. The filling time is 1 hour and 40 minutes, which we'll need to convert to seconds for our calculations. We also have the density of water, which is a crucial piece of information for relating volume to mass. And finally, the acceleration due to gravity helps us determine the weight of the water. Think of it like this: knowing how much water you have, how fast it's flowing, and how much each part weighs are the keys to solving this puzzle. This information is the backbone of the problem, so let's carefully consider each piece.

Now, let's think about the concepts involved here. We're dealing with volume, time, density, and gravity – all of which are interconnected. The volume of the water and the time it takes to fill the tank give us the volumetric flow rate. Density helps us convert that volumetric flow rate to a mass flow rate, telling us how much mass is flowing per second. And finally, the acceleration due to gravity links mass to weight, allowing us to find the weight flow rate, which is what we ultimately need. It's like a chain of calculations: volume to time to mass to weight. Each step builds on the previous one, and that’s how we'll get our answer. Understanding the relationships between these different quantities is key to success.

Step-by-Step Solution to the Flow Rate Calculation

Okay, guys, let's roll up our sleeves and get into the actual calculations! Here's how we can solve this step-by-step to find the weight flow rate. We'll break it down into manageable chunks so it's easy to follow. Remember, understanding each step is more important than just getting the right answer; it helps you grasp the underlying principles. Ready? Let's go!

First, we need to convert the filling time into seconds. 1 hour is equal to 60 minutes, and each minute has 60 seconds. So, 1 hour and 40 minutes equals (1 * 60 * 60) + (40 * 60) = 6000 seconds. This is a super important step; always make sure your units are consistent! Next, we need to convert liters to cubic meters. We know that 1 cubic meter is equal to 1000 liters. Therefore, 6,000 liters is equal to 6,000 / 1000 = 6 m³. Now, we can calculate the volumetric flow rate (Q), which is the volume of water divided by the time it takes to fill the tank. So, Q = 6 m³ / 6000 s = 0.001 m³/s. Boom, first step done!

Next up, we'll calculate the mass flow rate. The mass flow rate (${\dot{m}}$) is the density (ρ) of the water multiplied by the volumetric flow rate (Q). Therefore, ${\dot{m}}$ = ρ * Q = 1000 kg/m³ * 0.001 m³/s = 1 kg/s. So, 1 kg of water flows into the tank every second. Now, we're getting close to our answer. This value, the mass flow rate, tells us how many kilograms of water move into the tank per second. Note that at this point, we’ve found a key piece: the mass flow rate. We will move on to calculate the weight flow rate, which requires consideration of gravity.

Finally, we'll calculate the weight flow rate (W). Weight is calculated by multiplying mass by the acceleration due to gravity. The weight flow rate is calculated by multiplying the mass flow rate by the acceleration due to gravity (g). So, W = ${\dot{m}}$ * g = 1 kg/s * 10 m/s² = 10 N/s. And there you have it! The weight flow rate is 10 N/s. We now have our final answer, which is the weight flow rate of the water entering the tank. This result means that 10 Newtons of force are acting on the tank every second due to the weight of the water flowing into it. Pretty cool, right?

Conclusion and Key Takeaways

Alright, folks, we've successfully solved the problem! We determined that the weight flow rate is 10 N/s. Not bad, huh? We started with the basic information and worked our way through several calculations to get the final answer. Let's recap what we learned and what the key takeaways are from this problem. This is a very valuable process in physics, and in future problems, it can give you a lot of confidence.

Firstly, we used the volumetric flow rate, converting it from volume and time. We had to convert units from liters to cubic meters, and time from hours and minutes to seconds. Being able to convert units correctly is essential for these types of problems. Secondly, we calculated the mass flow rate using the density of water. Density is the critical link between the mass and volume of a substance. It also helps us in many other types of problems, so make sure you understand the concepts surrounding density and how to use it in calculations. Then, we used the acceleration due to gravity to calculate the weight flow rate. This step highlighted the relationship between mass and weight. Weight is essentially a force, and understanding how gravity acts on mass is fundamental to understanding this concept.

Now, here are the main things to remember. Fluid dynamics problems frequently require you to work with different flow rates and unit conversions. Always keep an eye on your units and make sure they're consistent throughout your calculations. Secondly, understanding the relationships between volume, mass, density, and weight is super important. These concepts are interconnected, and a good grasp of them is crucial for solving these types of problems. Lastly, always break down complex problems into smaller, more manageable steps. This makes it easier to understand and apply the principles involved. So, if you keep those key takeaways in mind, you'll be well on your way to mastering these kinds of physics problems. Good luck, and keep practicing!

I hope you enjoyed this journey through this physics problem. Keep exploring, keep learning, and don't be afraid to tackle challenges! If you've got questions, ask away! Physics can be super rewarding when you understand it. Keep up the excellent work! And remember, practice makes perfect!