Mass Flow Rate Calculation: Filling A 6,000-Liter Tank

Oct 28, 2025 by Admin 55 views

Hey guys! Let's dive into a super interesting physics problem today: calculating the mass flow rate needed to fill a 6,000-liter tank in a specific time. This is a classic problem that blends concepts from fluid mechanics and unit conversions, perfect for anyone prepping for the ENEM or just keen on understanding practical physics applications. So, buckle up, and let's get started!

Understanding the Problem

Okay, so the heart of the matter is this: we need to figure out how much mass of water needs to flow per second to fill a 6,000-liter tank in 1 hour and 40 minutes. Seems straightforward, right? But there are a few key details we need to unpack. First, we're given the volume of the tank (6,000 liters) and the time it takes to fill (1 hour and 40 minutes). We also have the density of water (rhoH2O = 1,000 kg/m³) and the acceleration due to gravity (g = 10 m/s²), although the gravity might be a bit of a red herring in this case – we'll see! Our main goal here is to find the mass flow rate, which is usually expressed in kilograms per second (kg/s).

Breaking Down the Givens

Let's list out everything we know to make it crystal clear:

Volume of the tank (V): 6,000 liters
Time to fill (t): 1 hour and 40 minutes
Density of water (ρ): 1,000 kg/m³
Acceleration due to gravity (g): 10 m/s²

Before we jump into calculations, it's super important to ensure all our units are consistent. We're aiming for kg/s, so we need to convert liters to cubic meters (m³) and the time from hours and minutes to seconds. This is a crucial step to avoid making silly mistakes that can throw off our final answer. Trust me, unit conversions are the unsung heroes of physics problems! Getting these right sets the stage for accurate calculations and a much smoother problem-solving experience. So, let's make sure everything lines up perfectly before we move on to the next steps.

Converting Units for Consistency

Alright, let’s get those units sorted out! This is where attention to detail really pays off. First up, we need to convert liters to cubic meters. Remember, 1 cubic meter (m³) is equal to 1000 liters. So, to convert 6,000 liters to cubic meters, we simply divide by 1000:

6,000 liters / 1000 liters/m³ = 6 m³

Easy peasy! Now we have the volume in the correct units. Next, we tackle the time. We’re given 1 hour and 40 minutes, and we need to convert this entirely into seconds. There are 60 minutes in an hour and 60 seconds in a minute, so let’s break it down:

1 hour = 60 minutes
60 minutes = 60 minutes * 60 seconds/minute = 3600 seconds
40 minutes = 40 minutes * 60 seconds/minute = 2400 seconds

Now, add those up:

3600 seconds (from 1 hour) + 2400 seconds (from 40 minutes) = 6000 seconds

So, 1 hour and 40 minutes is equivalent to 6000 seconds. It's kind of neat how the numbers worked out, isn't it? With these conversions done, we now have the volume in cubic meters (6 m³) and the time in seconds (6000 seconds), which perfectly aligns with our goal of finding the mass flow rate in kilograms per second. These conversions are super important because they ensure that our final calculation makes sense and gives us the correct units. Next up, we'll use these converted values to actually calculate the mass flow rate. Let’s keep this momentum going!

Calculating the Mass Flow Rate

Okay, guys, now for the main event: figuring out that mass flow rate! We've got the volume of the tank in cubic meters (6 m³) and the time it takes to fill it in seconds (6000 seconds). We also know the density of water (1,000 kg/m³). This is all the info we need! The formula we're going to use connects these pieces together:

Mass Flow Rate (ṁ) = (Density (ρ) * Volume (V)) / Time (t)

This formula basically tells us that the mass flow rate is the total mass of water divided by the time it takes to fill the tank. It makes sense when you think about it, right?

Let's plug in our values:

ṁ = (1,000 kg/m³ * 6 m³) / 6000 seconds

First, we multiply the density by the volume:

1,000 kg/m³ * 6 m³ = 6,000 kg

This tells us that the total mass of water needed to fill the tank is 6,000 kilograms. Now, we divide this by the time:

ṁ = 6,000 kg / 6000 seconds = 1 kg/s

And there we have it! The mass flow rate required to fill the 6,000-liter tank in 1 hour and 40 minutes is 1 kilogram per second. This means that every second, 1 kilogram of water needs to flow into the tank. How cool is that? We've taken a real-world problem and broken it down using physics principles and some careful calculations. In the next section, we'll wrap things up and highlight the key takeaways from this problem.

Wrapping Up: Key Takeaways

Alright, let’s recap what we've done and highlight some key points from this problem. First off, we successfully calculated the mass flow rate needed to fill a 6,000-liter tank in 1 hour and 40 minutes, and we found it to be 1 kg/s. That’s a fantastic result! But more than just getting the answer, it’s about the process we followed to get there. So, what were the big takeaways?

Unit Conversions are Crucial: This can't be stressed enough! We started with liters and hours/minutes, but to calculate mass flow rate in kg/s, we needed to convert everything to cubic meters and seconds. Getting the units right is often half the battle in physics problems. Always double-check your units and make sure they're consistent before you start plugging numbers into formulas.
Understanding the Formula: We used the formula Mass Flow Rate (ṁ) = (Density (ρ) * Volume (V)) / Time (t). Understanding what this formula means is just as important as knowing the formula itself. It tells us how mass, volume, density, and time are related in a flow scenario. If you grasp the underlying concepts, you can apply the formula confidently in different situations.
Breaking Down the Problem: Complex problems can seem daunting, but breaking them down into smaller, manageable steps makes them much easier to tackle. We started by listing what we knew, converted units, applied the formula, and then interpreted the result. This step-by-step approach is a powerful problem-solving strategy in physics and beyond.

So, there you have it! We've not only solved a practical problem but also reinforced some fundamental physics concepts. Keep practicing, keep breaking down those problems, and you’ll be a physics whiz in no time! Remember, guys, physics is all about understanding the world around us, and every problem you solve is another step towards that understanding.